From 3245eeb0f66ed7533a19002dd1f14eb7455981f3 Mon Sep 17 00:00:00 2001
From: ecmerkle <ecmerkle@gmail.com>
Date: Thu, 2 Nov 2023 18:02:52 +0000
Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20ecmerkle?=
 =?UTF-8?q?/blavaan@b8ac94f39116e7298d5600e7a398e26fd2fe9e9e=20?=
 =?UTF-8?q?=F0=9F=9A=80?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 404.html                                      |   2 +-
 articles/approx_fi.html                       |  38 ++--
 .../approx_fi_files/figure-html/plpi-1.png    | Bin 117667 -> 109527 bytes
 articles/convergence_efficiency.html          |  34 ++--
 articles/convergence_loop.html                |   4 +-
 .../figure-html/unnamed-chunk-4-1.png         | Bin 262245 -> 256931 bytes
 articles/cross_loadings_strong_priors.html    |  68 +++----
 articles/estimate.html                        |   2 +-
 articles/index.html                           |   2 +-
 articles/invariance.html                      |   2 +-
 articles/mod_indices.html                     |  62 +++---
 articles/model_comparison.html                | 110 +++++------
 articles/multilevel.html                      |   2 +-
 articles/ordinal.html                         |   2 +-
 articles/plotting.html                        |   2 +-
 articles/prior.html                           |   2 +-
 articles/prior_pred_checks.html               |   2 +-
 .../figure-html/unnamed-chunk-4-1.png         | Bin 84728 -> 85908 bytes
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 .../figure-html/unnamed-chunk-9-1.png         | Bin 84715 -> 84050 bytes
 articles/probability_direction.html           | 184 +++++++++---------
 articles/resources.html                       |   2 +-
 articles/start.html                           |   2 +-
 articles/summaries.html                       |   2 +-
 authors.html                                  |   2 +-
 index.html                                    |   2 +-
 news/index.html                               |   2 +-
 pkgdown.yml                                   |   2 +-
 reference/bcfa.html                           |   2 +-
 reference/bgrowth.html                        |   2 +-
 reference/blavCompare.html                    |   2 +-
 reference/blavFitIndices.html                 |   2 +-
 reference/blavInspect.html                    |   2 +-
 reference/blavPredict.html                    |   2 +-
 reference/blav_internal.html                  |   2 +-
 reference/blavaan-class.html                  |   2 +-
 reference/blavaan.html                        |   2 +-
 reference/bsem.html                           |   2 +-
 reference/dpriors.html                        |   2 +-
 reference/index.html                          |   2 +-
 reference/plot.blavaan.html                   |   2 +-
 reference/ppmc.html                           |   2 +-
 reference/standardizedPosterior.html          |   2 +-
 search.json                                   |   2 +-
 44 files changed, 282 insertions(+), 282 deletions(-)

diff --git a/404.html b/404.html
index da0c327c..eaeefb35 100644
--- a/404.html
+++ b/404.html
@@ -24,7 +24,7 @@
     
     <a class="navbar-brand me-2" href="http://ecmerkle.github.io/blavaan/index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/approx_fi.html b/articles/approx_fi.html
index 29289593..2a5ae678 100644
--- a/articles/approx_fi.html
+++ b/articles/approx_fi.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -154,10 +154,10 @@ <h3 id="noncentrality-based-fit-indices">Noncentrality-Based Fit Indices<a class
 <span><span class="co">## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for devm-based fit indices:</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">##                EAP Median   MAP    SD lower upper</span></span>
-<span><span class="co">## BRMSEA       0.100  0.100 0.098 0.005 0.092 0.109</span></span>
-<span><span class="co">## BGammaHat    0.956  0.956 0.958 0.004 0.950 0.964</span></span>
-<span><span class="co">## adjBGammaHat 0.904  0.905 0.908 0.010 0.890 0.921</span></span>
-<span><span class="co">## BMc          0.902  0.902 0.906 0.010 0.887 0.919</span></span></code></pre>
+<span><span class="co">## BRMSEA       0.097  0.096 0.095 0.005 0.088 0.105</span></span>
+<span><span class="co">## BGammaHat    0.957  0.957 0.958 0.004 0.950 0.964</span></span>
+<span><span class="co">## adjBGammaHat 0.910  0.911 0.913 0.009 0.896 0.925</span></span>
+<span><span class="co">## BMc          0.903  0.904 0.906 0.010 0.889 0.919</span></span></code></pre>
 </div>
 <div class="section level3">
 <h3 id="incremental-fit-indices">Incremental Fit Indices<a class="anchor" aria-label="anchor" href="#incremental-fit-indices"></a>
@@ -199,13 +199,13 @@ <h3 id="incremental-fit-indices">Incremental Fit Indices<a class="anchor" aria-l
 <span><span class="co">## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for devm-based fit indices:</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">##                EAP Median   MAP    SD lower upper</span></span>
-<span><span class="co">## BRMSEA       0.100  0.100 0.098 0.005 0.092 0.109</span></span>
-<span><span class="co">## BGammaHat    0.956  0.956 0.958 0.004 0.950 0.964</span></span>
-<span><span class="co">## adjBGammaHat 0.904  0.905 0.908 0.010 0.890 0.921</span></span>
-<span><span class="co">## BMc          0.902  0.902 0.906 0.010 0.887 0.919</span></span>
-<span><span class="co">## BCFI         0.929  0.930 0.933 0.008 0.918 0.942</span></span>
-<span><span class="co">## BTLI         0.878  0.880 0.885 0.013 0.859 0.901</span></span>
-<span><span class="co">## BNFI         0.910  0.910 0.913 0.007 0.899 0.923</span></span></code></pre>
+<span><span class="co">## BRMSEA       0.097  0.096 0.095 0.005 0.088 0.105</span></span>
+<span><span class="co">## BGammaHat    0.957  0.957 0.958 0.004 0.950 0.964</span></span>
+<span><span class="co">## adjBGammaHat 0.910  0.911 0.913 0.009 0.896 0.925</span></span>
+<span><span class="co">## BMc          0.903  0.904 0.906 0.010 0.889 0.919</span></span>
+<span><span class="co">## BCFI         0.930  0.931 0.933 0.007 0.919 0.942</span></span>
+<span><span class="co">## BTLI         0.887  0.888 0.891 0.012 0.869 0.906</span></span>
+<span><span class="co">## BNFI         0.910  0.910 0.912 0.007 0.899 0.921</span></span></code></pre>
 <p>The <code><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary()</a></code> method now presents the central tendicy
 measure you asked for, standard deviation, and credible interval for the
 noncentrality and incremental fit indices.</p>
@@ -219,13 +219,13 @@ <h3 id="access-the-indices-posterior-distributions">Access the indices posterior
 <div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">dist_fits</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span><span class="va">gl_fits_all</span><span class="op">@</span><span class="va">indices</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/utils/head.html" class="external-link">head</a></span><span class="op">(</span><span class="va">dist_fits</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">##      BRMSEA BGammaHat adjBGammaHat       BMc      BCFI      BTLI      BNFI</span></span>
-<span><span class="co">## 1 0.1049896 0.9520096    0.8950616 0.8927742 0.9230257 0.8676190 0.9036694</span></span>
-<span><span class="co">## 2 0.1012793 0.9551923    0.9020212 0.8998326 0.9283789 0.8768254 0.9088195</span></span>
-<span><span class="co">## 3 0.1087359 0.9487025    0.8878302 0.8854492 0.9170222 0.8572940 0.8978043</span></span>
-<span><span class="co">## 4 0.1009911 0.9554356    0.9025531 0.9003724 0.9286836 0.8773494 0.9090855</span></span>
-<span><span class="co">## 5 0.1004256 0.9559114    0.9035935 0.9014283 0.9300108 0.8796319 0.9105038</span></span>
-<span><span class="co">## 6 0.1051490 0.9518708    0.8947583 0.8924667 0.9233153 0.8681169 0.9040741</span></span></code></pre>
+<pre><code><span><span class="co">##       BRMSEA BGammaHat adjBGammaHat       BMc      BCFI      BTLI      BNFI</span></span>
+<span><span class="co">## 1 0.10222768 0.9522573    0.9004844 0.8933233 0.9232277 0.8750093 0.9026881</span></span>
+<span><span class="co">## 2 0.09272435 0.9603860    0.9174279 0.9113684 0.9363476 0.8963694 0.9151496</span></span>
+<span><span class="co">## 3 0.09481637 0.9586530    0.9138157 0.9075169 0.9340132 0.8925688 0.9130789</span></span>
+<span><span class="co">## 4 0.09097977 0.9618062    0.9203882 0.9145267 0.9387426 0.9002686 0.9174598</span></span>
+<span><span class="co">## 5 0.09824281 0.9557453    0.9077548 0.9010598 0.9291252 0.8846109 0.9083685</span></span>
+<span><span class="co">## 6 0.11322189 0.9420630    0.8792351 0.8707717 0.9050757 0.8454565 0.8850777</span></span></code></pre>
 <p>Once we have saved the posterior distributions, we can explore the
 the histogram and scatterplots between indices.</p>
 <div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
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diff --git a/articles/convergence_efficiency.html b/articles/convergence_efficiency.html
index c4c97d0d..f26de99c 100644
--- a/articles/convergence_efficiency.html
+++ b/articles/convergence_efficiency.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -165,25 +165,25 @@ <h3 id="convergence">Convergence<a class="anchor" aria-label="anchor" href="#con
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/blavInspect.html">blavInspect</a></span><span class="op">(</span><span class="va">fit</span>, <span class="st">"rhat"</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##   ind60=~x1   ind60=~x2   ind60=~x3           a           b           c </span></span>
-<span><span class="co">##   1.0005379   1.0020521   1.0020088   0.9997209   1.0007457   0.9998598 </span></span>
+<span><span class="co">##   1.0018687   1.0011498   1.0019669   1.0010774   1.0035505   1.0009847 </span></span>
 <span><span class="co">##           d           a           b           c           d dem60~ind60 </span></span>
-<span><span class="co">##   1.0000487   0.9997209   1.0007457   0.9998598   1.0000487   0.9994924 </span></span>
+<span><span class="co">##   1.0037108   1.0010774   1.0035505   1.0009847   1.0037108   1.0025700 </span></span>
 <span><span class="co">## dem65~ind60 dem65~dem60      y1~~y5      y2~~y4      y2~~y6      y3~~y7 </span></span>
-<span><span class="co">##   0.9998798   0.9998013   1.0008959   0.9996250   1.0006446   0.9991291 </span></span>
+<span><span class="co">##   0.9992636   1.0013518   1.0004050   0.9999044   0.9996021   0.9997691 </span></span>
 <span><span class="co">##      y4~~y8      y6~~y8      x1~~x1      x2~~x2      x3~~x3      y1~~y1 </span></span>
-<span><span class="co">##   1.0005873   0.9996670   1.0001871   1.0005173   1.0000525   1.0001748 </span></span>
+<span><span class="co">##   0.9993516   1.0003211   0.9992072   1.0001601   1.0013318   1.0006956 </span></span>
 <span><span class="co">##      y2~~y2      y3~~y3      y4~~y4      y5~~y5      y6~~y6      y7~~y7 </span></span>
-<span><span class="co">##   1.0000764   0.9998632   0.9993261   1.0009848   1.0000100   0.9997290 </span></span>
+<span><span class="co">##   1.0009872   1.0000227   0.9997030   1.0005515   0.9992962   1.0018510 </span></span>
 <span><span class="co">##      y8~~y8        x1~1        x2~1        x3~1        y1~1        y2~1 </span></span>
-<span><span class="co">##   0.9994271   1.0014272   1.0021355   1.0011416   0.9997846   0.9991185 </span></span>
+<span><span class="co">##   1.0000982   1.0011787   1.0012383   1.0013904   1.0017004   1.0011649 </span></span>
 <span><span class="co">##        y3~1        y4~1        y5~1        y6~1        y7~1        y8~1 </span></span>
-<span><span class="co">##   1.0000282   0.9994777   0.9996936   0.9999317   1.0000207   1.0010106</span></span></code></pre>
+<span><span class="co">##   1.0013353   1.0025494   1.0054546   1.0041114   1.0031621   1.0043085</span></span></code></pre>
 <p>With large models it can be cumbersome to look over all of these
 entries. We can instead find the largest <span class="math inline">\(\hat{R}\)</span> to see if they are all less than
 <span class="math inline">\(1.05\)</span></p>
 <div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Extremes.html" class="external-link">max</a></span><span class="op">(</span><span class="fu"><a href="../reference/blavInspect.html">blavInspect</a></span><span class="op">(</span><span class="va">fit</span>, <span class="st">"psrf"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## [1] 1.002135</span></span></code></pre>
+<pre><code><span><span class="co">## [1] 1.005455</span></span></code></pre>
 <p>If all <span class="math inline">\(\hat{R} &lt; 1.05\)</span> then we
 can establish that the MCMC chains have converged to a stable solution.
 If the model has not converged, you might increase the number of
@@ -224,19 +224,19 @@ <h3 id="efficiency">Efficiency<a class="anchor" aria-label="anchor" href="#effic
 <div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/blavInspect.html">blavInspect</a></span><span class="op">(</span><span class="va">fit</span>, <span class="st">"neff"</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">##   ind60=~x1   ind60=~x2   ind60=~x3           a           b           c </span></span>
-<span><span class="co">##   1711.6518   1532.0335   1674.0745   1799.7048   1930.9386   1970.0796 </span></span>
+<span><span class="co">##    1676.611    1626.443    1861.550    1413.085    1591.407    1675.781 </span></span>
 <span><span class="co">##           d           a           b           c           d dem60~ind60 </span></span>
-<span><span class="co">##   1793.3665   1799.7048   1930.9386   1970.0796   1793.3665   2149.0144 </span></span>
+<span><span class="co">##    1240.096    1413.085    1591.407    1675.781    1240.096    2218.345 </span></span>
 <span><span class="co">## dem65~ind60 dem65~dem60      y1~~y5      y2~~y4      y2~~y6      y3~~y7 </span></span>
-<span><span class="co">##   2653.6934   2917.5050   2035.4478   2029.8231   2743.6990   2234.4785 </span></span>
+<span><span class="co">##    2401.326    2458.749    1664.306    1924.265    2945.089    2255.887 </span></span>
 <span><span class="co">##      y4~~y8      y6~~y8      x1~~x1      x2~~x2      x3~~x3      y1~~y1 </span></span>
-<span><span class="co">##   2247.6868   1536.2891   2283.6237   1706.3360   3142.0541   2339.8884 </span></span>
+<span><span class="co">##    2026.768    1394.098    2632.528    2022.808    2820.950    2514.076 </span></span>
 <span><span class="co">##      y2~~y2      y3~~y3      y4~~y4      y5~~y5      y6~~y6      y7~~y7 </span></span>
-<span><span class="co">##   3118.2461   3354.9361   2151.5734   2200.5526   2416.0540   2375.5283 </span></span>
+<span><span class="co">##    2726.223    2835.621    1920.701    1780.442    2433.502    1597.422 </span></span>
 <span><span class="co">##      y8~~y8        x1~1        x2~1        x3~1        y1~1        y2~1 </span></span>
-<span><span class="co">##   1942.8772    992.9440    879.9432   1134.9757   1171.0180   1592.1328 </span></span>
+<span><span class="co">##    1278.782    1212.542    1200.562    1368.136    1367.420    1712.215 </span></span>
 <span><span class="co">##        y3~1        y4~1        y5~1        y6~1        y7~1        y8~1 </span></span>
-<span><span class="co">##   1393.5860   1165.4686   1071.9561   1059.1545   1121.8196    905.3216</span></span></code></pre>
+<span><span class="co">##    1608.132    1305.350    1199.165    1284.532    1220.148    1130.688</span></span></code></pre>
 <p>ESS is a sample size, so it should be at least 100 (optimally, much
 more than 100) times the number of chains in order to be reliable and to
 indicate that estimates of the posterior quantiles are reliable. In this
@@ -246,7 +246,7 @@ <h3 id="efficiency">Efficiency<a class="anchor" aria-label="anchor" href="#effic
 function:</p>
 <div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Extremes.html" class="external-link">min</a></span><span class="op">(</span><span class="fu"><a href="../reference/blavInspect.html">blavInspect</a></span><span class="op">(</span><span class="va">fit</span>, <span class="st">"neff"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## [1] 879.9432</span></span></code></pre>
+<pre><code><span><span class="co">## [1] 1130.688</span></span></code></pre>
 </div>
 <div class="section level3 unnumbered">
 <h3 class="unnumbered" id="references">References<a class="anchor" aria-label="anchor" href="#references"></a>
diff --git a/articles/convergence_loop.html b/articles/convergence_loop.html
index 49e21689..c1c1455e 100644
--- a/articles/convergence_loop.html
+++ b/articles/convergence_loop.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -158,7 +158,7 @@ <h3 id="convergence-loop">Convergence loop<a class="anchor" aria-label="anchor"
 you will see how far is the model from converging.</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="st">"Rhat="</span>,<span class="va">rhat</span><span class="op">)</span><span class="op">)</span>  </span></code></pre></div>
-<pre><code><span><span class="co">## [1] "Rhat=1.00224659247685"</span></span></code></pre>
+<pre><code><span><span class="co">## [1] "Rhat=1.00250742312635"</span></span></code></pre>
 <p>Note that we are only increasing the number burnin iterations, and
 keeping the number of saved samples the same (1000 in this case). If you
 want you can increase or decrease the number of saved iterations
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diff --git a/articles/cross_loadings_strong_priors.html b/articles/cross_loadings_strong_priors.html
index 8f7aa43e..4e2fdbcb 100644
--- a/articles/cross_loadings_strong_priors.html
+++ b/articles/cross_loadings_strong_priors.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -146,7 +146,7 @@ <h3 id="cross-loadings">Cross-loadings<a class="anchor" aria-label="anchor" href
 correlations, intercepts and variances.</p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit_df</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## blavaan 0.5.2.1189 ended normally after 1000 iterations</span></span>
+<pre><code><span><span class="co">## blavaan 0.5.2.1191 ended normally after 1000 iterations</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">##   Estimator                                      BAYES</span></span>
 <span><span class="co">##   Optimization method                             MCMC</span></span>
@@ -155,7 +155,7 @@ <h3 id="cross-loadings">Cross-loadings<a class="anchor" aria-label="anchor" href
 <span><span class="co">##   Number of observations                           301</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">##   Statistic                                 MargLogLik         PPP</span></span>
-<span><span class="co">##   Value                                      -3870.881       0.000</span></span>
+<span><span class="co">##   Value                                      -3870.865       0.000</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Parameter Estimates:</span></span>
 <span><span class="co">## </span></span>
@@ -163,52 +163,52 @@ <h3 id="cross-loadings">Cross-loadings<a class="anchor" aria-label="anchor" href
 <span><span class="co">## Latent Variables:</span></span>
 <span><span class="co">##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       </span></span>
 <span><span class="co">##   visual =~                                                                    </span></span>
-<span><span class="co">##     x1                0.912    0.089    0.738    1.088    1.000    normal(0,10)</span></span>
-<span><span class="co">##     x2                0.499    0.083    0.340    0.665    1.000    normal(0,10)</span></span>
-<span><span class="co">##     x3                0.660    0.082    0.499    0.819    1.001    normal(0,10)</span></span>
+<span><span class="co">##     x1                0.908    0.089    0.735    1.085    1.000    normal(0,10)</span></span>
+<span><span class="co">##     x2                0.502    0.082    0.344    0.664    0.999    normal(0,10)</span></span>
+<span><span class="co">##     x3                0.661    0.082    0.502    0.821    1.000    normal(0,10)</span></span>
 <span><span class="co">##   textual =~                                                                   </span></span>
-<span><span class="co">##     x4                1.000    0.059    0.887    1.120    1.000    normal(0,10)</span></span>
-<span><span class="co">##     x5                1.114    0.064    0.991    1.244    1.000    normal(0,10)</span></span>
-<span><span class="co">##     x6                0.925    0.057    0.818    1.040    1.000    normal(0,10)</span></span>
+<span><span class="co">##     x4                1.002    0.058    0.893    1.117    1.000    normal(0,10)</span></span>
+<span><span class="co">##     x5                1.116    0.065    0.994    1.245    1.000    normal(0,10)</span></span>
+<span><span class="co">##     x6                0.929    0.056    0.821    1.041    1.000    normal(0,10)</span></span>
 <span><span class="co">##   speed =~                                                                     </span></span>
-<span><span class="co">##     x7                0.617    0.077    0.457    0.765    1.002    normal(0,10)</span></span>
-<span><span class="co">##     x8                0.733    0.079    0.573    0.881    1.000    normal(0,10)</span></span>
-<span><span class="co">##     x9                0.680    0.079    0.537    0.836    1.002    normal(0,10)</span></span>
+<span><span class="co">##     x7                0.619    0.077    0.465    0.769    1.002    normal(0,10)</span></span>
+<span><span class="co">##     x8                0.735    0.078    0.580    0.887    1.000    normal(0,10)</span></span>
+<span><span class="co">##     x9                0.680    0.080    0.531    0.848    1.001    normal(0,10)</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Covariances:</span></span>
 <span><span class="co">##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       </span></span>
 <span><span class="co">##   visual ~~                                                                    </span></span>
-<span><span class="co">##     textual           0.448    0.066    0.308    0.569    1.000     lkj_corr(1)</span></span>
-<span><span class="co">##     speed             0.463    0.085    0.289    0.618    1.000     lkj_corr(1)</span></span>
+<span><span class="co">##     textual           0.450    0.064    0.315    0.570    0.999     lkj_corr(1)</span></span>
+<span><span class="co">##     speed             0.460    0.086    0.284    0.619    1.001     lkj_corr(1)</span></span>
 <span><span class="co">##   textual ~~                                                                   </span></span>
-<span><span class="co">##     speed             0.278    0.070    0.137    0.408    1.001     lkj_corr(1)</span></span>
+<span><span class="co">##     speed             0.276    0.073    0.129    0.414    0.999     lkj_corr(1)</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Intercepts:</span></span>
 <span><span class="co">##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       </span></span>
-<span><span class="co">##    .x1                4.935    0.068    4.797    5.068    1.001    normal(0,32)</span></span>
-<span><span class="co">##    .x2                6.088    0.066    5.959    6.216    1.001    normal(0,32)</span></span>
-<span><span class="co">##    .x3                2.250    0.068    2.115    2.383    1.001    normal(0,32)</span></span>
-<span><span class="co">##    .x4                3.060    0.067    2.930    3.192    1.001    normal(0,32)</span></span>
-<span><span class="co">##    .x5                4.340    0.077    4.193    4.489    1.000    normal(0,32)</span></span>
-<span><span class="co">##    .x6                2.185    0.065    2.062    2.316    1.000    normal(0,32)</span></span>
-<span><span class="co">##    .x7                4.187    0.063    4.066    4.309    1.001    normal(0,32)</span></span>
-<span><span class="co">##    .x8                5.526    0.059    5.411    5.642    1.001    normal(0,32)</span></span>
-<span><span class="co">##    .x9                5.373    0.058    5.257    5.487    1.000    normal(0,32)</span></span>
+<span><span class="co">##    .x1                4.937    0.067    4.810    5.072    0.999    normal(0,32)</span></span>
+<span><span class="co">##    .x2                6.088    0.065    5.959    6.217    1.000    normal(0,32)</span></span>
+<span><span class="co">##    .x3                2.251    0.066    2.121    2.381    1.000    normal(0,32)</span></span>
+<span><span class="co">##    .x4                3.061    0.068    2.932    3.195    1.000    normal(0,32)</span></span>
+<span><span class="co">##    .x5                4.341    0.075    4.196    4.483    1.000    normal(0,32)</span></span>
+<span><span class="co">##    .x6                2.186    0.065    2.061    2.314    1.000    normal(0,32)</span></span>
+<span><span class="co">##    .x7                4.187    0.063    4.064    4.311    0.999    normal(0,32)</span></span>
+<span><span class="co">##    .x8                5.528    0.059    5.412    5.639    1.000    normal(0,32)</span></span>
+<span><span class="co">##    .x9                5.375    0.060    5.257    5.493    0.999    normal(0,32)</span></span>
 <span><span class="co">##     visual            0.000                                                    </span></span>
 <span><span class="co">##     textual           0.000                                                    </span></span>
 <span><span class="co">##     speed             0.000                                                    </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Variances:</span></span>
 <span><span class="co">##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       </span></span>
-<span><span class="co">##    .x1                0.548    0.130    0.266    0.794    1.000 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##    .x2                1.155    0.110    0.954    1.388    1.000 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##    .x3                0.859    0.099    0.673    1.051    1.000 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##    .x4                0.378    0.050    0.286    0.481    0.999 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##    .x5                0.456    0.060    0.345    0.581    1.000 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##    .x6                0.363    0.045    0.282    0.456    1.000 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##    .x7                0.822    0.092    0.659    1.017    1.001 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##    .x8                0.501    0.093    0.327    0.685    1.000 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##    .x9                0.569    0.093    0.378    0.745    1.002 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##    .x1                0.557    0.131    0.278    0.800    1.000 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##    .x2                1.152    0.108    0.954    1.381    1.000 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##    .x3                0.859    0.102    0.664    1.065    1.000 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##    .x4                0.379    0.050    0.286    0.482    1.001 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##    .x5                0.455    0.059    0.342    0.572    1.000 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##    .x6                0.362    0.047    0.277    0.462    1.000 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##    .x7                0.819    0.092    0.652    1.009    1.002 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##    .x8                0.500    0.094    0.328    0.682    1.002 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##    .x9                0.570    0.095    0.373    0.750    1.001 gamma(1,.5)[sd]</span></span>
 <span><span class="co">##     visual            1.000                                                    </span></span>
 <span><span class="co">##     textual           1.000                                                    </span></span>
 <span><span class="co">##     speed             1.000</span></span></code></pre>
@@ -234,7 +234,7 @@ <h3 id="cross-loadings">Cross-loadings<a class="anchor" aria-label="anchor" href
 credible interval.</p>
 <div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit_cl</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## blavaan 0.5.2.1189 ended normally after 1000 iterations</span></span>
+<pre><code><span><span class="co">## blavaan 0.5.2.1191 ended normally after 1000 iterations</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">##   Estimator                                      BAYES</span></span>
 <span><span class="co">##   Optimization method                             MCMC</span></span>
diff --git a/articles/estimate.html b/articles/estimate.html
index 2a8efdd8..3b1b6be3 100644
--- a/articles/estimate.html
+++ b/articles/estimate.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/index.html b/articles/index.html
index 6a1ccade..11913c9e 100644
--- a/articles/index.html
+++ b/articles/index.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/invariance.html b/articles/invariance.html
index 4d697ef7..12f2beff 100644
--- a/articles/invariance.html
+++ b/articles/invariance.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/mod_indices.html b/articles/mod_indices.html
index 78d97056..6d3ac0f3 100644
--- a/articles/mod_indices.html
+++ b/articles/mod_indices.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -183,17 +183,17 @@ <h3 id="modification-indices">Modification Indices<a class="anchor" aria-label="
 <span><span class="co">## </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">##               EAP Median    MAP     SD  lower  upper PPP_sim_GreaterThan_obs</span></span>
-<span><span class="co">## visual=~x9 35.353 35.458 35.495 10.624 17.727 52.239                   0.012</span></span>
-<span><span class="co">## x7~~x8     32.891 35.539 39.626 14.716  4.604 52.733                   0.083</span></span>
-<span><span class="co">## x8~~x9     27.117 12.160  2.726 42.978  0.000 70.495                   0.321</span></span>
-<span><span class="co">## x4~~x6     19.784  7.015  1.388 36.713  0.000 52.503                   0.467</span></span>
-<span><span class="co">## visual=~x7 18.162 16.144 12.432  9.849  4.183 33.098                   0.016</span></span>
+<span><span class="co">## visual=~x9 35.353 35.458 35.495 10.624 17.727 52.239                   0.013</span></span>
+<span><span class="co">## x7~~x8     32.891 35.539 39.626 14.716  4.604 52.733                   0.084</span></span>
+<span><span class="co">## x8~~x9     27.117 12.160  2.726 42.978  0.000 70.495                   0.320</span></span>
+<span><span class="co">## x4~~x6     19.784  7.015  1.388 36.713  0.000 52.503                   0.468</span></span>
+<span><span class="co">## visual=~x7 18.162 16.144 12.432  9.849  4.183 33.098                   0.015</span></span>
 <span><span class="co">##            PPP_sim_LessThan_obs</span></span>
-<span><span class="co">## visual=~x9                0.988</span></span>
-<span><span class="co">## x7~~x8                    0.917</span></span>
-<span><span class="co">## x8~~x9                    0.679</span></span>
-<span><span class="co">## x4~~x6                    0.533</span></span>
-<span><span class="co">## visual=~x7                0.984</span></span></code></pre>
+<span><span class="co">## visual=~x9                0.987</span></span>
+<span><span class="co">## x7~~x8                    0.916</span></span>
+<span><span class="co">## x8~~x9                    0.680</span></span>
+<span><span class="co">## x4~~x6                    0.532</span></span>
+<span><span class="co">## visual=~x7                0.985</span></span></code></pre>
 <p>But according to the posterior median, the parameter that would have
 the highest impact would be the residual correlation between indicators
 <strong>x7</strong> and <strong>x8</strong></p>
@@ -204,17 +204,17 @@ <h3 id="modification-indices">Modification Indices<a class="anchor" aria-label="
 <span><span class="co">## </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">##                EAP Median    MAP     SD  lower  upper PPP_sim_GreaterThan_obs</span></span>
-<span><span class="co">## x7~~x8      32.891 35.539 39.626 14.716  4.604 52.733                   0.083</span></span>
-<span><span class="co">## visual=~x9  35.353 35.458 35.495 10.624 17.727 52.239                   0.012</span></span>
-<span><span class="co">## visual=~x7  18.162 16.144 12.432  9.849  4.183 33.098                   0.016</span></span>
-<span><span class="co">## x8~~x9      27.117 12.160  2.726 42.978  0.000 70.495                   0.321</span></span>
-<span><span class="co">## textual=~x1 11.011  9.976  5.705  8.318  0.000 22.179                   0.220</span></span>
+<span><span class="co">## x7~~x8      32.891 35.539 39.626 14.716  4.604 52.733                   0.084</span></span>
+<span><span class="co">## visual=~x9  35.353 35.458 35.495 10.624 17.727 52.239                   0.013</span></span>
+<span><span class="co">## visual=~x7  18.162 16.144 12.432  9.849  4.183 33.098                   0.015</span></span>
+<span><span class="co">## x8~~x9      27.117 12.160  2.726 42.978  0.000 70.495                   0.320</span></span>
+<span><span class="co">## textual=~x1 11.011  9.976  5.705  8.318  0.000 22.179                   0.222</span></span>
 <span><span class="co">##             PPP_sim_LessThan_obs</span></span>
-<span><span class="co">## x7~~x8                     0.917</span></span>
-<span><span class="co">## visual=~x9                 0.988</span></span>
-<span><span class="co">## visual=~x7                 0.984</span></span>
-<span><span class="co">## x8~~x9                     0.679</span></span>
-<span><span class="co">## textual=~x1                0.780</span></span></code></pre>
+<span><span class="co">## x7~~x8                     0.916</span></span>
+<span><span class="co">## visual=~x9                 0.987</span></span>
+<span><span class="co">## visual=~x7                 0.985</span></span>
+<span><span class="co">## x8~~x9                     0.680</span></span>
+<span><span class="co">## textual=~x1                0.778</span></span></code></pre>
 <p>The MI is still recommended as the best metric to indicate which
 parameter is best to include next, and we can use the SEPC to evaluate
 the <strong>likely</strong> effect size for the respective
@@ -226,17 +226,17 @@ <h3 id="modification-indices">Modification Indices<a class="anchor" aria-label="
 <span><span class="co">## </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">##               EAP Median   MAP    SD lower upper PPP_sim_GreaterThan_obs</span></span>
-<span><span class="co">## x7~~x8      0.799  0.790 0.742 0.383 0.487 1.274                   0.049</span></span>
-<span><span class="co">## visual=~x9  0.519  0.494 0.466 0.132 0.334 0.688                   0.006</span></span>
-<span><span class="co">## textual=~x1 0.272  0.298 0.314 0.175 0.036 0.513                   0.132</span></span>
-<span><span class="co">## x1~~x9      0.247  0.247 0.248 0.037 0.198 0.299                   0.017</span></span>
-<span><span class="co">## x2~~x3      0.223  0.223 0.219 0.037 0.171 0.282                   0.021</span></span>
+<span><span class="co">## x7~~x8      0.799  0.790 0.742 0.383 0.487 1.274                   0.047</span></span>
+<span><span class="co">## visual=~x9  0.519  0.494 0.466 0.132 0.334 0.688                   0.007</span></span>
+<span><span class="co">## textual=~x1 0.272  0.298 0.314 0.175 0.036 0.513                   0.120</span></span>
+<span><span class="co">## x1~~x9      0.247  0.247 0.248 0.037 0.198 0.299                   0.018</span></span>
+<span><span class="co">## x2~~x3      0.223  0.223 0.219 0.037 0.171 0.282                   0.026</span></span>
 <span><span class="co">##             PPP_sim_LessThan_obs</span></span>
-<span><span class="co">## x7~~x8                     0.951</span></span>
-<span><span class="co">## visual=~x9                 0.994</span></span>
-<span><span class="co">## textual=~x1                0.868</span></span>
-<span><span class="co">## x1~~x9                     0.983</span></span>
-<span><span class="co">## x2~~x3                     0.979</span></span></code></pre>
+<span><span class="co">## x7~~x8                     0.953</span></span>
+<span><span class="co">## visual=~x9                 0.993</span></span>
+<span><span class="co">## textual=~x1                0.880</span></span>
+<span><span class="co">## x1~~x9                     0.982</span></span>
+<span><span class="co">## x2~~x3                     0.974</span></span></code></pre>
 <p>Here we see that for the 2 highest parameters, the likely SEPC is
 x7~~x8 = 0.799229902211115 and visual=~x9 = 0.518551878229323. With this
 information we can decide to include one of these new parameters in the
diff --git a/articles/model_comparison.html b/articles/model_comparison.html
index 0f6ddd7e..db53a0b5 100644
--- a/articles/model_comparison.html
+++ b/articles/model_comparison.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -254,46 +254,46 @@ <h3 id="model-comparison">Model comparison<a class="anchor" aria-label="anchor"
 <span><span class="co">## </span></span>
 <span><span class="co">## $loo</span></span>
 <span><span class="co">## $loo[[1]]</span></span>
-<span><span class="co">##             Estimate       SE</span></span>
-<span><span class="co">## elpd_loo -1606.70149 19.54461</span></span>
-<span><span class="co">## p_loo       38.39532  3.01202</span></span>
-<span><span class="co">## looic     3213.40298 39.08921</span></span>
+<span><span class="co">##             Estimate        SE</span></span>
+<span><span class="co">## elpd_loo -1606.11441 19.535855</span></span>
+<span><span class="co">## p_loo       37.57331  2.931881</span></span>
+<span><span class="co">## looic     3212.22882 39.071710</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $loo[[2]]</span></span>
 <span><span class="co">##             Estimate        SE</span></span>
-<span><span class="co">## elpd_loo -1647.03938 18.862661</span></span>
-<span><span class="co">## p_loo       34.70032  2.714831</span></span>
-<span><span class="co">## looic     3294.07877 37.725323</span></span>
+<span><span class="co">## elpd_loo -1646.98380 18.865450</span></span>
+<span><span class="co">## p_loo       34.72419  2.768238</span></span>
+<span><span class="co">## looic     3293.96759 37.730900</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $diff_loo</span></span>
 <span><span class="co">##  elpd_diff    se_diff </span></span>
-<span><span class="co">## -40.337894   7.985821 </span></span>
+<span><span class="co">## -40.869388   7.883331 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $waic</span></span>
 <span><span class="co">## $waic[[1]]</span></span>
 <span><span class="co">##              Estimate        SE</span></span>
-<span><span class="co">## elpd_waic -1606.36062 19.504892</span></span>
-<span><span class="co">## p_waic       38.05445  2.953732</span></span>
-<span><span class="co">## waic       3212.72124 39.009784</span></span>
+<span><span class="co">## elpd_waic -1605.82594 19.502689</span></span>
+<span><span class="co">## p_waic       37.28485  2.892072</span></span>
+<span><span class="co">## waic       3211.65189 39.005379</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $waic[[2]]</span></span>
-<span><span class="co">##              Estimate        SE</span></span>
-<span><span class="co">## elpd_waic -1646.76532 18.829025</span></span>
-<span><span class="co">## p_waic       34.42626  2.673588</span></span>
-<span><span class="co">## waic       3293.53065 37.658049</span></span>
+<span><span class="co">##              Estimate       SE</span></span>
+<span><span class="co">## elpd_waic -1646.68503 18.82321</span></span>
+<span><span class="co">## p_waic       34.42542  2.70925</span></span>
+<span><span class="co">## waic       3293.37005 37.64643</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $diff_waic</span></span>
 <span><span class="co">##  elpd_diff    se_diff </span></span>
-<span><span class="co">## -40.404702   7.965641</span></span></code></pre>
+<span><span class="co">## -40.859084   7.870287</span></span></code></pre>
 <p>In this case we can see that model 1 has lower LOOIC, and the ratio
 shows that the LOO differences is 5 SE of magnitude. This indicates that
 the model with the estimated regressions is better</p>
 <div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">abs</a></span><span class="op">(</span><span class="va">bc12</span><span class="op">$</span><span class="va">diff_loo</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span> <span class="op">/</span> <span class="va">bc12</span><span class="op">$</span><span class="va">diff_loo</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## elpd_diff </span></span>
-<span><span class="co">##  5.051189</span></span></code></pre>
+<span><span class="co">##  5.184279</span></span></code></pre>
 <p>Now, lets look at an example with a smaller difference between
 models, where only the smallest regression (<code>dem65~ind60</code>) is
 fixed to 0.</p>
@@ -333,43 +333,43 @@ <h3 id="model-comparison">Model comparison<a class="anchor" aria-label="anchor"
 <span><span class="co">## </span></span>
 <span><span class="co">## $loo</span></span>
 <span><span class="co">## $loo[[1]]</span></span>
-<span><span class="co">##             Estimate       SE</span></span>
-<span><span class="co">## elpd_loo -1606.70149 19.54461</span></span>
-<span><span class="co">## p_loo       38.39532  3.01202</span></span>
-<span><span class="co">## looic     3213.40298 39.08921</span></span>
+<span><span class="co">##             Estimate        SE</span></span>
+<span><span class="co">## elpd_loo -1606.11441 19.535855</span></span>
+<span><span class="co">## p_loo       37.57331  2.931881</span></span>
+<span><span class="co">## looic     3212.22882 39.071710</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $loo[[2]]</span></span>
-<span><span class="co">##             Estimate       SE</span></span>
-<span><span class="co">## elpd_loo -1606.66331 19.44934</span></span>
-<span><span class="co">## p_loo       37.43281  2.91784</span></span>
-<span><span class="co">## looic     3213.32661 38.89868</span></span>
+<span><span class="co">##             Estimate        SE</span></span>
+<span><span class="co">## elpd_loo -1606.72727 19.416513</span></span>
+<span><span class="co">## p_loo       37.59722  2.921451</span></span>
+<span><span class="co">## looic     3213.45454 38.833026</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $diff_loo</span></span>
-<span><span class="co">##   elpd_diff     se_diff </span></span>
-<span><span class="co">## -0.03818196  0.92891040 </span></span>
+<span><span class="co">##  elpd_diff    se_diff </span></span>
+<span><span class="co">## -0.6128641  0.9821245 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $waic</span></span>
 <span><span class="co">## $waic[[1]]</span></span>
 <span><span class="co">##              Estimate        SE</span></span>
-<span><span class="co">## elpd_waic -1606.36062 19.504892</span></span>
-<span><span class="co">## p_waic       38.05445  2.953732</span></span>
-<span><span class="co">## waic       3212.72124 39.009784</span></span>
+<span><span class="co">## elpd_waic -1605.82594 19.502689</span></span>
+<span><span class="co">## p_waic       37.28485  2.892072</span></span>
+<span><span class="co">## waic       3211.65189 39.005379</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $waic[[2]]</span></span>
-<span><span class="co">##              Estimate       SE</span></span>
-<span><span class="co">## elpd_waic -1606.19859 19.38086</span></span>
-<span><span class="co">## p_waic       36.96809  2.82711</span></span>
-<span><span class="co">## waic       3212.39717 38.76172</span></span>
+<span><span class="co">##            Estimate        SE</span></span>
+<span><span class="co">## elpd_waic -1606.447 19.387422</span></span>
+<span><span class="co">## p_waic       37.317  2.880573</span></span>
+<span><span class="co">## waic       3212.894 38.774843</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $diff_waic</span></span>
 <span><span class="co">##  elpd_diff    se_diff </span></span>
-<span><span class="co">## -0.1620357  0.9355731</span></span></code></pre>
+<span><span class="co">## -0.6211150  0.9806277</span></span></code></pre>
 <div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">abs</a></span><span class="op">(</span><span class="va">bc13</span><span class="op">$</span><span class="va">diff_loo</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span> <span class="op">/</span> <span class="va">bc13</span><span class="op">$</span><span class="va">diff_loo</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">##  elpd_diff </span></span>
-<span><span class="co">## 0.04110403</span></span></code></pre>
+<pre><code><span><span class="co">## elpd_diff </span></span>
+<span><span class="co">## 0.6240187</span></span></code></pre>
 <p>Lets do one last model, where only the largest regression
 (<code>dem65~dem60</code>) is fixed to 0.</p>
 <div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
@@ -407,43 +407,43 @@ <h3 id="model-comparison">Model comparison<a class="anchor" aria-label="anchor"
 <span><span class="co">## </span></span>
 <span><span class="co">## $loo</span></span>
 <span><span class="co">## $loo[[1]]</span></span>
-<span><span class="co">##             Estimate       SE</span></span>
-<span><span class="co">## elpd_loo -1606.70149 19.54461</span></span>
-<span><span class="co">## p_loo       38.39532  3.01202</span></span>
-<span><span class="co">## looic     3213.40298 39.08921</span></span>
+<span><span class="co">##             Estimate        SE</span></span>
+<span><span class="co">## elpd_loo -1606.11441 19.535855</span></span>
+<span><span class="co">## p_loo       37.57331  2.931881</span></span>
+<span><span class="co">## looic     3212.22882 39.071710</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $loo[[2]]</span></span>
 <span><span class="co">##             Estimate        SE</span></span>
-<span><span class="co">## elpd_loo -1629.27107 19.863567</span></span>
-<span><span class="co">## p_loo       37.79969  2.966613</span></span>
-<span><span class="co">## looic     3258.54214 39.727133</span></span>
+<span><span class="co">## elpd_loo -1629.39258 19.862092</span></span>
+<span><span class="co">## p_loo       37.75678  2.984498</span></span>
+<span><span class="co">## looic     3258.78516 39.724184</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $diff_loo</span></span>
-<span><span class="co">##  elpd_diff    se_diff </span></span>
-<span><span class="co">## -22.569579   4.066783 </span></span>
+<span><span class="co">## elpd_diff   se_diff </span></span>
+<span><span class="co">## -23.27817   3.98061 </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $waic</span></span>
 <span><span class="co">## $waic[[1]]</span></span>
 <span><span class="co">##              Estimate        SE</span></span>
-<span><span class="co">## elpd_waic -1606.36062 19.504892</span></span>
-<span><span class="co">## p_waic       38.05445  2.953732</span></span>
-<span><span class="co">## waic       3212.72124 39.009784</span></span>
+<span><span class="co">## elpd_waic -1605.82594 19.502689</span></span>
+<span><span class="co">## p_waic       37.28485  2.892072</span></span>
+<span><span class="co">## waic       3211.65189 39.005379</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $waic[[2]]</span></span>
 <span><span class="co">##              Estimate        SE</span></span>
-<span><span class="co">## elpd_waic -1629.01215 19.843132</span></span>
-<span><span class="co">## p_waic       37.54077  2.938398</span></span>
-<span><span class="co">## waic       3258.02429 39.686264</span></span>
+<span><span class="co">## elpd_waic -1629.01598 19.814740</span></span>
+<span><span class="co">## p_waic       37.38018  2.925757</span></span>
+<span><span class="co">## waic       3258.03196 39.629480</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## $diff_waic</span></span>
 <span><span class="co">##  elpd_diff    se_diff </span></span>
-<span><span class="co">## -22.651524   4.062466</span></span></code></pre>
+<span><span class="co">## -23.190036   3.968117</span></span></code></pre>
 <div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/MathFun.html" class="external-link">abs</a></span><span class="op">(</span><span class="va">bc14</span><span class="op">$</span><span class="va">diff_loo</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span> <span class="op">/</span> <span class="va">bc14</span><span class="op">$</span><span class="va">diff_loo</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## elpd_diff </span></span>
-<span><span class="co">##  5.549737</span></span></code></pre>
+<span><span class="co">##  5.847892</span></span></code></pre>
 </div>
 <div class="section level3">
 <h3 id="bayes-factor">Bayes factor<a class="anchor" aria-label="anchor" href="#bayes-factor"></a>
diff --git a/articles/multilevel.html b/articles/multilevel.html
index 1e5c7f09..a4f46151 100644
--- a/articles/multilevel.html
+++ b/articles/multilevel.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/ordinal.html b/articles/ordinal.html
index 0c295203..288c0f79 100644
--- a/articles/ordinal.html
+++ b/articles/ordinal.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/plotting.html b/articles/plotting.html
index b341205b..fe5849f2 100644
--- a/articles/plotting.html
+++ b/articles/plotting.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/prior.html b/articles/prior.html
index 6a8b51d3..f0b6a021 100644
--- a/articles/prior.html
+++ b/articles/prior.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/prior_pred_checks.html b/articles/prior_pred_checks.html
index ea6bc7b5..4bb57539 100644
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diff --git a/articles/probability_direction.html b/articles/probability_direction.html
index 65b7d750..fda8a397 100644
--- a/articles/probability_direction.html
+++ b/articles/probability_direction.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
@@ -164,7 +164,7 @@ <h3 id="probability-of-direction-pd">Probability of Direction (pd)<a class="anch
 standardized estimates, and <span class="math inline">\(R^2\)</span></p>
 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit</span>, standardize<span class="op">=</span><span class="cn">T</span>, rsquare<span class="op">=</span><span class="cn">T</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## blavaan 0.5.2.1189 ended normally after 1000 iterations</span></span>
+<pre><code><span><span class="co">## blavaan 0.5.2.1191 ended normally after 1000 iterations</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">##   Estimator                                      BAYES</span></span>
 <span><span class="co">##   Optimization method                             MCMC</span></span>
@@ -182,154 +182,154 @@ <h3 id="probability-of-direction-pd">Probability of Direction (pd)<a class="anch
 <span><span class="co">## Latent Variables:</span></span>
 <span><span class="co">##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all</span></span>
 <span><span class="co">##   ind60 =~                                                              </span></span>
-<span><span class="co">##     x1                0.702    0.071    0.577    0.857    0.702    0.921</span></span>
-<span><span class="co">##     x2                1.532    0.144    1.280    1.843    1.532    0.973</span></span>
-<span><span class="co">##     x3                1.270    0.143    1.012    1.578    1.270    0.870</span></span>
+<span><span class="co">##     x1                0.708    0.075    0.578    0.866    0.708    0.923</span></span>
+<span><span class="co">##     x2                1.543    0.146    1.291    1.854    1.543    0.973</span></span>
+<span><span class="co">##     x3                1.280    0.149    1.013    1.601    1.280    0.872</span></span>
 <span><span class="co">##   dem60 =~                                                              </span></span>
-<span><span class="co">##     y1         (a)    1.458    0.167    1.136    1.794    1.782    0.759</span></span>
-<span><span class="co">##     y2         (b)    1.734    0.228    1.307    2.207    2.118    0.585</span></span>
-<span><span class="co">##     y3         (c)    1.816    0.203    1.423    2.219    2.219    0.700</span></span>
-<span><span class="co">##     y4         (d)    1.950    0.199    1.585    2.349    2.382    0.790</span></span>
+<span><span class="co">##     y1         (a)    1.466    0.171    1.138    1.806    1.794    0.764</span></span>
+<span><span class="co">##     y2         (b)    1.738    0.229    1.300    2.199    2.127    0.585</span></span>
+<span><span class="co">##     y3         (c)    1.816    0.201    1.435    2.227    2.223    0.701</span></span>
+<span><span class="co">##     y4         (d)    1.951    0.195    1.577    2.344    2.388    0.790</span></span>
 <span><span class="co">##   dem65 =~                                                              </span></span>
-<span><span class="co">##     y5         (a)    1.458    0.167    1.136    1.794    2.298    0.811</span></span>
-<span><span class="co">##     y6         (b)    1.734    0.228    1.307    2.207    2.732    0.770</span></span>
-<span><span class="co">##     y7         (c)    1.816    0.203    1.423    2.219    2.861    0.836</span></span>
-<span><span class="co">##     y8         (d)    1.950    0.199    1.585    2.349    3.071    0.869</span></span>
+<span><span class="co">##     y5         (a)    1.466    0.171    1.138    1.806    2.314    0.814</span></span>
+<span><span class="co">##     y6         (b)    1.738    0.229    1.300    2.199    2.743    0.771</span></span>
+<span><span class="co">##     y7         (c)    1.816    0.201    1.435    2.227    2.867    0.837</span></span>
+<span><span class="co">##     y8         (d)    1.951    0.195    1.577    2.344    3.080    0.871</span></span>
 <span><span class="co">##      Rhat    Prior       </span></span>
 <span><span class="co">##                          </span></span>
-<span><span class="co">##     1.000    normal(0,10)</span></span>
-<span><span class="co">##     1.000    normal(0,10)</span></span>
-<span><span class="co">##     0.999    normal(0,10)</span></span>
+<span><span class="co">##     1.001    normal(0,10)</span></span>
+<span><span class="co">##     1.001    normal(0,10)</span></span>
+<span><span class="co">##     1.001    normal(0,10)</span></span>
 <span><span class="co">##                          </span></span>
-<span><span class="co">##     1.000    normal(0,10)</span></span>
-<span><span class="co">##     1.000    normal(0,10)</span></span>
-<span><span class="co">##     1.002    normal(0,10)</span></span>
+<span><span class="co">##     1.001    normal(0,10)</span></span>
+<span><span class="co">##     0.999    normal(0,10)</span></span>
+<span><span class="co">##     1.001    normal(0,10)</span></span>
 <span><span class="co">##     1.000    normal(0,10)</span></span>
 <span><span class="co">##                          </span></span>
-<span><span class="co">##     1.000                </span></span>
-<span><span class="co">##     1.000                </span></span>
-<span><span class="co">##     1.002                </span></span>
+<span><span class="co">##     1.001                </span></span>
+<span><span class="co">##     0.999                </span></span>
+<span><span class="co">##     1.001                </span></span>
 <span><span class="co">##     1.000                </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Regressions:</span></span>
 <span><span class="co">##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all</span></span>
 <span><span class="co">##   dem60 ~                                                               </span></span>
-<span><span class="co">##     ind60             0.702    0.173    0.382    1.055    0.574    0.574</span></span>
+<span><span class="co">##     ind60             0.705    0.172    0.384    1.065    0.576    0.576</span></span>
 <span><span class="co">##   dem65 ~                                                               </span></span>
-<span><span class="co">##     ind60             0.241    0.172   -0.098    0.575    0.153    0.153</span></span>
-<span><span class="co">##     dem60             0.870    0.130    0.624    1.129    0.675    0.675</span></span>
+<span><span class="co">##     ind60             0.250    0.173   -0.094    0.596    0.158    0.158</span></span>
+<span><span class="co">##     dem60             0.866    0.129    0.624    1.124    0.672    0.672</span></span>
 <span><span class="co">##      Rhat    Prior       </span></span>
 <span><span class="co">##                          </span></span>
-<span><span class="co">##     1.000    normal(0,10)</span></span>
+<span><span class="co">##     1.001    normal(0,10)</span></span>
 <span><span class="co">##                          </span></span>
 <span><span class="co">##     0.999    normal(0,10)</span></span>
-<span><span class="co">##     0.999    normal(0,10)</span></span>
+<span><span class="co">##     1.000    normal(0,10)</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Covariances:</span></span>
 <span><span class="co">##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all</span></span>
 <span><span class="co">##  .y1 ~~                                                                 </span></span>
-<span><span class="co">##    .y5                0.754    0.443   -0.006    1.731    0.754    0.298</span></span>
+<span><span class="co">##    .y5                0.737    0.440   -0.022    1.689    0.737    0.295</span></span>
 <span><span class="co">##  .y2 ~~                                                                 </span></span>
-<span><span class="co">##    .y4                1.752    0.807    0.331    3.456    1.752    0.322</span></span>
-<span><span class="co">##    .y6                2.216    0.780    0.809    3.948    2.216    0.333</span></span>
+<span><span class="co">##    .y4                1.784    0.829    0.350    3.686    1.784    0.326</span></span>
+<span><span class="co">##    .y6                2.222    0.853    0.713    4.068    2.222    0.332</span></span>
 <span><span class="co">##  .y3 ~~                                                                 </span></span>
-<span><span class="co">##    .y7                1.298    0.671    0.104    2.748    1.298    0.306</span></span>
+<span><span class="co">##    .y7                1.319    0.675    0.116    2.760    1.319    0.312</span></span>
 <span><span class="co">##  .y4 ~~                                                                 </span></span>
-<span><span class="co">##    .y8                0.386    0.491   -0.519    1.452    0.386    0.120</span></span>
+<span><span class="co">##    .y8                0.381    0.493   -0.515    1.411    0.381    0.118</span></span>
 <span><span class="co">##  .y6 ~~                                                                 </span></span>
-<span><span class="co">##    .y8                1.100    0.755   -0.258    2.730    1.100    0.278</span></span>
+<span><span class="co">##    .y8                1.092    0.691   -0.186    2.550    1.092    0.277</span></span>
 <span><span class="co">##      Rhat    Prior       </span></span>
 <span><span class="co">##                          </span></span>
-<span><span class="co">##     0.999       beta(1,1)</span></span>
+<span><span class="co">##     1.000       beta(1,1)</span></span>
 <span><span class="co">##                          </span></span>
 <span><span class="co">##     1.000       beta(1,1)</span></span>
-<span><span class="co">##     0.999       beta(1,1)</span></span>
+<span><span class="co">##     1.000       beta(1,1)</span></span>
 <span><span class="co">##                          </span></span>
-<span><span class="co">##     1.002       beta(1,1)</span></span>
+<span><span class="co">##     1.000       beta(1,1)</span></span>
 <span><span class="co">##                          </span></span>
-<span><span class="co">##     0.999       beta(1,1)</span></span>
+<span><span class="co">##     1.000       beta(1,1)</span></span>
 <span><span class="co">##                          </span></span>
-<span><span class="co">##     1.002       beta(1,1)</span></span>
+<span><span class="co">##     1.001       beta(1,1)</span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Intercepts:</span></span>
 <span><span class="co">##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all</span></span>
-<span><span class="co">##    .x1                5.055    0.088    4.875    5.223    5.055    6.634</span></span>
-<span><span class="co">##    .x2                4.794    0.181    4.423    5.135    4.794    3.046</span></span>
-<span><span class="co">##    .x3                3.560    0.168    3.225    3.884    3.560    2.439</span></span>
-<span><span class="co">##    .y1                5.462    0.275    4.929    6.017    5.462    2.328</span></span>
-<span><span class="co">##    .y2                4.255    0.432    3.406    5.091    4.255    1.175</span></span>
-<span><span class="co">##    .y3                6.560    0.366    5.834    7.281    6.560    2.069</span></span>
-<span><span class="co">##    .y4                4.456    0.354    3.760    5.145    4.456    1.478</span></span>
-<span><span class="co">##    .y5                5.140    0.333    4.474    5.794    5.140    1.814</span></span>
-<span><span class="co">##    .y6                2.982    0.418    2.150    3.786    2.982    0.840</span></span>
-<span><span class="co">##    .y7                6.200    0.394    5.432    6.950    6.200    1.812</span></span>
-<span><span class="co">##    .y8                4.048    0.417    3.222    4.862    4.048    1.146</span></span>
+<span><span class="co">##    .x1                5.053    0.091    4.872    5.226    5.053    6.588</span></span>
+<span><span class="co">##    .x2                4.789    0.188    4.411    5.153    4.789    3.022</span></span>
+<span><span class="co">##    .x3                3.554    0.175    3.200    3.886    3.554    2.423</span></span>
+<span><span class="co">##    .y1                5.461    0.276    4.913    6.000    5.461    2.326</span></span>
+<span><span class="co">##    .y2                4.251    0.433    3.422    5.143    4.251    1.170</span></span>
+<span><span class="co">##    .y3                6.556    0.372    5.822    7.282    6.556    2.069</span></span>
+<span><span class="co">##    .y4                4.451    0.348    3.757    5.116    4.451    1.472</span></span>
+<span><span class="co">##    .y5                5.133    0.330    4.462    5.776    5.133    1.806</span></span>
+<span><span class="co">##    .y6                2.970    0.413    2.142    3.769    2.970    0.834</span></span>
+<span><span class="co">##    .y7                6.190    0.407    5.393    6.979    6.190    1.807</span></span>
+<span><span class="co">##    .y8                4.038    0.412    3.193    4.813    4.038    1.142</span></span>
 <span><span class="co">##     ind60             0.000                               0.000    0.000</span></span>
 <span><span class="co">##    .dem60             0.000                               0.000    0.000</span></span>
 <span><span class="co">##    .dem65             0.000                               0.000    0.000</span></span>
 <span><span class="co">##      Rhat    Prior       </span></span>
-<span><span class="co">##     1.001    normal(0,32)</span></span>
-<span><span class="co">##     1.001    normal(0,32)</span></span>
-<span><span class="co">##     1.001    normal(0,32)</span></span>
-<span><span class="co">##     1.002    normal(0,32)</span></span>
+<span><span class="co">##     1.005    normal(0,32)</span></span>
 <span><span class="co">##     1.003    normal(0,32)</span></span>
 <span><span class="co">##     1.002    normal(0,32)</span></span>
 <span><span class="co">##     1.001    normal(0,32)</span></span>
-<span><span class="co">##     1.001    normal(0,32)</span></span>
 <span><span class="co">##     1.000    normal(0,32)</span></span>
+<span><span class="co">##     1.001    normal(0,32)</span></span>
 <span><span class="co">##     1.002    normal(0,32)</span></span>
 <span><span class="co">##     1.001    normal(0,32)</span></span>
+<span><span class="co">##     1.000    normal(0,32)</span></span>
+<span><span class="co">##     1.000    normal(0,32)</span></span>
+<span><span class="co">##     1.002    normal(0,32)</span></span>
 <span><span class="co">##                          </span></span>
 <span><span class="co">##                          </span></span>
 <span><span class="co">##                          </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## Variances:</span></span>
 <span><span class="co">##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all</span></span>
-<span><span class="co">##    .x1                0.088    0.023    0.048    0.136    0.088    0.151</span></span>
-<span><span class="co">##    .x2                0.132    0.083    0.003    0.311    0.132    0.053</span></span>
-<span><span class="co">##    .x3                0.516    0.099    0.347    0.734    0.516    0.242</span></span>
-<span><span class="co">##    .y1                2.330    0.593    1.331    3.665    2.330    0.423</span></span>
-<span><span class="co">##    .y2                8.638    1.573    6.004   12.097    8.638    0.658</span></span>
-<span><span class="co">##    .y3                5.126    1.067    3.382    7.486    5.126    0.510</span></span>
-<span><span class="co">##    .y4                3.421    0.905    1.798    5.464    3.421    0.376</span></span>
-<span><span class="co">##    .y5                2.749    0.663    1.683    4.205    2.749    0.342</span></span>
-<span><span class="co">##    .y6                5.139    1.061    3.310    7.364    5.139    0.408</span></span>
-<span><span class="co">##    .y7                3.519    0.882    2.061    5.447    3.519    0.301</span></span>
-<span><span class="co">##    .y8                3.054    0.929    1.402    5.033    3.054    0.245</span></span>
+<span><span class="co">##    .x1                0.088    0.023    0.048    0.138    0.088    0.149</span></span>
+<span><span class="co">##    .x2                0.132    0.081    0.001    0.305    0.132    0.052</span></span>
+<span><span class="co">##    .x3                0.514    0.105    0.338    0.745    0.514    0.239</span></span>
+<span><span class="co">##    .y1                2.295    0.589    1.266    3.588    2.295    0.416</span></span>
+<span><span class="co">##    .y2                8.687    1.621    5.949   12.160    8.687    0.658</span></span>
+<span><span class="co">##    .y3                5.102    1.037    3.353    7.429    5.102    0.508</span></span>
+<span><span class="co">##    .y4                3.444    0.922    1.872    5.473    3.444    0.377</span></span>
+<span><span class="co">##    .y5                2.724    0.648    1.652    4.118    2.724    0.337</span></span>
+<span><span class="co">##    .y6                5.148    1.082    3.170    7.515    5.148    0.406</span></span>
+<span><span class="co">##    .y7                3.515    0.852    2.089    5.450    3.515    0.300</span></span>
+<span><span class="co">##    .y8                3.014    0.885    1.324    4.874    3.014    0.241</span></span>
 <span><span class="co">##     ind60             1.000                               1.000    1.000</span></span>
-<span><span class="co">##    .dem60             1.000                               0.670    0.670</span></span>
-<span><span class="co">##    .dem65             1.000                               0.403    0.403</span></span>
+<span><span class="co">##    .dem60             1.000                               0.668    0.668</span></span>
+<span><span class="co">##    .dem65             1.000                               0.401    0.401</span></span>
 <span><span class="co">##      Rhat    Prior       </span></span>
-<span><span class="co">##     1.001 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##     1.000 gamma(1,.5)[sd]</span></span>
 <span><span class="co">##     1.003 gamma(1,.5)[sd]</span></span>
 <span><span class="co">##     1.000 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##     0.999 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##     0.999 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##     1.001 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##     1.001 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##     1.001 gamma(1,.5)[sd]</span></span>
 <span><span class="co">##     1.000 gamma(1,.5)[sd]</span></span>
-<span><span class="co">##     1.005 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##     1.000 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##     1.000 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##     1.000 gamma(1,.5)[sd]</span></span>
 <span><span class="co">##     1.001 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##     1.000 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##     0.999 gamma(1,.5)[sd]</span></span>
+<span><span class="co">##     1.000 gamma(1,.5)[sd]</span></span>
 <span><span class="co">##                          </span></span>
 <span><span class="co">##                          </span></span>
 <span><span class="co">##                          </span></span>
 <span><span class="co">## </span></span>
 <span><span class="co">## R-Square:</span></span>
 <span><span class="co">##                    Estimate</span></span>
-<span><span class="co">##     x1                0.849</span></span>
-<span><span class="co">##     x2                0.947</span></span>
-<span><span class="co">##     x3                0.758</span></span>
-<span><span class="co">##     y1                0.577</span></span>
+<span><span class="co">##     x1                0.851</span></span>
+<span><span class="co">##     x2                0.948</span></span>
+<span><span class="co">##     x3                0.761</span></span>
+<span><span class="co">##     y1                0.584</span></span>
 <span><span class="co">##     y2                0.342</span></span>
-<span><span class="co">##     y3                0.490</span></span>
-<span><span class="co">##     y4                0.624</span></span>
-<span><span class="co">##     y5                0.658</span></span>
-<span><span class="co">##     y6                0.592</span></span>
-<span><span class="co">##     y7                0.699</span></span>
-<span><span class="co">##     y8                0.755</span></span>
-<span><span class="co">##     dem60             0.330</span></span>
-<span><span class="co">##     dem65             0.597</span></span></code></pre>
+<span><span class="co">##     y3                0.492</span></span>
+<span><span class="co">##     y4                0.623</span></span>
+<span><span class="co">##     y5                0.663</span></span>
+<span><span class="co">##     y6                0.594</span></span>
+<span><span class="co">##     y7                0.700</span></span>
+<span><span class="co">##     y8                0.759</span></span>
+<span><span class="co">##     dem60             0.332</span></span>
+<span><span class="co">##     dem65             0.599</span></span></code></pre>
 <p>To calculate the probability of direction we will use a function from
 the package <code>brms</code> <span class="citation">(Bürkner
 2017)</span></p>
@@ -442,7 +442,7 @@ <h3 id="probability-of-direction-pd">Probability of Direction (pd)<a class="anch
 <span><span class="co">## <span style="color: #00BBBB;">•</span> `ly_sign[7]` -&gt; `ly_sign[7]...11`</span></span></code></pre>
 <pre><code><span><span class="co">## Hypothesis Tests for class :</span></span>
 <span><span class="co">##          Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob</span></span>
-<span><span class="co">## 1 (bet_sign[2]) &gt; 0     0.24      0.17    -0.05     0.52      10.95      0.92</span></span>
+<span><span class="co">## 1 (bet_sign[2]) &gt; 0     0.25      0.17    -0.04     0.53      13.15      0.93</span></span>
 <span><span class="co">##   Star</span></span>
 <span><span class="co">## 1     </span></span>
 <span><span class="co">## ---</span></span>
@@ -477,7 +477,7 @@ <h3 id="probability-of-direction-pd">Probability of Direction (pd)<a class="anch
 <span><span class="co">## <span style="color: #00BBBB;">•</span> `ly_sign[7]` -&gt; `ly_sign[7]...11`</span></span></code></pre>
 <pre><code><span><span class="co">## Hypothesis Tests for class :</span></span>
 <span><span class="co">##          Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob</span></span>
-<span><span class="co">## 1 (bet_sign[1]) &gt; 0      0.7      0.17     0.43     0.99        Inf         1</span></span>
+<span><span class="co">## 1 (bet_sign[1]) &gt; 0     0.71      0.17     0.44     1.01        Inf         1</span></span>
 <span><span class="co">##   Star</span></span>
 <span><span class="co">## 1    *</span></span>
 <span><span class="co">## ---</span></span>
@@ -505,9 +505,9 @@ <h3 id="probability-of-direction-pd">Probability of Direction (pd)<a class="anch
 <span><span class="co">## <span style="color: #00BBBB;">•</span> `ly_sign[7]` -&gt; `ly_sign[7]...11`</span></span></code></pre>
 <pre><code><span><span class="co">## Hypothesis Tests for class :</span></span>
 <span><span class="co">##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio</span></span>
-<span><span class="co">## 1 (bet_sign[1]-bet_... &gt; 0     0.46      0.25     0.06      0.9      39.54</span></span>
+<span><span class="co">## 1 (bet_sign[1]-bet_... &gt; 0     0.46      0.26     0.06     0.91      32.71</span></span>
 <span><span class="co">##   Post.Prob Star</span></span>
-<span><span class="co">## 1      0.98    *</span></span>
+<span><span class="co">## 1      0.97    *</span></span>
 <span><span class="co">## ---</span></span>
 <span><span class="co">## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.</span></span>
 <span><span class="co">## '*': For one-sided hypotheses, the posterior probability exceeds 95%;</span></span>
@@ -552,9 +552,9 @@ <h3 id="region-of-practical-equivalence-rope">Region of Practical Equivalence (R
 <span><span class="co">## <span style="color: #00BBBB;">•</span> `ly_sign[7]` -&gt; `ly_sign[7]...11`</span></span></code></pre>
 <pre><code><span><span class="co">## Hypothesis Tests for class :</span></span>
 <span><span class="co">##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio</span></span>
-<span><span class="co">## 1 (bet_sign[2])-(.1) &gt; 0     0.14      0.17    -0.15     0.42       3.88</span></span>
+<span><span class="co">## 1 (bet_sign[2])-(.1) &gt; 0     0.15      0.17    -0.14     0.43        4.3</span></span>
 <span><span class="co">##   Post.Prob Star</span></span>
-<span><span class="co">## 1       0.8     </span></span>
+<span><span class="co">## 1      0.81     </span></span>
 <span><span class="co">## ---</span></span>
 <span><span class="co">## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.</span></span>
 <span><span class="co">## '*': For one-sided hypotheses, the posterior probability exceeds 95%;</span></span>
diff --git a/articles/resources.html b/articles/resources.html
index 1a0df2f4..64f08122 100644
--- a/articles/resources.html
+++ b/articles/resources.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
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diff --git a/articles/start.html b/articles/start.html
index 04f2ba99..d0f293af 100644
--- a/articles/start.html
+++ b/articles/start.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/articles/summaries.html b/articles/summaries.html
index cbf270b9..cf54e1e3 100644
--- a/articles/summaries.html
+++ b/articles/summaries.html
@@ -26,7 +26,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
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diff --git a/authors.html b/authors.html
index a5b3dc51..541f3f3b 100644
--- a/authors.html
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@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
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diff --git a/index.html b/index.html
index 047a74f6..5171d74a 100644
--- a/index.html
+++ b/index.html
@@ -28,7 +28,7 @@
     
     <a class="navbar-brand me-2" href="index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
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diff --git a/news/index.html b/news/index.html
index 162f0a81..19aad2ac 100644
--- a/news/index.html
+++ b/news/index.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
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diff --git a/pkgdown.yml b/pkgdown.yml
index efc9e182..832bf62b 100644
--- a/pkgdown.yml
+++ b/pkgdown.yml
@@ -19,7 +19,7 @@ articles:
   resources: resources.html
   start: start.html
   summaries: summaries.html
-last_built: 2023-10-31T16:04Z
+last_built: 2023-11-02T17:42Z
 urls:
   reference: http://ecmerkle.github.io/blavaan/reference
   article: http://ecmerkle.github.io/blavaan/articles
diff --git a/reference/bcfa.html b/reference/bcfa.html
index bc9195d5..a0fbffb8 100644
--- a/reference/bcfa.html
+++ b/reference/bcfa.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
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diff --git a/reference/bgrowth.html b/reference/bgrowth.html
index 2a988388..ad2aefdf 100644
--- a/reference/bgrowth.html
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@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/blavCompare.html b/reference/blavCompare.html
index 8414b02e..01bd7431 100644
--- a/reference/blavCompare.html
+++ b/reference/blavCompare.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/blavFitIndices.html b/reference/blavFitIndices.html
index 5d267af6..85b4853c 100644
--- a/reference/blavFitIndices.html
+++ b/reference/blavFitIndices.html
@@ -12,7 +12,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
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diff --git a/reference/blavInspect.html b/reference/blavInspect.html
index 673e45ea..640b0087 100644
--- a/reference/blavInspect.html
+++ b/reference/blavInspect.html
@@ -14,7 +14,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/blavPredict.html b/reference/blavPredict.html
index c76ef847..9ef08c8d 100644
--- a/reference/blavPredict.html
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@@ -14,7 +14,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/blav_internal.html b/reference/blav_internal.html
index b848137c..fdbefa68 100644
--- a/reference/blav_internal.html
+++ b/reference/blav_internal.html
@@ -12,7 +12,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
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     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/blavaan-class.html b/reference/blavaan-class.html
index 1953aa28..cf71fe2f 100644
--- a/reference/blavaan-class.html
+++ b/reference/blavaan-class.html
@@ -18,7 +18,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/blavaan.html b/reference/blavaan.html
index c73b2df6..df26748a 100644
--- a/reference/blavaan.html
+++ b/reference/blavaan.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
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diff --git a/reference/bsem.html b/reference/bsem.html
index 1aeff1c8..5dd26878 100644
--- a/reference/bsem.html
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@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/dpriors.html b/reference/dpriors.html
index 888aeb23..350d80cf 100644
--- a/reference/dpriors.html
+++ b/reference/dpriors.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/index.html b/reference/index.html
index 1f9b3621..db3a857e 100644
--- a/reference/index.html
+++ b/reference/index.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
     <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation">
diff --git a/reference/plot.blavaan.html b/reference/plot.blavaan.html
index 5ccba622..ef8f8aa4 100644
--- a/reference/plot.blavaan.html
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@@ -12,7 +12,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
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index 2fa38279..acf55a57 100644
--- a/reference/ppmc.html
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@@ -14,7 +14,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
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diff --git a/reference/standardizedPosterior.html b/reference/standardizedPosterior.html
index 35ecee1c..19403f20 100644
--- a/reference/standardizedPosterior.html
+++ b/reference/standardizedPosterior.html
@@ -10,7 +10,7 @@
     
     <a class="navbar-brand me-2" href="../index.html">blavaan</a>
 
-    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1189</small>
+    <small class="nav-text text-muted me-auto" data-bs-toggle="tooltip" data-bs-placement="bottom" title="">0.5-2.1191</small>
 
     
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diff --git a/search.json b/search.json
index 5f92bbfc..284d5484 100644
--- a/search.json
+++ b/search.json
@@ -1 +1 @@
-[{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Approximate fit indices","text":"SEM, one first steps evaluate model’s global fit. commonly done presenting multiple fit indices, common based model’s \\(\\chi^2\\). developed Bayesian versions indices (Garnier-Villarreal Jorgensen 2020) can computed blavaan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"noncentrality-based-fit-indices","dir":"Articles","previous_headings":"","what":"Noncentrality-Based Fit Indices","title":"Approximate fit indices","text":"group indices compares hypothesized model perfect saturated model. specifically uses noncentrality parameter \\(\\hat{\\lambda} = \\chi^2 - df\\), df adjusted different model/data characterictics. Specific indices include Root Mean Square Error approximation (RMSEA), McDonald’s centrality index (Mc), gamma-hat (\\(\\hat{\\Gamma}\\)), adjusted gamma-hat (\\(\\hat{\\Gamma}_{adj}\\)). show example Holzinger Swineford (1939) example. first estimate SEM/CFA model usual need pass model blavFitIndices() function Finally, can describe posterior distribution indices summary() function. call, see 3 central tendency measures (mean median, mode), standard deviation, 90% Credible Interval","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939, std.lv=TRUE) gl_fits <- blavFitIndices(fit) summary(gl_fits, central.tendency = c(\"mean\",\"median\",\"mode\"), prob = .90) ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for devm-based fit indices: ##  ##                EAP Median   MAP    SD lower upper ## BRMSEA       0.100  0.100 0.098 0.005 0.092 0.109 ## BGammaHat    0.956  0.956 0.958 0.004 0.950 0.964 ## adjBGammaHat 0.904  0.905 0.908 0.010 0.890 0.921 ## BMc          0.902  0.902 0.906 0.010 0.887 0.919"},{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"incremental-fit-indices","dir":"Articles","previous_headings":"","what":"Incremental Fit Indices","title":"Approximate fit indices","text":"Another group fit indices compares hypothesized model worst possible model, called incremental indices. indices compare model’s \\(\\chi^2_H\\) null model’s \\(\\chi^2_0\\) different ways. Indices include Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), Normed Fit Index (NFI). estimate indices need defined estimate respective null model. standard null model used default frequentist SEM programs (like lavaan) includes indicators variances intercepts, covariances items. can specify null model including respective indicator variances model syntax, hypothesized null models, pass blavFitIndices function, now provide types fit indices summary() method now presents central tendicy measure asked , standard deviation, credible interval noncentrality incremental fit indices.","code":"HS.model_null <- ' x1 ~~ x1  x2 ~~ x2  x3 ~~ x3 x4 ~~ x4 x5 ~~ x5 x6 ~~ x6 x7 ~~ x7 x8 ~~ x8 x9 ~~ x9 '  fit_null <- bcfa(HS.model_null, data=HolzingerSwineford1939) gl_fits_all <- blavFitIndices(fit, baseline.model = fit_null)  summary(gl_fits_all, central.tendency = c(\"mean\",\"median\",\"mode\"), prob = .90) ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for devm-based fit indices: ##  ##                EAP Median   MAP    SD lower upper ## BRMSEA       0.100  0.100 0.098 0.005 0.092 0.109 ## BGammaHat    0.956  0.956 0.958 0.004 0.950 0.964 ## adjBGammaHat 0.904  0.905 0.908 0.010 0.890 0.921 ## BMc          0.902  0.902 0.906 0.010 0.887 0.919 ## BCFI         0.929  0.930 0.933 0.008 0.918 0.942 ## BTLI         0.878  0.880 0.885 0.013 0.859 0.901 ## BNFI         0.910  0.910 0.913 0.007 0.899 0.923"},{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"access-the-indices-posterior-distributions","dir":"Articles","previous_headings":"","what":"Access the indices posterior distributions","title":"Approximate fit indices","text":"can also extract posterior distributions respective indices, way can explore details. example, diagnostic plots using bayesplot package. saved posterior distributions, can explore histogram scatterplots indices.","code":"dist_fits <- data.frame(gl_fits_all@indices) head(dist_fits) ##      BRMSEA BGammaHat adjBGammaHat       BMc      BCFI      BTLI      BNFI ## 1 0.1049896 0.9520096    0.8950616 0.8927742 0.9230257 0.8676190 0.9036694 ## 2 0.1012793 0.9551923    0.9020212 0.8998326 0.9283789 0.8768254 0.9088195 ## 3 0.1087359 0.9487025    0.8878302 0.8854492 0.9170222 0.8572940 0.8978043 ## 4 0.1009911 0.9554356    0.9025531 0.9003724 0.9286836 0.8773494 0.9090855 ## 5 0.1004256 0.9559114    0.9035935 0.9014283 0.9300108 0.8796319 0.9105038 ## 6 0.1051490 0.9518708    0.8947583 0.8924667 0.9233153 0.8681169 0.9040741 mcmc_pairs(dist_fits, pars = c(\"BRMSEA\",\"BGammaHat\",\"BCFI\",\"BTLI\"),            diag_fun = \"hist\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"summary","dir":"Articles","previous_headings":"","what":"Summary","title":"Approximate fit indices","text":"can estimate posterior distributions \\(\\chi^2\\) based global fit indices. Notice presented fit indices based recommended method devM recommended number parameters metric loo. can adjusted user desired. general recommendation prefer \\(\\hat{\\Gamma}\\) CFI, shown less sensitive model data characteristics. defaults recommendations made based previous simulation research. details fit indices please see Garnier-Villarreal Jorgensen (2020).","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_efficiency.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Convergence and Efficiency Evaluation","text":"Bayesian models estimated Markov-Chain Monte Carlo (MCMC) sampler, model estimation doesn’t stop achieved convergence criteria. run long desired (determined burnin sample arguments), need evaluate convergence efficiency estimated posterior distributions. analyze results convergence achieved, judged metrics described . example use Industrialization Political Democracy example (Bollen 1989).","code":"model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000)"},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_efficiency.html","id":"convergence","dir":"Articles","previous_headings":"","what":"Convergence","title":"Convergence and Efficiency Evaluation","text":"primary convergence diagnostic \\(\\hat{R}\\), compares - within-chain samples model parameters univariate quantities interest (Vehtari et al. 2021). chains mixed well (ie, - within-chain estimates don’t agree), \\(\\hat{R}\\) larger 1. recommend running least three chains default using posterior samples \\(\\hat{R} < 1.05\\) parameters. blavaan presents \\(\\hat{R}\\) reported underlying MCMC program, either Stan JAGS (Stan default). can obtain \\(\\hat{R}\\) summary() function, can also extract blavInspect() function large models can cumbersome look entries. can instead find largest \\(\\hat{R}\\) see less \\(1.05\\) \\(\\hat{R} < 1.05\\) can establish MCMC chains converged stable solution. model converged, might increase number burnin iterations /change model priors dpriors() function. address issues model failed converge due needing iterations due model misspecification (bad priors). rule thumb, seldom see model require 1,000 burnin samples Stan. model converging 1,000 burnin samples, likely default prior distributions clash data. can happen, e.g., variables contain values 100s 1000s.","code":"blavInspect(fit, \"rhat\") ##   ind60=~x1   ind60=~x2   ind60=~x3           a           b           c  ##   1.0005379   1.0020521   1.0020088   0.9997209   1.0007457   0.9998598  ##           d           a           b           c           d dem60~ind60  ##   1.0000487   0.9997209   1.0007457   0.9998598   1.0000487   0.9994924  ## dem65~ind60 dem65~dem60      y1~~y5      y2~~y4      y2~~y6      y3~~y7  ##   0.9998798   0.9998013   1.0008959   0.9996250   1.0006446   0.9991291  ##      y4~~y8      y6~~y8      x1~~x1      x2~~x2      x3~~x3      y1~~y1  ##   1.0005873   0.9996670   1.0001871   1.0005173   1.0000525   1.0001748  ##      y2~~y2      y3~~y3      y4~~y4      y5~~y5      y6~~y6      y7~~y7  ##   1.0000764   0.9998632   0.9993261   1.0009848   1.0000100   0.9997290  ##      y8~~y8        x1~1        x2~1        x3~1        y1~1        y2~1  ##   0.9994271   1.0014272   1.0021355   1.0011416   0.9997846   0.9991185  ##        y3~1        y4~1        y5~1        y6~1        y7~1        y8~1  ##   1.0000282   0.9994777   0.9996936   0.9999317   1.0000207   1.0010106 max(blavInspect(fit, \"psrf\")) ## [1] 1.002135 fit <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=1000, sample=1000)"},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_efficiency.html","id":"efficiency","dir":"Articles","previous_headings":"","what":"Efficiency","title":"Convergence and Efficiency Evaluation","text":"also evaluate efficiency posterior samples. Effective sample size (ESS) useful measure sampling efficiency, well defined even chains finite mean variance (Vehtari et al. 2021). short, posterior samples produced MCMC autocorrelated. means , draw 500 posterior samples, 500 independent pieces information posterior distribution, samples autocorlated. ESS metric like currency conversion, telling much autocorrelated samples worth convert indepndent samples. blavaan can print summary function neff argument can also extract blavInspect() function ESS sample size, least 100 (optimally, much 100) times number chains order reliable indicate estimates posterior quantiles reliable. example, 3 chains, want see least neff=300 every parameter. can easily find lowest ESS min() function:","code":"summary(fit, neff=T) blavInspect(fit, \"neff\") ##   ind60=~x1   ind60=~x2   ind60=~x3           a           b           c  ##   1711.6518   1532.0335   1674.0745   1799.7048   1930.9386   1970.0796  ##           d           a           b           c           d dem60~ind60  ##   1793.3665   1799.7048   1930.9386   1970.0796   1793.3665   2149.0144  ## dem65~ind60 dem65~dem60      y1~~y5      y2~~y4      y2~~y6      y3~~y7  ##   2653.6934   2917.5050   2035.4478   2029.8231   2743.6990   2234.4785  ##      y4~~y8      y6~~y8      x1~~x1      x2~~x2      x3~~x3      y1~~y1  ##   2247.6868   1536.2891   2283.6237   1706.3360   3142.0541   2339.8884  ##      y2~~y2      y3~~y3      y4~~y4      y5~~y5      y6~~y6      y7~~y7  ##   3118.2461   3354.9361   2151.5734   2200.5526   2416.0540   2375.5283  ##      y8~~y8        x1~1        x2~1        x3~1        y1~1        y2~1  ##   1942.8772    992.9440    879.9432   1134.9757   1171.0180   1592.1328  ##        y3~1        y4~1        y5~1        y6~1        y7~1        y8~1  ##   1393.5860   1165.4686   1071.9561   1059.1545   1121.8196    905.3216 min(blavInspect(fit, \"neff\")) ## [1] 879.9432"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_loop.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Convergence loop","text":"many cases need run BSEM models multiple times converged. can take might want R . tutorial shows use loop increase number burnin samples model converges, can let run without adjust every time","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_loop.html","id":"convergence-loop","dir":"Articles","previous_headings":"","what":"Convergence loop","title":"Convergence loop","text":"start writing model syntax always. instead running blavaan functions usual, run inside loop follows. loop starts need define starting BURN <- 0 number iterations, convergence value higher desired rhat <- 20. loop set sto stop convergence criteria (rhat) lower desired value, like \\(\\hat{R} < 1.05\\), specify (rhat > 1.05), meaning loop continue long rhat higher 1.05. Thn inside loop increase number BURN iterations 1000 example. estimating model, evaluate convergence getting highest estimated \\(\\hat{R}\\), printing screen see far model converging. Note increasing number burnin iterations, keeping number saved samples (1000 case). want can increase decrease number saved iterations according case. can visualize convergence trace plots","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  BURN <- 0 rhat <- 20 while(rhat > 1.05) {      BURN <- BURN + 1000 ### increase burn in by 1000 iterations every time      fit <- bcfa(HS.model, std.lv=T,                data=HolzingerSwineford1939,                n.chains = 3, burnin = BURN,               sample=1000)   rhat <- max(blavInspect(fit, \"psrf\"), na.rm=T)   print(paste0(\"Rhat=\",rhat))   } print(paste0(\"Rhat=\",rhat)) ## [1] \"Rhat=1.00224659247685\" plot(fit, pars = 1:9, plot.type = \"trace\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_loop.html","id":"convergence-criteria","dir":"Articles","previous_headings":"","what":"Convergence criteria","title":"Convergence loop","text":"example use \\(\\hat{R} < 1.05\\) convergence criteria. recommend use \\(\\hat{R} < 1.01\\) convergence criteria, higher. \\(\\hat{R}\\) approximates 1, can argue model converged estimates achieve stability within chains (Gelman et al. 2014)","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/cross_loadings_strong_priors.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Cross-loadings with strong priors","text":"advantage BSEM can use priors set soft constraints model, estimating parameter strong prior. way parameter estimated, prior restrict possible values. suggested Muthén Asparouhov (2012), way estimate possible cross-loadings CFA. way, posterior distribution restricted parameters includes values outside strong prior, can interpreted model modification. means parameters less restricted, prior distribution relaxed. tutorial present estimate CFA possible cross-loadings restricted strong priors.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/cross_loadings_strong_priors.html","id":"cross-loadings","dir":"Articles","previous_headings":"","what":"Cross-loadings","title":"Cross-loadings with strong priors","text":"show example Holzinger Swineford (1939) data. First estimate regular model cross-loadings default priors. can see overall model results summary() function, looking posterior distribution factor loadings, correlations, intercepts variances. Next, add possible cross-loadings strong prior \\(N(0, \\sigma = 0.08)\\). prior centers loadings around 0 allows little space move. can look summary() model evaluate cross-loadings. can specifically see whether cross-loadings seem large enough suggest kept model, looking posterior mean (Estimate) credible interval. suggest simply look whether CI excludes 0 (similar null hypothesis), evaluate whether minimum value CI (value closer 0) far enough away 0 relavant instead just different 0.","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit_df <- bcfa(HS.model, data=HolzingerSwineford1939,              std.lv=TRUE, meanstructure=T) summary(fit_df) ## blavaan 0.5.2.1189 ended normally after 1000 iterations ##  ##   Estimator                                      BAYES ##   Optimization method                             MCMC ##   Number of model parameters                        30 ##  ##   Number of observations                           301 ##  ##   Statistic                                 MargLogLik         PPP ##   Value                                      -3870.881       0.000 ##  ## Parameter Estimates: ##  ##  ## Latent Variables: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##   visual =~                                                                     ##     x1                0.912    0.089    0.738    1.088    1.000    normal(0,10) ##     x2                0.499    0.083    0.340    0.665    1.000    normal(0,10) ##     x3                0.660    0.082    0.499    0.819    1.001    normal(0,10) ##   textual =~                                                                    ##     x4                1.000    0.059    0.887    1.120    1.000    normal(0,10) ##     x5                1.114    0.064    0.991    1.244    1.000    normal(0,10) ##     x6                0.925    0.057    0.818    1.040    1.000    normal(0,10) ##   speed =~                                                                      ##     x7                0.617    0.077    0.457    0.765    1.002    normal(0,10) ##     x8                0.733    0.079    0.573    0.881    1.000    normal(0,10) ##     x9                0.680    0.079    0.537    0.836    1.002    normal(0,10) ##  ## Covariances: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##   visual ~~                                                                     ##     textual           0.448    0.066    0.308    0.569    1.000     lkj_corr(1) ##     speed             0.463    0.085    0.289    0.618    1.000     lkj_corr(1) ##   textual ~~                                                                    ##     speed             0.278    0.070    0.137    0.408    1.001     lkj_corr(1) ##  ## Intercepts: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##    .x1                4.935    0.068    4.797    5.068    1.001    normal(0,32) ##    .x2                6.088    0.066    5.959    6.216    1.001    normal(0,32) ##    .x3                2.250    0.068    2.115    2.383    1.001    normal(0,32) ##    .x4                3.060    0.067    2.930    3.192    1.001    normal(0,32) ##    .x5                4.340    0.077    4.193    4.489    1.000    normal(0,32) ##    .x6                2.185    0.065    2.062    2.316    1.000    normal(0,32) ##    .x7                4.187    0.063    4.066    4.309    1.001    normal(0,32) ##    .x8                5.526    0.059    5.411    5.642    1.001    normal(0,32) ##    .x9                5.373    0.058    5.257    5.487    1.000    normal(0,32) ##     visual            0.000                                                     ##     textual           0.000                                                     ##     speed             0.000                                                     ##  ## Variances: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##    .x1                0.548    0.130    0.266    0.794    1.000 gamma(1,.5)[sd] ##    .x2                1.155    0.110    0.954    1.388    1.000 gamma(1,.5)[sd] ##    .x3                0.859    0.099    0.673    1.051    1.000 gamma(1,.5)[sd] ##    .x4                0.378    0.050    0.286    0.481    0.999 gamma(1,.5)[sd] ##    .x5                0.456    0.060    0.345    0.581    1.000 gamma(1,.5)[sd] ##    .x6                0.363    0.045    0.282    0.456    1.000 gamma(1,.5)[sd] ##    .x7                0.822    0.092    0.659    1.017    1.001 gamma(1,.5)[sd] ##    .x8                0.501    0.093    0.327    0.685    1.000 gamma(1,.5)[sd] ##    .x9                0.569    0.093    0.378    0.745    1.002 gamma(1,.5)[sd] ##     visual            1.000                                                     ##     textual           1.000                                                     ##     speed             1.000 HS.model.cl<-' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9                     ## Cross-loadings               visual =~  prior(\"normal(0,.08)\")*x4 + prior(\"normal(0,.08)\")*x5 + prior(\"normal(0,.08)\")*x6 + prior(\"normal(0,.08)\")*x7 + prior(\"normal(0,.08)\")*x8 + prior(\"normal(0,.08)\")*x9               textual =~ prior(\"normal(0,.08)\")*x1 + prior(\"normal(0,.08)\")*x2 + prior(\"normal(0,.08)\")*x3 + prior(\"normal(0,.08)\")*x7 + prior(\"normal(0,.08)\")*x8 + prior(\"normal(0,.08)\")*x9                speed =~ prior(\"normal(0,.08)\")*x1 + prior(\"normal(0,.08)\")*x2 + prior(\"normal(0,.08)\")*x3 + prior(\"normal(0,.08)\")*x4 + prior(\"normal(0,.08)\")*x5 + prior(\"normal(0,.08)\")*x6'  fit_cl <- bcfa(HS.model.cl, data=HolzingerSwineford1939,              std.lv=TRUE, meanstructure=T) summary(fit_cl) ## blavaan 0.5.2.1189 ended normally after 1000 iterations ##  ##   Estimator                                      BAYES ##   Optimization method                             MCMC ##   Number of model parameters                        48 ##  ##   Number of observations                           301 ##  ##   Statistic                                 MargLogLik         PPP ##   Value                                      -3858.783       0.134 ##  ## Parameter Estimates: ##  ##  ## Latent Variables: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##   visual =~                                                                     ##     x1                0.761    0.099    0.574    0.959    1.001    normal(0,10) ##     x2                0.567    0.093    0.390    0.751    1.000    normal(0,10) ##     x3                0.769    0.097    0.586    0.964    1.000    normal(0,10) ##   textual =~                                                                    ##     x4                0.983    0.064    0.861    1.110    1.000    normal(0,10) ##     x5                1.155    0.071    1.014    1.298    1.000    normal(0,10) ##     x6                0.894    0.060    0.781    1.018    1.000    normal(0,10) ##   speed =~                                                                      ##     x7                0.728    0.086    0.554    0.892    1.003    normal(0,10) ##     x8                0.792    0.085    0.636    0.973    1.008    normal(0,10) ##     x9                0.542    0.076    0.394    0.695    1.004    normal(0,10) ##   visual =~                                                                     ##     x4                0.032    0.058   -0.080    0.148    0.999   normal(0,.08) ##     x5               -0.073    0.062   -0.193    0.050    0.999   normal(0,.08) ##     x6                0.063    0.055   -0.047    0.171    1.000   normal(0,.08) ##     x7               -0.130    0.065   -0.259   -0.004    1.003   normal(0,.08) ##     x8               -0.005    0.067   -0.138    0.124    0.999   normal(0,.08) ##     x9                0.193    0.060    0.075    0.309    1.000   normal(0,.08) ##   textual =~                                                                    ##     x1                0.111    0.065   -0.019    0.237    1.000   normal(0,.08) ##     x2                0.007    0.059   -0.110    0.130    0.999   normal(0,.08) ##     x3               -0.084    0.063   -0.212    0.037    1.000   normal(0,.08) ##     x7                0.015    0.062   -0.111    0.135    1.000   normal(0,.08) ##     x8               -0.039    0.062   -0.161    0.082    0.999   normal(0,.08) ##     x9                0.032    0.054   -0.077    0.135    1.000   normal(0,.08) ##   speed =~                                                                      ##     x1                0.042    0.065   -0.081    0.172    1.000   normal(0,.08) ##     x2               -0.048    0.063   -0.172    0.076    1.000   normal(0,.08) ##     x3                0.027    0.064   -0.097    0.149    1.000   normal(0,.08) ##     x4               -0.006    0.056   -0.116    0.104    1.001   normal(0,.08) ##     x5                0.005    0.061   -0.114    0.123    1.000   normal(0,.08) ##     x6               -0.001    0.053   -0.103    0.106    1.000   normal(0,.08) ##  ## Covariances: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##   visual ~~                                                                     ##     textual           0.374    0.095    0.186    0.549    1.000     lkj_corr(1) ##     speed             0.353    0.111    0.125    0.559    1.000     lkj_corr(1) ##   textual ~~                                                                    ##     speed             0.259    0.103    0.044    0.451    1.000     lkj_corr(1) ##  ## Intercepts: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##    .x1                4.937    0.068    4.804    5.070    0.999    normal(0,32) ##    .x2                6.087    0.066    5.961    6.213    0.999    normal(0,32) ##    .x3                2.251    0.067    2.119    2.385    1.000    normal(0,32) ##    .x4                3.063    0.066    2.931    3.191    1.000    normal(0,32) ##    .x5                4.342    0.074    4.193    4.481    1.000    normal(0,32) ##    .x6                2.188    0.063    2.061    2.307    0.999    normal(0,32) ##    .x7                4.187    0.064    4.060    4.312    1.000    normal(0,32) ##    .x8                5.529    0.060    5.410    5.649    0.999    normal(0,32) ##    .x9                5.374    0.060    5.257    5.492    1.000    normal(0,32) ##     visual            0.000                                                     ##     textual           0.000                                                     ##     speed             0.000                                                     ##  ## Variances: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##    .x1                0.677    0.107    0.457    0.885    1.001 gamma(1,.5)[sd] ##    .x2                1.090    0.107    0.897    1.307    1.000 gamma(1,.5)[sd] ##    .x3                0.718    0.114    0.497    0.938    1.000 gamma(1,.5)[sd] ##    .x4                0.388    0.051    0.289    0.490    0.999 gamma(1,.5)[sd] ##    .x5                0.411    0.065    0.291    0.543    1.000 gamma(1,.5)[sd] ##    .x6                0.372    0.044    0.290    0.461    0.999 gamma(1,.5)[sd] ##    .x7                0.714    0.099    0.524    0.914    1.002 gamma(1,.5)[sd] ##    .x8                0.434    0.100    0.218    0.609    1.015 gamma(1,.5)[sd] ##    .x9                0.589    0.067    0.461    0.726    1.003 gamma(1,.5)[sd] ##     visual            1.000                                                     ##     textual           1.000                                                     ##     speed             1.000"},{"path":"http://ecmerkle.github.io/blavaan/articles/cross_loadings_strong_priors.html","id":"caveats","dir":"Articles","previous_headings":"","what":"Caveats","title":"Cross-loadings with strong priors","text":"model possible cross-loadings kept final analysis model, used step make decisions model changes. two main reasons, (1) model overfitted present good overall fit just due inclusion lot nuisance parameters. example posterior predictive p-value goes ppp = 0 ppp = 0.134, model better theoretically inflating model fit. (2), addition small-variance priors can prevent detection important misspecifications Bayesian confirmatory factor analysis, can obscure underlying problems model diluting large number nuisance parameters (Jorgensen et al. 2019).","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/estimate.html","id":"primary-arguments","dir":"Articles","previous_headings":"","what":"Primary arguments","title":"Model Estimation","text":"Primary arguments model estimation commands include burnin, sample, n.chains, target. burnin sample arguments used specify desired number burn-iterations posterior samples n.chains chains (burnin argument controls warm-iterations Stan). target argument, hand, used specify MCMC strategy used estimation. default, target = \"stan\", tends fastest efficient. options slightly flexible, including target = \"stanclassic\" target = \"jags\". approaches sample latent variables model parameters, whereas target = \"stan\" marginalizes latent variables. detail approaches, see JSS paper.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/estimate.html","id":"secondary-arguments","dir":"Articles","previous_headings":"","what":"Secondary arguments","title":"Model Estimation","text":"Noteworthy secondary arguments include save.lvs, mcmcfile, mcmcextra, inits. save.lvs argument controls whether latent variables sampled model estimation. defaults FALSE latent variable sampling can take large amount memory, can slow post-estimation summaries. setting save.lvs = TRUE allows model summaries latent variables observed variable predictions using blavPredict() functions. setting mcmcfile = TRUE, users can obtain Stan (JAGS) code data specified model. files written lavExport folder within user’s working directory. One file extension .jag .stan, second file R data file (extension .rda). rda file can loaded R (via load()) list including elements data, monitors, inits. elements can supplied stan() model estimation outside blavaan. mcmcextra argument used supply extra information Stan JAGS. Users can supply list element names monitor, data, syntax, llnsamp. elements respectively used specify extra parameters monitor, extra data pass model estimation, extra syntax include model file (JAGS ), number importance samples likelihood approximation (relevant models ordinal variables). inits argument used control starting values MCMC estimation. can sometimes salvage model immediately crashes. default, inits = \"simple\", initializes model parameters 0 1 fashion similar lavaan’s use argument. second option, inits = \"prior\", draws initial values prior distributions. user can also specify list initial values via argument, though required list format somewhat cumbersome. recommend exporting model data using mcmcfile = TRUE, loading resulting rda file, looking format initial values blavaan created .","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/estimate.html","id":"parallelization","dir":"Articles","previous_headings":"","what":"Parallelization","title":"Model Estimation","text":"Speed always issue sample via MCMC, especially using software like Stan JAGS. computers multiple cores, estimation can sped sending MCMC chain separate core. accomplished bcontrol argument, list whose elements correspond stan() run.jags() arguments. parallelizing chains Stan, want use argument bcontrol = list(cores = 3). Many arguments available control aspects estimation; see ?stan ?run.jags possibilities. Parallelization can also helpful speed post-estimation computations. future package controls parallelization, requires extra command prior estimation. common commands ","code":"library(\"future\") plan(\"multicore\") ## mac or linux plan(\"multisession\") ## windows"},{"path":"http://ecmerkle.github.io/blavaan/articles/invariance.html","id":"model-estimation","dir":"Articles","previous_headings":"","what":"Model Estimation","title":"Measurement Invariance","text":"Consider measurement invariance study Holzinger Swineford (1939) data. lavaan, may first estimate two models: examine absolute fit fit1. also compare fit2 fit1 via Likelihood Ratio Test. Instead , wish something similar via Bayesian methods. accomplish via blavaan, can fit Bayesian versions fit1 fit2 using similar syntax. Model fit comparison statistics available via fitMeasures() blavCompare() functions:","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit1 <- cfa(HS.model, data = HolzingerSwineford1939, group = \"school\")  fit2 <- cfa(HS.model, data = HolzingerSwineford1939, group = \"school\",             group.equal = \"loadings\") bfit1 <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\")  bfit2 <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\",                group.equal = \"loadings\") fitMeasures(bfit1)  fitMeasures(bfit2)  blavCompare(bfit1, bfit2)"},{"path":"http://ecmerkle.github.io/blavaan/articles/invariance.html","id":"approximate-invariance","dir":"Articles","previous_headings":"","what":"Approximate Invariance","title":"Measurement Invariance","text":"approximate measurement invariance studies, replace hard equality constraints soft constraints using informative prior distributions. wiggle argument can used invoke types constraints. example: constrains loadings associated x2 x3 approximately equal across groups, informative priors associated constraints normal standard deviations 0.05. Using strategy, syntax can become cumbersome. many cases, group.equal argument can help . example: example, model intercepts loadings across-group constraints. loadings approximately equal across groups, due argument wiggle = \"loadings\". intercepts constrained exactly equal across groups. way, becomes easy use exact approximate equality constraints model, desired.","code":"HS.model <- ' visual  =~ x1 + c(\"a\", \"a\")*x2 + c(\"b\", \"b\")*x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  bfit3 <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\", wiggle = c(\"a\", \"b\"),               wiggle.sd = 0.05) HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '       bfit4 <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\",               group.equal = c(\"intercepts\", \"loadings\"), wiggle = \"loadings\",               wiggle.sd = 0.05)"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/mod_indices.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Modification indices","text":"SEM, one first steps evaluate model’s global fit. global fit, need evaluate local fit model, meaning model reproduces specific correlations observed variables. couple common methods , () testing high residual correlations, (b) modification indices. tutorial focuses second. Modification indices test likely change model fit single parameter added model originally included. test can carried every possible parameter included (Bentler 1990).","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/mod_indices.html","id":"modification-indices","dir":"Articles","previous_headings":"","what":"Modification Indices","title":"Modification indices","text":"Modification indices present different indices quantify effect parameter, focus two . () modification index (MI) Lagrange multiplier, estimates extent model’s chi-square (\\(\\chi^2\\)) test statistic decrease parameter added model freely estimated, (b) standardized expected parameter change (SEPC), approximated standardized value parameter estimated model (Whittaker 2012). MI presents possible effect overall model, SEPC presents effect size missed parameter. show example Holzinger Swineford (1939) model. first estimate SEM/CFA model usual need write discrepancy function collect modification indices. list contains two functions estimate save MI SEPC. pass function ppmc() function blavaan. function, MI SEPC computed posterior sample, leading posterior distributions . view top 5 parameters arrange posterior mean (EAP) MI, case shows parameter highest impact overall model fit (according EAP) visual=~x9, cross-loading Visual factor item x9. according posterior median, parameter highest impact residual correlation indicators x7 x8 MI still recommended best metric indicate parameter best include next, can use SEPC evaluate likely effect size respective parameters. see 2 highest parameters, likely SEPC x7~~x8 = 0.799229902211115 visual=~x9 = 0.518551878229323. information can decide include one new parameters model (one time). example, factor loadings larger impact model-implied covariance matrix, choose visual=~x9 can check added parameter expected impact overall fit blavFitIndices() summary() functions. important consider also theoretical relevance suggested parameters, ensure make sense, instead just adding parameters good fit.","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939, std.lv=TRUE) discFUN <- list(   mod.ind_mi = function(object){     temp <- modificationindices(object, free.remove = F)     mods <- temp$mi     names(mods) <- paste0(temp$lhs, temp$op, temp$rhs)     return(mods)   },   mod.ind_sepc.all = function(object){     temp <- modificationindices(object, free.remove = F)     sepc.all <- temp$sepc.all     names(sepc.all) <- paste0(temp$lhs, temp$op, temp$rhs)     return(sepc.all)   } ) out <- ppmc(fit, discFUN = discFUN) summary(out, prob=.9, discFUN = \"mod.ind_mi\", sort.by=\"EAP\", decreasing=T)[1:5,] ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for the posterior distribution of realized discrepancy-function values based on observed data, along with posterior predictive p values to test hypotheses in either direction: ##  ##  ##               EAP Median    MAP     SD  lower  upper PPP_sim_GreaterThan_obs ## visual=~x9 35.353 35.458 35.495 10.624 17.727 52.239                   0.012 ## x7~~x8     32.891 35.539 39.626 14.716  4.604 52.733                   0.083 ## x8~~x9     27.117 12.160  2.726 42.978  0.000 70.495                   0.321 ## x4~~x6     19.784  7.015  1.388 36.713  0.000 52.503                   0.467 ## visual=~x7 18.162 16.144 12.432  9.849  4.183 33.098                   0.016 ##            PPP_sim_LessThan_obs ## visual=~x9                0.988 ## x7~~x8                    0.917 ## x8~~x9                    0.679 ## x4~~x6                    0.533 ## visual=~x7                0.984 summary(out, prob=.9, discFUN = \"mod.ind_mi\", sort.by=\"Median\", decreasing=T)[1:5,] ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for the posterior distribution of realized discrepancy-function values based on observed data, along with posterior predictive p values to test hypotheses in either direction: ##  ##  ##                EAP Median    MAP     SD  lower  upper PPP_sim_GreaterThan_obs ## x7~~x8      32.891 35.539 39.626 14.716  4.604 52.733                   0.083 ## visual=~x9  35.353 35.458 35.495 10.624 17.727 52.239                   0.012 ## visual=~x7  18.162 16.144 12.432  9.849  4.183 33.098                   0.016 ## x8~~x9      27.117 12.160  2.726 42.978  0.000 70.495                   0.321 ## textual=~x1 11.011  9.976  5.705  8.318  0.000 22.179                   0.220 ##             PPP_sim_LessThan_obs ## x7~~x8                     0.917 ## visual=~x9                 0.988 ## visual=~x7                 0.984 ## x8~~x9                     0.679 ## textual=~x1                0.780 summary(out, prob=.9, discFUN = \"mod.ind_sepc.all\", sort.by=\"EAP\", decreasing=T)[1:5,] ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for the posterior distribution of realized discrepancy-function values based on observed data, along with posterior predictive p values to test hypotheses in either direction: ##  ##  ##               EAP Median   MAP    SD lower upper PPP_sim_GreaterThan_obs ## x7~~x8      0.799  0.790 0.742 0.383 0.487 1.274                   0.049 ## visual=~x9  0.519  0.494 0.466 0.132 0.334 0.688                   0.006 ## textual=~x1 0.272  0.298 0.314 0.175 0.036 0.513                   0.132 ## x1~~x9      0.247  0.247 0.248 0.037 0.198 0.299                   0.017 ## x2~~x3      0.223  0.223 0.219 0.037 0.171 0.282                   0.021 ##             PPP_sim_LessThan_obs ## x7~~x8                     0.951 ## visual=~x9                 0.994 ## textual=~x1                0.868 ## x1~~x9                     0.983 ## x2~~x3                     0.979 HS.model <- ' visual  =~ x1 + x2 + x3 + x9               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit2 <- bcfa(HS.model, data=HolzingerSwineford1939, std.lv=TRUE)"},{"path":"http://ecmerkle.github.io/blavaan/articles/mod_indices.html","id":"summary","dir":"Articles","previous_headings":"","what":"Summary","title":"Modification indices","text":"tutorial show calculate MI SEPC across posterior distributions, evaluate parameters can added. ppmc() function able calculate relevant information model estimation, build posterior distributions . general recommendations use MI identify likely parameter add, SEPC effect size new parameter.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Model Comparison","text":"traditional method model comparison frequentist SEM (fSEM) \\(\\chi^2\\) (Likelihood Ratio Test) variations. BSEM, take Bayesian model comparison methods, apply SEM. Specifically, focus two information criteria, (1) Widely Applicable Information Criterion (WAIC), (2) Leave-One-cross-validation (LOO). methods intend evaluate --sample predictive accuracy models, compare performance. ability predict datapoint hasn’t used training model (McElreath 2020) example use Industrialization Political Democracy example (Bollen 1989).","code":"model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit1 <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000)"},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"widely-applicable-information-criterion","dir":"Articles","previous_headings":"","what":"Widely Applicable Information Criterion","title":"Model Comparison","text":"WAIC (Watanabe 2010) can seen fully Bayesian generalization Akaike Information Criteria (AIC), measure uncertainty/information model prediction row data across posterior draws. Log-Pointwise-Predictive-Density (lppd). WAIC defined \\[\\begin{equation} WAIC= -2lppd + 2efp_{WAIC}, \\end{equation}\\] first term involves log-likelihoods observed data (marginal latent variables) second term effective number parameters. first term, \\(lppd\\), estimated : \\[\\begin{equation} \\widehat{lppd} = \\sum^{n}_{= 1} log \\Bigg(\\frac{1}{S}\\sum^{S}_{S=1}f(y_{}|\\theta^{S}) \\Bigg) \\end{equation}\\] \\(S\\) number posterior draws \\(f(y_{}|\\theta^{S})\\) density observation \\(\\) respect parameter sampled iteration \\(s\\). effective number parameter (\\(efp_{WAIC}\\)) calculated : \\[\\begin{equation}\\label{eq:efpWAIC} efp_{WAIC} = \\sum^n_{=1}var_{s}(logf(y_{}|\\theta)) \\end{equation}\\] separate variance estimated observation \\(\\) across \\(S\\) posterior draws.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"leave-one-out-cross-validation","dir":"Articles","previous_headings":"","what":"Leave-One-Out cross-validation","title":"Model Comparison","text":"LOO measures predictive density observation holding one observation time use rest observations update prior. estimation calculated via (Vehtari, Gelman, Gabry 2017): \\[\\begin{equation}     LOO = -2\\sum_{=1}^{n} log \\Bigg(\\frac{\\sum^{S}_{s =1} w^{s}_{}f(y_{}|\\theta^{s})}{\\sum^{s}_{s=1} w^{s}_{}}\\Bigg) \\end{equation}\\] \\(w^s_{}\\) Pareto-smoothed sampling weights based relative magnitude individual \\(\\) density function across \\(S\\) posterior samples. LOO effective number parameters involves \\(lppd\\) term WAIC: \\[\\begin{equation}     efp_{LOO} = lppd + LOO/2 \\end{equation}\\]","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"model-comparison","dir":"Articles","previous_headings":"","what":"Model comparison","title":"Model Comparison","text":"WAIC LOO approximate models’ performance across posterior draws, able calculate standard error model comparisons involving . model differences estimate differences across Expected Log-Pointwise-Predictive-Density (elpd), standard error respective difference. clear cutoff rules interpret present comparisons, researchers need use expert knowledge part decision process. best recommendation present differences elpd \\(\\Delta elpd\\), standard error, ratio . ratio least 2 can consider evidence differences models, ratio 4 considered stronger evidence. first example, compare standard political democracy model, model factor regressions fixed 0. 2 models, can compare blavCompare looking comparison object, can see WAIC, LOO, estimates, respective differences . information criteria, best model one lowest value case can see model 1 lower LOOIC, ratio shows LOO differences 5 SE magnitude. indicates model estimated regressions better Now, lets look example smaller difference models, smallest regression (dem65~ind60) fixed 0. see LOOIC, see difference two models minimal, ratio 0.21. indicates models functionally equivalent. case like , researchers decide model better representation, theoretically stronger. Lets one last model, largest regression (dem65~dem60) fixed 0. case, looking LOOIC, see model one better (lower value), ratio difference shows model 5 SE magnitude. Indicating evidence model predictive differences","code":"model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ 0*ind60     dem65 ~ 0*ind60 + 0*dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit2 <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000) bc12 <- blavCompare(fit1, fit2) bc12 ## $bf ##   bf mll1 mll2  ##   NA   NA   NA  ##  ## $loo ## $loo[[1]] ##             Estimate       SE ## elpd_loo -1606.70149 19.54461 ## p_loo       38.39532  3.01202 ## looic     3213.40298 39.08921 ##  ## $loo[[2]] ##             Estimate        SE ## elpd_loo -1647.03938 18.862661 ## p_loo       34.70032  2.714831 ## looic     3294.07877 37.725323 ##  ##  ## $diff_loo ##  elpd_diff    se_diff  ## -40.337894   7.985821  ##  ## $waic ## $waic[[1]] ##              Estimate        SE ## elpd_waic -1606.36062 19.504892 ## p_waic       38.05445  2.953732 ## waic       3212.72124 39.009784 ##  ## $waic[[2]] ##              Estimate        SE ## elpd_waic -1646.76532 18.829025 ## p_waic       34.42626  2.673588 ## waic       3293.53065 37.658049 ##  ##  ## $diff_waic ##  elpd_diff    se_diff  ## -40.404702   7.965641 abs(bc12$diff_loo[1] / bc12$diff_loo[2]) ## elpd_diff  ##  5.051189 model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ 0*ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit3 <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000) bc13 <- blavCompare(fit1, fit3) bc13 ## $bf ##   bf mll1 mll2  ##   NA   NA   NA  ##  ## $loo ## $loo[[1]] ##             Estimate       SE ## elpd_loo -1606.70149 19.54461 ## p_loo       38.39532  3.01202 ## looic     3213.40298 39.08921 ##  ## $loo[[2]] ##             Estimate       SE ## elpd_loo -1606.66331 19.44934 ## p_loo       37.43281  2.91784 ## looic     3213.32661 38.89868 ##  ##  ## $diff_loo ##   elpd_diff     se_diff  ## -0.03818196  0.92891040  ##  ## $waic ## $waic[[1]] ##              Estimate        SE ## elpd_waic -1606.36062 19.504892 ## p_waic       38.05445  2.953732 ## waic       3212.72124 39.009784 ##  ## $waic[[2]] ##              Estimate       SE ## elpd_waic -1606.19859 19.38086 ## p_waic       36.96809  2.82711 ## waic       3212.39717 38.76172 ##  ##  ## $diff_waic ##  elpd_diff    se_diff  ## -0.1620357  0.9355731 abs(bc13$diff_loo[1] / bc13$diff_loo[2]) ##  elpd_diff  ## 0.04110403 model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + 0*dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit4 <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000) bc14 <- blavCompare(fit1, fit4) bc14 ## $bf ##   bf mll1 mll2  ##   NA   NA   NA  ##  ## $loo ## $loo[[1]] ##             Estimate       SE ## elpd_loo -1606.70149 19.54461 ## p_loo       38.39532  3.01202 ## looic     3213.40298 39.08921 ##  ## $loo[[2]] ##             Estimate        SE ## elpd_loo -1629.27107 19.863567 ## p_loo       37.79969  2.966613 ## looic     3258.54214 39.727133 ##  ##  ## $diff_loo ##  elpd_diff    se_diff  ## -22.569579   4.066783  ##  ## $waic ## $waic[[1]] ##              Estimate        SE ## elpd_waic -1606.36062 19.504892 ## p_waic       38.05445  2.953732 ## waic       3212.72124 39.009784 ##  ## $waic[[2]] ##              Estimate        SE ## elpd_waic -1629.01215 19.843132 ## p_waic       37.54077  2.938398 ## waic       3258.02429 39.686264 ##  ##  ## $diff_waic ##  elpd_diff    se_diff  ## -22.651524   4.062466 abs(bc14$diff_loo[1] / bc14$diff_loo[2]) ## elpd_diff  ##  5.549737"},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"bayes-factor","dir":"Articles","previous_headings":"","what":"Bayes factor","title":"Model Comparison","text":"Bayesian literature use Bayes factor (BF) compare models. number criticisms related use BF BSEM, including (1) BF unstable large models (like SEMs), (2) highly sensitive model priors, (3) requires strong priors stable estimation , (4) can require large number posterior draws, (5) estimation using marginal likelihood ignores lot information posterior distributions. details discussion please see Tendeiro Kiers (2019) Schad et al. (2022). criticisms lead us recommend use BF everyday BSEM estimation. researchers commit prior distributions commit exploring noise computations, BF can used describe relative odds one model another, intuitive model comparison metrics.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"summary","dir":"Articles","previous_headings":"","what":"Summary","title":"Model Comparison","text":"recommend use LOO WAIC general model comparison metrics BSEM. allow us estimate models’ --sample predictive accuracies, respective differences across posterior draws. also provide us uncertainty estimates comparison. cases LOO WAIC lead similar results, LOO recommended stable metric (Vehtari, Gelman, Gabry 2017). general, \\(\\Delta elpd\\) least 2 standard errors preferably 4 standard errors can interpreted evidence differential predictive accuracy.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/multilevel.html","id":"blavaan-coverage","dir":"Articles","previous_headings":"","what":"blavaan Coverage","title":"Two-level SEM","text":"version 0.5-1, blavaan handles two-level, random intercept models complete, continuous data. Handling missing data (assuming missingness random) come future release. meantime, multiple imputation might used combination current blavaan functionality (though currently automatic way ). Alternatively, much missing data occurs lower-level units, listwise deletion work. blavaan approach model estimation mimics lavaan approach, uses matrix results (see Rosseel 2021) enable us efficiently evaluate multilevel SEM likelihood. often lead efficient MCMC estimation, compared sampling level 1 level 2 latent variables working conditional likelihoods (see Merkle et al. 2021 discussion marginal vs conditional likelihoods). Similar single-level models, users can sample latent variables using save.lvs = TRUE argument bcfa/bsem/bgrowth/blavaan commands. Marginal information criteria (marginal latent variables) also automatically computed, information criteria generally preferred condition latent variables (see Merkle, Furr, Rabe-Hesketh 2019 detail context single-level models).","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/multilevel.html","id":"bayes-specific-options","dir":"Articles","previous_headings":"","what":"Bayes-specific Options","title":"Two-level SEM","text":"Bayesian models require prior distributions. previous blavaan defaults single-level models now used two-level models. can continue use commands like dpriors(lambda = \"normal(1,.5)\") specify Normal(1,.5) prior factor loadings , two-level models, specification apply level 1 level 2 loadings. Depending model, may also useful specify priors individual parameters via prior() argument inside model specification syntax. default prior distributions always work well observed variables whose values far 0. continue encourage users consider prior distributions, possibly using prisamp = TRUE option draw samples prior (used prior predictive checking). Model checking also differs Bayesian frequentist methods. Just like one-level models, blavaan reports posterior predictive p-value general model assessment. computed comparing marginal likelihood observed data (marginal latent variables) marginal likelihood artificial data, iteration MCMC sampling. finer-grained model assessment, encourage users try ppmc(). allows compute posterior predictive p-value using , custom model assessment (defined R function).","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/multilevel.html","id":"concluding-thoughts","dir":"Articles","previous_headings":"","what":"Concluding Thoughts","title":"Two-level SEM","text":"think new blavaan functionality provides viable option Bayesian two-level SEM, provide solid base future model developments. always, underlying Stan files supporting data available via mcmcfile = TRUE argument, blavaan code available Github. Bug reports appreciated, either blavaan Google group Github issue.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Ordinal Models in blavaan","text":"Structural equation models ordinal observed variables supported starting blavaan 0.4-1 (target=\"stan\" ). document describes overall approach, includes model estimation, threshold parameters, log-likelihood calculation, posterior predictive p-values, Jacobians. assume somewhat familiar layout SEM; , technical detail examples found Merkle Rosseel (2018) , recently, Merkle et al. (2021) (links papers references section). aim provide enough detail elucidate new blavaan features, informal enough get () bored.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"estimation","dir":"Articles","previous_headings":"","what":"Estimation","title":"Ordinal Models in blavaan","text":"Ordinal observed variables handled via data augmentation, style Chib Greenberg (1998). might already know , phrase data augmentation imprecise context SEM. many possible things augmented, can make model estimation easier. augmenting observed data predictions missing data, related multiple imputation methods. augmenting observed data latent variables, can simplify likelihood calculation (leading sometimes called conditional likelihood, though conditional also many meanings). augmenting categorical observed variables underlying, latent continuous variables. last type augmentation . testing, found faster efficient approaches sample latent variables alongside model parameters (latent variables integrated likelihoods ; similar description Merkle et al. (2021)). data augmentation implementation, ordinal observation (e.g., \\(y\\)) used generate continuous, underlying counterpart (e.g., \\(y^\\ast\\)). \\(y^\\ast\\) must obey model’s threshold parameters (commonly denoted \\(\\mathbf{\\tau}\\)), based value observed data. example, ignoring subscripts \\(y^\\ast\\) assuming ordinal variable 4 categories, \\[\\begin{align*} y^* < \\tau_1 &\\text{ }y = 1 \\\\ \\tau_1 <\\ y^* < \\tau_2 &\\text{ }y = 2 \\\\ \\tau_2 <\\ y^* < \\tau_3 &\\text{ }y = 3 \\\\ y^* >\\ \\tau_3 &\\text{ }y = 4 \\end{align*}\\] require \\(\\tau_1 < \\tau_2 < \\tau_3\\). generate \\(y^*\\) separately ordinal observation dataset. become additional, bounded parameters Stan file. Stan User’s Guide helpful example multivariate probit regression using related approach; see https://mc-stan.org/docs/2_27/stan-users-guide/multivariate-outcomes.html. trickiest parts involve enforcing boundaries \\(y^*\\) variables, ensuring threshold parameters ordinal variable ordered correctly (allowing possibility different ordinal variables different numbers thresholds). require Jacobian adjustments took good deal time code correctly (detail appears later section). parameters defined generated, remainder model estimation similar simpler situation observed variables continuous. terms Stan file, ordinal overhead comes transformed parameters block. get model block, things operate continuous data.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"thresholds-priors","dir":"Articles","previous_headings":"","what":"Thresholds & Priors","title":"Ordinal Models in blavaan","text":"prior distributions threshold (\\(\\tau\\)) parameters involved may appear. , described previous section, threshold parameters single variable must ordered. say, example, thresholds normal(0,1) prior distribution, ignoring fact one threshold’s value influences size thresholds’ values. Michael Betancourt describes Stan Discourse, prior “interacts (ordering) constraint enforce sort uniform repulsion interior points, resulting rigid differences.” quote https://discourse.mc-stan.org/t/prior-choice--ordered-inverse-transformed-parameters/16378/3 address issue, first define unconstrained, unordered parameter vector whose length equals number thresholds model. Call vector \\(\\mathbf{\\tau}^*\\). obtain ordered thresholds exponentiating unordered parameter vector specific manner. manner works exactly Stan defines parameter type ordered. See https://mc-stan.org/docs/2_28/reference-manual/ordered-vector.html. Additionally, similar idea independently developed signal detection models Paulewicz Blaut (2020) (see bhsdtr package). idea easily shown via example. Say ordinal variable 4 categories. three thresholds variable obtained via: \\[\\begin{align*} \\tau_1 &= \\tau^*_1 \\\\ \\tau_2 &= \\tau^*_1 + \\exp(\\tau^*_2) \\\\ \\tau_3 &= \\tau^*_1 + \\exp(\\tau^*_2) + \\exp(\\tau^*_3). \\end{align*}\\] place normal prior distributions unordered \\(\\tau^*\\) parameters, opposed placing priors ordered \\(\\tau\\) parameters. normal priors imply lowest threshold (\\(\\tau_1\\) ) normal prior, differences successive \\(\\tau\\)’s log-normal priors. blavaan, priors can specified usual two ways. First, add dp argument model estimation command follows. assign prior unordered \\(\\tau^*\\) parameters model. Second, specify priors specific threshold parameters model specification syntax. example, say 4-category observed variable called x1. unique priors three thresholds specified model syntax via clear time priors \\(\\tau^*\\) parameters best option. 2019 paper, Michael Betancourt describes Dirichlet prior regularizes thresholds ordinal regression model. strategy seem work SEM, especially useful datasets categories ordinal variable sparse. issues warrant study. https://betanalpha.github.io/assets/case_studies/ordinal_regression.html","code":"dp = dpriors(tau = \"normal(0, .5)\") x1 | prior(\"normal(-1, 1)\") * t1 + prior(\"normal(0, .5)\") * t2 + prior(\"normal(0, 1)\") * t3"},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"likelihood-computations","dir":"Articles","previous_headings":"","what":"Likelihood Computations","title":"Ordinal Models in blavaan","text":"get continuous data model block, seems reasonable expect simple likelihood computations. depends likelihood want compute. likelihood used sampling Stan simple multivariate normal \\(y^*\\) observations, combined continuous observed variables model. indeed simple compute. likelihood want use model comparison. one thing, \\(y^*\\) parameters associated ordinal data involved likelihood, quantities like effective number parameters become inflated. number parameters involved likelihood also increases sample size, generally bad land model comparison metrics. See Merkle, Furr, Rabe-Hesketh (2019) detail . means , quantities like WAIC PSIS-LOO, must compute second model likelihood involves observed, ordinal \\(y\\) variables integrates latent \\(y^*\\) variables. difficult problem amounts evaluating CDF sometimes-high-dimensional, multivariate normal distribution (see Chib Greenberg 1998, Equation 11). multiple possibilities approximating CDF. currently rely sadmvn() function mnormt package (Azzalini Genz 2020), uses subregion adaptive integration method Genz (1992) fast accurate (15 fewer ordinal variables model). second possibility involves Monte Carlo simulation, implemented tmvnsim package (Bhattacjarjee 2016). case, generate many random samples appropriate truncated multivariate normal average resulting importance sampling weights. procedure computationally intensive also time intensive, balance number random samples drawn amount time takes. users wish use tmvnsim(), must declare number importance samples draw. accomplished setting llnsamp within mcmcextra$data argument. example, draw 100 samples approximation, call bsem() similar functions include argument Beyond two methods, also possible use quadrature latent variables. Many people consider quadrature gold standard , quadrature reduce dimension integration many models (usually fewer latent variables observed variables). quadrature specific SEM, fast, efficient, open implementations method appear currently exist (implementations hidden blavaan, pure R implementations fairly slow). hand, approximation multivariate normal CDF general problem multiple fast, efficient, open implementations, long many ordinal variables model. also exists relatively new method Z. . Botev (2017) evaluating CDF multivariate normal, implementation method appearing package TruncatedNormal (Z. Botev Belzile 2021). method especially useful evaluating high-dimensional normal distributions (case, 15 ordinal variables), may incorporated future versions blavaan.","code":"mcmcextra = list(data = list(llnsamp = 100))"},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"comparison-to-lavaan","dir":"Articles","previous_headings":"","what":"Comparison to lavaan","title":"Ordinal Models in blavaan","text":"Ordinal SEM associated two types model parameterizations: delta theta. refer different scale parameterizations \\(y^*\\) variables: delta refers total standard deviation \\(y^*\\) (including variability due latent variables), theta refers residual standard deviation \\(y^*\\). blavaan, theta parameterization implemented. , want compare lavaan results blavaan results, need use argument parameterization = \"theta\" estimate lavaan model. Also, default lavaan estimator ordinal models multiple-step procedure involves weighted least squares discrepancy function. resulting parameter estimates sometimes far posterior means reported blavaan. blavaan estimates usually closer estimator=\"PML\" lavaan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"posterior-predictive-p-values","dir":"Articles","previous_headings":"","what":"Posterior Predictive p-values","title":"Ordinal Models in blavaan","text":"Posterior predictive p-value (ppp) computations receive speed boost 0.4 series. computations now occur Stan, whereas previously occurred R model estimation. discussed Asparouhov Muthén (2021), ppp computations needed models missing data can excessively slow, requiring us run EM algorithm posterior sample order find “H1” (“saturated”) model covariance matrix. solution Asparouhov Muthén (2021) involves realization need use fully-optimized H1 covariance matrix order compute ppp. blavaan, consequently run EM algorithm fixed number iterations order compute H1 covariance matrix “good enough” ppp. default number iterations set 20, users can change default supplying emiter value via mcmcextra argument. example,","code":"mcmcextra = list(data = list(emiter = 50))"},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"jacobians","dir":"Articles","previous_headings":"","what":"Jacobians","title":"Ordinal Models in blavaan","text":"(section likely relevant editing/writing Stan models.) Stan model underlying blavaan currently requires Jacobian adjustments two places. section briefly reviews ideas underneath adjustments, future self may wish remember. need Jacobian adjustment place prior something appear Stan parameters block. Jacobian tells us implied priors things parameters block, based priors appear model block. Jacobian comes statistics literature “change variables”: applying function random variables, finding distribution function based original distribution random variables. comes Stan models, means starting priors model block finding implied priors parameters block. confused long time , Stan file, functions naturally go opposite direction: starting parameters block, moving model block. fact functions go model parameters convenient, though, Jacobian adjustments require inverse functions. inverse functions move us parameters model, already exist Stan model. just need find appropriate derivatives functions, lead Jacobian. example, consider fact blavaan allows users choose whether priors go standard deviation, variance, precision parameters. standard deviations appear parameters block regardless user chooses (Stan model precompiled time package installation). Say user wants priors precisions. transform standard deviations precisions model block, put prior precision. addition prior, need Jacobian function starts standard deviation (call \\(\\sigma\\)) transforms precision (\\(\\sigma^{-2}\\)). derivative \\(\\sigma^{-2}\\) respect \\(\\sigma\\) \\(-2 \\sigma^{-3}\\). simple function mapping single parameter different value, Jacobian absolute value derivative, \\(2 \\sigma^{-3}\\). Stan file, add log Jacobian target: examples discussion can found : https://mc-stan.org/users/documentation/case-studies/mle-params.html","code":"target += log(2) - 3*log(sigma)"},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"summary","dir":"Articles","previous_headings":"","what":"Summary","title":"Ordinal Models in blavaan","text":"blavaan 0.4 series offers enhanced functionality variety areas. computational decisions made reflect balance estimation precision estimation speed. case software defaults behave poorly situations. example, default prior distributions can problematic certain situations, likelihood approximations ordinal models may precise desired, new ppp computations may behave differently previous computations. encourage users carry sensitivity analyses, also report bugs!","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/plotting.html","id":"basics","dir":"Articles","previous_headings":"","what":"Basics","title":"Plot Functionality","text":"many blavaan models many parameters, users generally need specify parameters wish plot. accomplished supplying numbers pars argument, numbers correspond order parameters coef() command (numbers also appear free column parameter table). Users must also specify type plot desire via plot.type argument. , example, trace plot first four model parameters looks like  Many plot types available, coming bayesplot package. general, bayesplot functions begin mcmc_, corresponding plot.type remainder function name without leading mcmc_. Examples many plots can found bayesplot vignette.","code":"plot(fit, pars = 1:4, plot.type = \"trace\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/plotting.html","id":"customization","dir":"Articles","previous_headings":"","what":"Customization","title":"Plot Functionality","text":"Users may wish customize aspects resulting plots. , plot() function output ggplot object. makes possible modify plot ggplot object, allows many possibilities. One starting point exploring ggplot2 .  Alternatively, users may wish create plot entirely different available via plot(). can facilitated extracting posterior samples Stan model, via blavInspect():","code":"p <- plot(fit, pars = 1:4, plot.type = \"trace\", showplot = FALSE)  p + facet_text(size=15) + legend_none() ## list of draws ## (one list entry per chain): draws <- blavInspect(fit, \"mcmc\")  ## convert the list to a matrix ## (each row is a sample, ##  each column is a parameter) draws <- do.call(\"rbind\", draws)  ## Stan (or JAGS) model modobj <- blavInspect(fit, \"mcobj\")"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/prior.html","id":"defaults","dir":"Articles","previous_headings":"","what":"Defaults","title":"Specifying Prior Distributions","text":"default priors can seen via important note prior distributions correspond Stan parameterizations. similar R parameterizations necessarily exactly . Greek(ish) names correspond following parameter types (MV manifest/observed variable LV latent variable): information priors thresholds, see ordinal modeling details. target = \"stan\" (default), priors currently restricted one distribution per parameter type. can change prior distribution parameters (example, mean standard deviation normal), change prior distribution type. exceptions “theta” “psi” parameters: , can use modifiers “[sd]”, “[var]”, “[prec]” specify whether want priors apply standard deviation, variance, precision. require flexibility prior specification, change target either \"stanclassic\" (old Stan approach) \"jags\" (JAGS approach). Alternatively, can export Stan model via mcmcfile = TRUE, edit file needed, fit via rstan package. modify prior distributions, simply supply new text string dpriors() like : default prior loadings now normal mean 1 standard deviation 2, rest parameters remain original defaults. next time estimate model (via bsem(), bcfa(), bgrowth(), blavaan()), add argument dp=mydp use new set default priors.","code":"dpriors() ##                nu             alpha            lambda              beta  ##    \"normal(0,32)\"    \"normal(0,10)\"    \"normal(0,10)\"    \"normal(0,10)\"  ##             theta               psi               rho             ibpsi  ## \"gamma(1,.5)[sd]\" \"gamma(1,.5)[sd]\"       \"beta(1,1)\" \"wishart(3,iden)\"  ##               tau  ##   \"normal(0,1.5)\" ##                  nu               alpha              lambda                beta  ##      \"MV intercept\"      \"LV intercept\"           \"Loading\"        \"Regression\"  ##               theta                 psi                 rho               ibpsi  ##      \"MV precision\"      \"LV precision\"       \"Correlation\" \"Covariance matrix\"  ##                 tau  ##         \"Threshold\" mydp <- dpriors(lambda=\"normal(1,2)\") mydp ##                nu             alpha            lambda              beta  ##    \"normal(0,32)\"    \"normal(0,10)\"     \"normal(1,2)\"    \"normal(0,10)\"  ##             theta               psi               rho             ibpsi  ## \"gamma(1,.5)[sd]\" \"gamma(1,.5)[sd]\"       \"beta(1,1)\" \"wishart(3,iden)\"  ##               tau  ##   \"normal(0,1.5)\""},{"path":"http://ecmerkle.github.io/blavaan/articles/prior.html","id":"individual-parameters","dir":"Articles","previous_headings":"","what":"Individual Parameters","title":"Specifying Prior Distributions","text":"addition setting prior one type model parameter, user may wish set prior specific model parameter. accomplished using prior() modifier within model specification. example, consider following syntax Holzinger Swineford (1939) confirmatory factor model: loading visual x2 now normal prior mean 1 standard deviation 2, loading textual x6 normal prior mean 3 standard deviation 1.5. loadings default prior distribution. syntax, additionally specified gamma(3,3) prior associated residual x1. [sd] text end distribution says prior goes residual standard deviation, opposed residual precision residual variance. exist two options : [var] option residual variance, brackets precision (also use [prec]). bracketed text can used model variance/SD/precision parameter also used default prior specification desired.","code":"HS.model <- ' visual  =~ x1 + prior(\"normal(1,2)\")*x2 + x3               textual =~ x4 + x5 + prior(\"normal(3,1.5)\")*x6               speed   =~ x7 + x8 + x9                x1 ~~ prior(\"gamma(3,3)[sd]\")*x1 '"},{"path":"http://ecmerkle.github.io/blavaan/articles/prior.html","id":"covariance-parameters","dir":"Articles","previous_headings":"","what":"Covariance Parameters","title":"Specifying Prior Distributions","text":"One additional note covariance parameters defined model syntax: prior() syntax specifies prior correlation associated covariance parameter, opposed covariance . specified distribution support (0,1), blavaan automatically translates prior equivalent distribution support (-1,1). safest stick beta priors . example, syntax places Beta(1,1) (uniform) prior correlation visual textual factors. desired, also specify priors standard deviations (variances precisions) visual textual factors. Together prior correlation, priors imply prior covariance visual textual.","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9                visual ~~ prior(\"beta(1,1)\")*textual '"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/prior_pred_checks.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Prior Predictive Checks","text":"Bayesian models need specify priors model parameters. Priors distribution think parameters follow, even data. can represent high low uncertainty, diffuse prior indicates don know lot parameter behave, informative prior means quite certain expected distribution.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/prior_pred_checks.html","id":"prior-predictive-checks","dir":"Articles","previous_headings":"","what":"Prior Predictive Checks","title":"Prior Predictive Checks","text":"Prior predictive checks (PPC) generate data according prior order asses whether prior appropriate (Gabry et al. 2019). posterior predictive check generates replicated data according posterior predictive distribution. contrast, prior predictive check generates data according prior predictive distribution \\(y^{sim} ∼ p(y)\\). prior predictive distribution just like posterior predictive distribution observed data, prior predictive check nothing limiting case posterior predictive check data. easy carry mechanically simulating parameters \\(θ^{sim}∼p(\\theta)\\) according priors, simulating data \\(y^{sim}∼p(y∣ \\theta^{sim})\\) according sampling distribution given simulated parameters. result simulation joint distribution, \\((y^{sim},θ^{sim})∼p(y,\\theta)\\) thus \\(y^{sim}∼p(y)\\) simulation prior predictive distribution. blavaan can get PPC use argument prisamp=TRUE , tell blavaan ignore data buil distributions priors. start adjusting priors, instead using default priors.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/prior_pred_checks.html","id":"weakly-informative-priors","dir":"Articles","previous_headings":"Prior Predictive Checks","what":"Weakly informative priors","title":"Prior Predictive Checks","text":"show example Holzinger Swineford (1939) data, first case weakly informative priors. stpecifying observeded variable intercepts prior \\(N(3, 2)\\), factor loadings prior \\(N(0.4, 2)\\), residual standard deviation prior \\(\\Gamma(1,1)\\). estimate BSEM model respective priors dp argument, prisamp=TRUE, getting PPC instead posterior distributions. might get warning messages either divergent /failed convergence. ignore messages likely issues evaluations prior predictions. now blavaan object prior predictive distributions, can use package functions describe , see parameters within expected ranges. example can get PPC density distributions first 9 parameters (factor loadings case). basic plot() method calls functions bayesplot package (Gabry Mahr 2021) plot.type = \"dens\" argument can plot density distributions  can also pick parameters plot, like factor correlations chossing parameters 19:21 case  factor loadings distributions see first loading factor bounded 0, due modeling identification constraint blavaan, maximum values aroun 6. distributions range -6 6 -4 4, priors likely value around 0. described weakly informative priors allows range begative positive values without allowing crazy high/low values Note realistic range dependen parameter, model specification, data. , consider priors function characterictics. factor correlations kept deafult diffuse priors, allowed high low correlation, prior distributions flat across possible correlation values.","code":"priors <- dpriors(nu=\"normal(3,2)\",                   lambda=\"normal(0.4, 2)\",                   theta=\"gamma(1,1)[sd]\") HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit_wi <- bcfa(HS.model, data=HolzingerSwineford1939,              std.lv=TRUE, meanstructure=T, test = \"none\",             dp=priors, prisamp = T) plot(fit_wi, pars=1:9, plot.type = \"dens\") plot(fit_wi, pars=19:21, plot.type = \"dens\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/prior_pred_checks.html","id":"default-priors","dir":"Articles","previous_headings":"Prior Predictive Checks","what":"Default priors","title":"Prior Predictive Checks","text":"next example, estimate PPC package default priors, consider diffuse priors. can see blavaan default priors function dpriors() estimate BSEM model ignore dp argument letting run default priors, prisamp=TRUE, getting PPC instead posterior distributions. can plot density distributions compare . see default diffuse priors, model allows high values -30 30  way can see diffuse priors allows higher range values. researcher decide range priors better present expectations. important note PPC allows see expected distributions based priors, might priors used estimation process, priors interact model specification constraints (o bound constraint first factor loading) (Merkle et al. 2023)","code":"dpriors() ##                nu             alpha            lambda              beta  ##    \"normal(0,32)\"    \"normal(0,10)\"    \"normal(0,10)\"    \"normal(0,10)\"  ##             theta               psi               rho             ibpsi  ## \"gamma(1,.5)[sd]\" \"gamma(1,.5)[sd]\"       \"beta(1,1)\" \"wishart(3,iden)\"  ##               tau  ##   \"normal(0,1.5)\" fit_df <- bcfa(HS.model, data=HolzingerSwineford1939,              std.lv=TRUE, meanstructure=T, test = \"none\",              prisamp = T) plot(fit_df, pars=1:9, plot.type = \"dens\")"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Probability of Direction","text":"Probability Direction (pd) index effect existence, ranging 0% 100%, representing certainty effect goes particular direction (.e., positive negative) (Makowski et al. 2019). Beyond simplicity interpretation, understanding computation, index also presents interesting properties: independent model: solely based posterior distributions require additional information data model. robust scale response variable predictors. *strongly correlated frequentist p-value, can thus used draw parallels give reference readers non-familiar Bayesian statistics. Can interpreted probability parameter (described posterior distribution) chosen cutoff, explicit hypothesis. mathematically defined proportion posterior distribution satisfies specified hypothesis. Although differently expressed, index fairly similar (.e., strongly correlated) frequentist p-value.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"probability-of-direction-pd","dir":"Articles","previous_headings":"","what":"Probability of Direction (pd)","title":"Probability of Direction","text":"example use Industrialization Political Democracy example (Bollen 1989). first estimate latent regression model can look overall model results summary function, case also asking standardized estimates, \\(R^2\\) calculate probability direction use function package brms (Bürkner 2017) Ans need extract posterior draws matrix, also important note parameters posterior draws named Stan underlying object names, instead (b)lavaan parameter names. can see parameter name equates partable() function, follows example focus regressions factors Now, can calculate pd, hypothesis() function brms can ask specific question posterior distributions, example want know proportion regression dem65~ind60 higher 0. function requires 2 arguments, posterior draws (mc_out) hypothesis (bet_sign[2] > 0), also adding ``alpha``` argument specifies size credible intervals estimate presents mean posterior distribution, respective measures variability (deviation credible interval). Post.Prob pd stated hypothesis, example can say 91% posterior distribution dem65~ind60 lower 0. equivalent one-tail test. Evid.Ratio evidence ratio hypothesis, hypothesis form \\(> b\\), evidence ratio ratio posterior probability \\(> b\\) posterior probability \\(< b\\) another example, want know proportion regression dem60~ind60 higher 0. can see 100% posterior probability higher 0, case Evid.Ratio = Inf, happens whole distribution fulfills hypothesis. another possible case interest, use test equalities parameters, example can test dem60~ind60 higher dem65~ind60. see 97% posteriors state dem60~ind60 higher dem65~ind60, mean difference (dem60~ind60 - dem65~ind60) Estimate=0.46","code":"model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T) summary(fit, standardize=T, rsquare=T) ## blavaan 0.5.2.1189 ended normally after 1000 iterations ##  ##   Estimator                                      BAYES ##   Optimization method                             MCMC ##   Number of model parameters                        42 ##   Number of equality constraints                     4 ##  ##   Number of observations                            75 ##  ##   Statistic                                 MargLogLik         PPP ##   Value                                             NA       0.023 ##  ## Parameter Estimates: ##  ##  ## Latent Variables: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##   ind60 =~                                                               ##     x1                0.702    0.071    0.577    0.857    0.702    0.921 ##     x2                1.532    0.144    1.280    1.843    1.532    0.973 ##     x3                1.270    0.143    1.012    1.578    1.270    0.870 ##   dem60 =~                                                               ##     y1         (a)    1.458    0.167    1.136    1.794    1.782    0.759 ##     y2         (b)    1.734    0.228    1.307    2.207    2.118    0.585 ##     y3         (c)    1.816    0.203    1.423    2.219    2.219    0.700 ##     y4         (d)    1.950    0.199    1.585    2.349    2.382    0.790 ##   dem65 =~                                                               ##     y5         (a)    1.458    0.167    1.136    1.794    2.298    0.811 ##     y6         (b)    1.734    0.228    1.307    2.207    2.732    0.770 ##     y7         (c)    1.816    0.203    1.423    2.219    2.861    0.836 ##     y8         (d)    1.950    0.199    1.585    2.349    3.071    0.869 ##      Rhat    Prior        ##                           ##     1.000    normal(0,10) ##     1.000    normal(0,10) ##     0.999    normal(0,10) ##                           ##     1.000    normal(0,10) ##     1.000    normal(0,10) ##     1.002    normal(0,10) ##     1.000    normal(0,10) ##                           ##     1.000                 ##     1.000                 ##     1.002                 ##     1.000                 ##  ## Regressions: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##   dem60 ~                                                                ##     ind60             0.702    0.173    0.382    1.055    0.574    0.574 ##   dem65 ~                                                                ##     ind60             0.241    0.172   -0.098    0.575    0.153    0.153 ##     dem60             0.870    0.130    0.624    1.129    0.675    0.675 ##      Rhat    Prior        ##                           ##     1.000    normal(0,10) ##                           ##     0.999    normal(0,10) ##     0.999    normal(0,10) ##  ## Covariances: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##  .y1 ~~                                                                  ##    .y5                0.754    0.443   -0.006    1.731    0.754    0.298 ##  .y2 ~~                                                                  ##    .y4                1.752    0.807    0.331    3.456    1.752    0.322 ##    .y6                2.216    0.780    0.809    3.948    2.216    0.333 ##  .y3 ~~                                                                  ##    .y7                1.298    0.671    0.104    2.748    1.298    0.306 ##  .y4 ~~                                                                  ##    .y8                0.386    0.491   -0.519    1.452    0.386    0.120 ##  .y6 ~~                                                                  ##    .y8                1.100    0.755   -0.258    2.730    1.100    0.278 ##      Rhat    Prior        ##                           ##     0.999       beta(1,1) ##                           ##     1.000       beta(1,1) ##     0.999       beta(1,1) ##                           ##     1.002       beta(1,1) ##                           ##     0.999       beta(1,1) ##                           ##     1.002       beta(1,1) ##  ## Intercepts: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##    .x1                5.055    0.088    4.875    5.223    5.055    6.634 ##    .x2                4.794    0.181    4.423    5.135    4.794    3.046 ##    .x3                3.560    0.168    3.225    3.884    3.560    2.439 ##    .y1                5.462    0.275    4.929    6.017    5.462    2.328 ##    .y2                4.255    0.432    3.406    5.091    4.255    1.175 ##    .y3                6.560    0.366    5.834    7.281    6.560    2.069 ##    .y4                4.456    0.354    3.760    5.145    4.456    1.478 ##    .y5                5.140    0.333    4.474    5.794    5.140    1.814 ##    .y6                2.982    0.418    2.150    3.786    2.982    0.840 ##    .y7                6.200    0.394    5.432    6.950    6.200    1.812 ##    .y8                4.048    0.417    3.222    4.862    4.048    1.146 ##     ind60             0.000                               0.000    0.000 ##    .dem60             0.000                               0.000    0.000 ##    .dem65             0.000                               0.000    0.000 ##      Rhat    Prior        ##     1.001    normal(0,32) ##     1.001    normal(0,32) ##     1.001    normal(0,32) ##     1.002    normal(0,32) ##     1.003    normal(0,32) ##     1.002    normal(0,32) ##     1.001    normal(0,32) ##     1.001    normal(0,32) ##     1.000    normal(0,32) ##     1.002    normal(0,32) ##     1.001    normal(0,32) ##                           ##                           ##                           ##  ## Variances: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##    .x1                0.088    0.023    0.048    0.136    0.088    0.151 ##    .x2                0.132    0.083    0.003    0.311    0.132    0.053 ##    .x3                0.516    0.099    0.347    0.734    0.516    0.242 ##    .y1                2.330    0.593    1.331    3.665    2.330    0.423 ##    .y2                8.638    1.573    6.004   12.097    8.638    0.658 ##    .y3                5.126    1.067    3.382    7.486    5.126    0.510 ##    .y4                3.421    0.905    1.798    5.464    3.421    0.376 ##    .y5                2.749    0.663    1.683    4.205    2.749    0.342 ##    .y6                5.139    1.061    3.310    7.364    5.139    0.408 ##    .y7                3.519    0.882    2.061    5.447    3.519    0.301 ##    .y8                3.054    0.929    1.402    5.033    3.054    0.245 ##     ind60             1.000                               1.000    1.000 ##    .dem60             1.000                               0.670    0.670 ##    .dem65             1.000                               0.403    0.403 ##      Rhat    Prior        ##     1.001 gamma(1,.5)[sd] ##     1.003 gamma(1,.5)[sd] ##     1.000 gamma(1,.5)[sd] ##     0.999 gamma(1,.5)[sd] ##     0.999 gamma(1,.5)[sd] ##     1.001 gamma(1,.5)[sd] ##     1.001 gamma(1,.5)[sd] ##     1.001 gamma(1,.5)[sd] ##     1.000 gamma(1,.5)[sd] ##     1.005 gamma(1,.5)[sd] ##     1.001 gamma(1,.5)[sd] ##                           ##                           ##                           ##  ## R-Square: ##                    Estimate ##     x1                0.849 ##     x2                0.947 ##     x3                0.758 ##     y1                0.577 ##     y2                0.342 ##     y3                0.490 ##     y4                0.624 ##     y5                0.658 ##     y6                0.592 ##     y7                0.699 ##     y8                0.755 ##     dem60             0.330 ##     dem65             0.597 library(brms) mc_out <- as.matrix(blavInspect(fit, \"mcmc\")) dim(mc_out) ## [1] 3000   42 colnames(mc_out) ##  [1] \"ly_sign[1]\"    \"ly_sign[2]\"    \"ly_sign[3]\"    \"ly_sign[4]\"    ##  [5] \"ly_sign[5]\"    \"ly_sign[6]\"    \"ly_sign[7]\"    \"ly_sign[4]\"    ##  [9] \"ly_sign[5]\"    \"ly_sign[6]\"    \"ly_sign[7]\"    \"bet_sign[1]\"   ## [13] \"bet_sign[2]\"   \"bet_sign[3]\"   \"Theta_cov[1]\"  \"Theta_cov[2]\"  ## [17] \"Theta_cov[3]\"  \"Theta_cov[4]\"  \"Theta_cov[5]\"  \"Theta_cov[6]\"  ## [21] \"Theta_var[1]\"  \"Theta_var[2]\"  \"Theta_var[3]\"  \"Theta_var[4]\"  ## [25] \"Theta_var[5]\"  \"Theta_var[6]\"  \"Theta_var[7]\"  \"Theta_var[8]\"  ## [29] \"Theta_var[9]\"  \"Theta_var[10]\" \"Theta_var[11]\" \"Nu_free[1]\"    ## [33] \"Nu_free[2]\"    \"Nu_free[3]\"    \"Nu_free[4]\"    \"Nu_free[5]\"    ## [37] \"Nu_free[6]\"    \"Nu_free[7]\"    \"Nu_free[8]\"    \"Nu_free[9]\"    ## [41] \"Nu_free[10]\"   \"Nu_free[11]\" pt <- partable(fit)[,c(\"lhs\",\"op\",\"rhs\",\"pxnames\")] pt ##      lhs op   rhs       pxnames ## 1  ind60 =~    x1    ly_sign[1] ## 2  ind60 =~    x2    ly_sign[2] ## 3  ind60 =~    x3    ly_sign[3] ## 4  dem60 =~    y1    ly_sign[4] ## 5  dem60 =~    y2    ly_sign[5] ## 6  dem60 =~    y3    ly_sign[6] ## 7  dem60 =~    y4    ly_sign[7] ## 8  dem65 =~    y5    ly_sign[4] ## 9  dem65 =~    y6    ly_sign[5] ## 10 dem65 =~    y7    ly_sign[6] ## 11 dem65 =~    y8    ly_sign[7] ## 12 dem60  ~ ind60   bet_sign[1] ## 13 dem65  ~ ind60   bet_sign[2] ## 14 dem65  ~ dem60   bet_sign[3] ## 15    y1 ~~    y5  Theta_cov[1] ## 16    y2 ~~    y4  Theta_cov[2] ## 17    y2 ~~    y6  Theta_cov[3] ## 18    y3 ~~    y7  Theta_cov[4] ## 19    y4 ~~    y8  Theta_cov[5] ## 20    y6 ~~    y8  Theta_cov[6] ## 21    x1 ~~    x1  Theta_var[1] ## 22    x2 ~~    x2  Theta_var[2] ## 23    x3 ~~    x3  Theta_var[3] ## 24    y1 ~~    y1  Theta_var[4] ## 25    y2 ~~    y2  Theta_var[5] ## 26    y3 ~~    y3  Theta_var[6] ## 27    y4 ~~    y4  Theta_var[7] ## 28    y5 ~~    y5  Theta_var[8] ## 29    y6 ~~    y6  Theta_var[9] ## 30    y7 ~~    y7 Theta_var[10] ## 31    y8 ~~    y8 Theta_var[11] ## 32 ind60 ~~ ind60          <NA> ## 33 dem60 ~~ dem60          <NA> ## 34 dem65 ~~ dem65          <NA> ## 35    x1 ~1          Nu_free[1] ## 36    x2 ~1          Nu_free[2] ## 37    x3 ~1          Nu_free[3] ## 38    y1 ~1          Nu_free[4] ## 39    y2 ~1          Nu_free[5] ## 40    y3 ~1          Nu_free[6] ## 41    y4 ~1          Nu_free[7] ## 42    y5 ~1          Nu_free[8] ## 43    y6 ~1          Nu_free[9] ## 44    y7 ~1         Nu_free[10] ## 45    y8 ~1         Nu_free[11] ## 46 ind60 ~1                <NA> ## 47 dem60 ~1                <NA> ## 48 dem65 ~1                <NA> ## 49  .p4. ==  .p8.          <NA> ## 50  .p5. ==  .p9.          <NA> ## 51  .p6. == .p10.          <NA> ## 52  .p7. == .p11.          <NA> pt[pt$op==\"~\",] ##      lhs op   rhs     pxnames ## 12 dem60  ~ ind60 bet_sign[1] ## 13 dem65  ~ ind60 bet_sign[2] ## 14 dem65  ~ dem60 bet_sign[3] hypothesis(mc_out, \"bet_sign[2] > 0\", alpha = 0.05) ## New names: ## • `ly_sign[4]` -> `ly_sign[4]...4` ## • `ly_sign[5]` -> `ly_sign[5]...5` ## • `ly_sign[6]` -> `ly_sign[6]...6` ## • `ly_sign[7]` -> `ly_sign[7]...7` ## • `ly_sign[4]` -> `ly_sign[4]...8` ## • `ly_sign[5]` -> `ly_sign[5]...9` ## • `ly_sign[6]` -> `ly_sign[6]...10` ## • `ly_sign[7]` -> `ly_sign[7]...11` ## Hypothesis Tests for class : ##          Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob ## 1 (bet_sign[2]) > 0     0.24      0.17    -0.05     0.52      10.95      0.92 ##   Star ## 1      ## --- ## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses. ## '*': For one-sided hypotheses, the posterior probability exceeds 95%; ## for two-sided hypotheses, the value tested against lies outside the 95%-CI. ## Posterior probabilities of point hypotheses assume equal prior probabilities. hypothesis(mc_out, \"bet_sign[1] > 0\", alpha = 0.05) ## New names: ## • `ly_sign[4]` -> `ly_sign[4]...4` ## • `ly_sign[5]` -> `ly_sign[5]...5` ## • `ly_sign[6]` -> `ly_sign[6]...6` ## • `ly_sign[7]` -> `ly_sign[7]...7` ## • `ly_sign[4]` -> `ly_sign[4]...8` ## • `ly_sign[5]` -> `ly_sign[5]...9` ## • `ly_sign[6]` -> `ly_sign[6]...10` ## • `ly_sign[7]` -> `ly_sign[7]...11` ## Hypothesis Tests for class : ##          Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob ## 1 (bet_sign[1]) > 0      0.7      0.17     0.43     0.99        Inf         1 ##   Star ## 1    * ## --- ## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses. ## '*': For one-sided hypotheses, the posterior probability exceeds 95%; ## for two-sided hypotheses, the value tested against lies outside the 95%-CI. ## Posterior probabilities of point hypotheses assume equal prior probabilities. hypothesis(mc_out, \"bet_sign[1] - bet_sign[2] > 0\", alpha = 0.05) ## New names: ## • `ly_sign[4]` -> `ly_sign[4]...4` ## • `ly_sign[5]` -> `ly_sign[5]...5` ## • `ly_sign[6]` -> `ly_sign[6]...6` ## • `ly_sign[7]` -> `ly_sign[7]...7` ## • `ly_sign[4]` -> `ly_sign[4]...8` ## • `ly_sign[5]` -> `ly_sign[5]...9` ## • `ly_sign[6]` -> `ly_sign[6]...10` ## • `ly_sign[7]` -> `ly_sign[7]...11` ## Hypothesis Tests for class : ##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio ## 1 (bet_sign[1]-bet_... > 0     0.46      0.25     0.06      0.9      39.54 ##   Post.Prob Star ## 1      0.98    * ## --- ## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses. ## '*': For one-sided hypotheses, the posterior probability exceeds 95%; ## for two-sided hypotheses, the value tested against lies outside the 95%-CI. ## Posterior probabilities of point hypotheses assume equal prior probabilities."},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"region-of-practical-equivalence-rope","dir":"Articles","previous_headings":"","what":"Region of Practical Equivalence (ROPE)","title":"Probability of Direction","text":"Note far tested hypothesis 0, equivalent frequentist null hypothesis tests. can test . Bayesian inference based statistical significance, effects tested “zero”. Indeed, Bayesian framework offers probabilistic view parameters, allowing assessment uncertainty related . Thus, rather concluding effect present simply differs zero, conclude probability outside specific range can considered “practically effect” (.e., negligible magnitude) sufficient. range called region practical equivalence (ROPE). Indeed, statistically, probability posterior distribution different 0 make much sense (probability different single point infinite). Therefore, idea underlining ROPE let user define area around null value enclosing values equivalent null value practical purposes (Kruschke Liddell 2018) examples, change value tested, common recommendations use |0.1| minimally relevant value standardized regressions, case find 0.79 proportion posterior 0.1","code":"hypothesis(mc_out, \"bet_sign[2] > .1\", alpha = 0.05) ## New names: ## • `ly_sign[4]` -> `ly_sign[4]...4` ## • `ly_sign[5]` -> `ly_sign[5]...5` ## • `ly_sign[6]` -> `ly_sign[6]...6` ## • `ly_sign[7]` -> `ly_sign[7]...7` ## • `ly_sign[4]` -> `ly_sign[4]...8` ## • `ly_sign[5]` -> `ly_sign[5]...9` ## • `ly_sign[6]` -> `ly_sign[6]...10` ## • `ly_sign[7]` -> `ly_sign[7]...11` ## Hypothesis Tests for class : ##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio ## 1 (bet_sign[2])-(.1) > 0     0.14      0.17    -0.15     0.42       3.88 ##   Post.Prob Star ## 1       0.8      ## --- ## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses. ## '*': For one-sided hypotheses, the posterior probability exceeds 95%; ## for two-sided hypotheses, the value tested against lies outside the 95%-CI. ## Posterior probabilities of point hypotheses assume equal prior probabilities."},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"vs--95-ci","dir":"Articles","previous_headings":"","what":"89% vs. 95% CI","title":"Probability of Direction","text":"commonly frequentist tradition see use 95% Credible interval. Using 89% another popular choice, used default long time. start? Naturally, came choosing CI level report default, people started using 95%, arbitrary convention used frequentist world. However, authors suggested 95% might appropriate Bayesian posterior distributions, potentially lacking stability enough posterior samples drawn (McElreath 2020). proposition use 90% instead 95%. However, recently, McElreath (2020) suggested use arbitrary thresholds first place, use 89%? Moreover, 89 highest prime number exceed already unstable 95% threshold. anything? Nothing, reminds us total arbitrariness conventions (McElreath 2020). can use argument alpha argument hypothesis function, interpretation values Post.Prob","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"caveats","dir":"Articles","previous_headings":"","what":"Caveats","title":"Probability of Direction","text":"Although allows testing hypotheses similar manner frequentist null-hypothesis testing framework, strongly argue using arbitrary cutoffs (e.g., p < .05) determine ‘existence’ effect. ROPE sensitive scale, aware value interest representative respective scale. , standardize parameters useful commonly used scale","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/start.html","id":"installation","dir":"Articles","previous_headings":"","what":"Installation","title":"Getting Started with blavaan","text":"blavaan can installed CRAN usual way: situations, may wish install blavaan GitHub. GitHub version sometimes contains bug fixes yet CRAN, though can also less stable. install GitHub, use following command. command requires system can compile Stan models, guaranteed usually install blavaan CRAN. trouble, may help look RStan Getting Started page.","code":"install.packages(\"blavaan\") remotes::install_github(\"ecmerkle/blavaan\", INSTALL_opts = \"--no-multiarch\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/start.html","id":"commands-and-syntax","dir":"Articles","previous_headings":"","what":"Commands and Syntax","title":"Getting Started with blavaan","text":"blavaan package depends lavaan package model specification computations. means , already know lavaan, already able many things blavaan. particular, many blavaan commands add letter “b” start lavaan command. example, sem() becomes bsem(), lavInspect() becomes blavInspect(). also sometimes possible use lavaan command blavaan object, though results may always expect. details mind, look lavaan tutorial many examples models. can translate many examples blavaan adding “b” start commands. look pages , learn additional blavaan arguments specific Bayesian methods.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/summaries.html","id":"convergence","dir":"Articles","previous_headings":"","what":"Convergence","title":"Model Summaries","text":"Following model estimation, immediately wish look “goodness” posterior samples, including convergence stationary distribution autocorrelation. Popular convergence metrics available via blavInspect() function: R-hat values near 1.00 indicate convergence, large effective sample sizes (hundreds ) preferred. details metrics, see, e.g., Posterior Analysis section Stan Reference Manual. model definitely converged (judged Rhat), blavaan issue multiple warnings. Lack convergence sometimes caused bad initial values chain strays extreme region posterior space. cases, can helpful re-estimate model second time. also helpful specify mildly-informative priors loading parameters, chains wander extreme loading values. example, expect variables positively correlated loadings fixed 1 identification, Normal(1,.5) often mildly-informative prior. Otherwise, lack convergence may imply prior distributions severely conflict data, ill-defined model. sometimes helpful try fit model lavaan, observe whether errors occur .","code":"blavInspect(fit, 'rhat') blavInspect(fit, 'neff')"},{"path":"http://ecmerkle.github.io/blavaan/articles/summaries.html","id":"model-fit-comparison","dir":"Articles","previous_headings":"","what":"Model Fit & Comparison","title":"Model Summaries","text":"Next, may wish examine model fit metrics. many metrics available summary() output, available fitMeasures() function: judging absolute fit, blavaan supplies posterior predictive p-value based likelihood ratio statistic. Good-fitting models values near 0.5 metric. examining models’ relative fits, blavaan supplies DIC, WAIC, LOOIC. latter two metrics computed help loo package (Vehtari et al. 2020). Comparison multiple models criteria facilitated via blavCompare(), provides standard errors difference two criteria. notable functions include blavFitIndices() alternative measures absolute fit ppmc() general posterior predictive checks.","code":"summary(fit) fitMeasures(fit)"},{"path":"http://ecmerkle.github.io/blavaan/articles/summaries.html","id":"latent-variables-standardization","dir":"Articles","previous_headings":"","what":"Latent Variables & Standardization","title":"Model Summaries","text":"often-discussed advantage Bayesian models abilities describe uncertainty “random” parameters, including random effects latent variables. access functionality blavaan, users must set save.lvs = TRUE model estimation, done top page. model estimation, uses can access information via blavInspect() blavPredict(). Relevant arguments blavInspect() include lvmeans lvs. former returns posterior means latent variables, similar predictions supplied frequentist models. latter returns posterior samples latent variables, users summarize uncertainties functions latent variables. posterior samples returned list length n.chains, list entry row per posterior sample (number columns total number latent variables model): related, different, information can obtained blavPredict(). function also return posterior samples latent variables, matrix instead list: blavPredict() function also return predictions observed variables conditioned sampled latent variables. type = \"yhat\" argument returns expected values observed variables conditioned latent variable samples; type = \"ypred\" argument returns posterior predictions observed variables including residual noise (essentially yhat + error); type = \"ymis\" argument returns posterior predictions missing variables conditioned observed. expected values predictions returned list format; matrix, see last line code . Finally, fully related latent variables: standardizedPosterior() function return standardized posterior draws. calls lavaan function standardizedSolution() background function’s flexibility.","code":"postmns <- blavInspect(fit, what = \"lvmeans\") postsamps <- blavInspect(fit, what = \"lvs\") postsamps <- blavPredict(fit, type = \"lv\") evpreds <- blavPredict(fit, type = \"yhat\") postpreds <- blavPredict(fit, type = \"ypred\") mispreds <- blavPredict(fit, type = \"ymis\")  ## convert to matrix from list: evpreds <- do.call(\"rbind\", evpreds)"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Edgar Merkle. Author, maintainer. Yves Rosseel. Author. Ben Goodrich. Author. Mauricio Garnier-Villarreal. Contributor.            R/blav_compare.RR/ctr_bayes_fit.Rvignettes Terrence D. Jorgensen. Contributor.            R/ctr_bayes_fit.RR/ctr_ppmc.RR/blav_predict.R Huub Hoofs. Contributor.            R/ctr_bayes_fit.R Rens van de Schoot. Contributor.            R/ctr_bayes_fit.R Andrew Johnson. Contributor.            Makevars Matthew Emery. Contributor.            loo moment_match","code":""},{"path":"http://ecmerkle.github.io/blavaan/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Merkle EC, Fitzsimmons E, Uanhoro J, Goodrich B (2021). “Efficient Bayesian Structural Equation Modeling Stan.” Journal Statistical Software, 100(6), 1–22. doi:10.18637/jss.v100.i06. Merkle EC, Rosseel Y (2018). “blavaan: Bayesian Structural Equation Models via Parameter Expansion.” Journal Statistical Software, 85(4), 1–30. doi:10.18637/jss.v085.i04.","code":"@Article{,   title = {Efficient {Bayesian} Structural Equation Modeling in {Stan}},   author = {Edgar C. Merkle and Ellen Fitzsimmons and James Uanhoro and Ben Goodrich},   journal = {Journal of Statistical Software},   year = {2021},   volume = {100},   number = {6},   pages = {1--22},   doi = {10.18637/jss.v100.i06}, } @Article{,   title = {{blavaan: Bayesian} Structural Equation Models via Parameter Expansion},   author = {Edgar C. Merkle and Yves Rosseel},   journal = {Journal of Statistical Software},   year = {2018},   volume = {85},   number = {4},   pages = {1--30},   doi = {10.18637/jss.v085.i04}, }"},{"path":"http://ecmerkle.github.io/blavaan/index.html","id":"blavaan","dir":"","previous_headings":"","what":"Bayesian Latent Variable Analysis","title":"Bayesian Latent Variable Analysis","text":"blavaan free, open source R package Bayesian latent variable analysis. relies JAGS Stan estimate models via MCMC. blavaan functions syntax similar lavaan. example, consider Political Democracy example Bollen (1989): development version blavaan (containing updates yet CRAN) can installed via command . Compilation required; may problem users currently rely binary version blavaan CRAN. information, see: Merkle, E. C., Fitzsimmons, E., Uanhoro, J., & Goodrich, B. (2021). Efficient Bayesian structural equation modeling Stan. Journal Statistical Software, 100(6), 1–22. Merkle, E. C., & Rosseel, Y. (2018). blavaan: Bayesian structural equation models via parameter expansion. Journal Statistical Software, 85(4), 1–30. blavaan supported Institute Education Sciences, U.S. Department Education, Grant R305D210044, well NSF grants SES-1061334 1460719.","code":"library(blavaan)  model <- '    # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ y1 + y2 + y3 + y4      dem65 =~ y5 + y6 + y7 + y8    # regressions      dem60 ~ ind60      dem65 ~ ind60 + dem60    # residual covariances      y1 ~~ y5      y2 ~~ y4 + y6      y3 ~~ y7      y4 ~~ y8      y6 ~~ y8 ' fit <- bsem(model, data = PoliticalDemocracy) summary(fit) remotes::install_github(\"ecmerkle/blavaan\", INSTALL_opts = \"--no-multiarch\")"},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit Confirmatory Factor Analysis Models — bcfa","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"Fit Confirmatory Factor Analysis (CFA) model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"","code":"bcfa(..., cp = \"srs\",      dp = NULL, n.chains = 3, burnin, sample,      adapt, mcmcfile = FALSE, mcmcextra = list(), inits = \"simple\",      convergence = \"manual\", target = \"stan\", save.lvs = FALSE,      wiggle = NULL, wiggle.sd = 0.1, prisamp = FALSE, jags.ic = FALSE,      seed = NULL, bcontrol = list())"},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"... Default lavaan arguments.  See lavaan. cp Handling prior distributions covariance parameters:   possible values \"srs\" (default)     \"fa\". Option \"fa\" available target=\"jags\". dp Default prior distributions different types     parameters, typically result call dpriors().     See dpriors() help file information. n.chains Number desired MCMC chains. burnin Number burnin/warmup iterations (including adaptive   iterations, target=\"jags\"). Defaults 4000 target=\"jags\"   500 Stan targets. sample total number samples take burnin. Defaults 10000 target=\"jags\" 1000 Stan targets. adapt target=\"jags\", number adaptive iterations use start   sampling. Defaults 1000. mcmcfile TRUE, JAGS/Stan model written file   (lavExport directory). Can also supply character   string, serves name directory files written. mcmcextra list potential names syntax (unavailable   target=\"stan\"),   monitor, data, llnsamp. syntax object text string containing extra   code insert JAGS/Stan model syntax. data object   list extra data send JAGS/Stan model.    moment_match_k_threshold specified within data looic    model calculated using moment matching. monitor object   character vector containing extra JAGS/Stan parameters   monitor. llnsamp object relevant models ordinal   variables, specifies number samples drawn approximate   model log-likelihood (larger numbers imply higher accuracy   longer time). log-likelihood specifically used compute   information criteria. inits character string, options currently     \"simple\" (default), \"Mplus\", \"prior\", \"jags\".  first two     cases, parameter values set though estimated via     ML (see lavaan).  starting parameter value     chain perturbed original values     addition random uniform noise.  \"prior\" used, starting     parameter values obtained based prior distributions     (also trying ensure starting values crash     model estimation).  \"jags\", starting values     specified JAGS choose values (probably     crash Stan targets). can also supply     list starting values chain, list format can     obtained , e.g., blavInspect(fit, \"inits\"). Finally,     can specify starting values similar way lavaan,     using lavaan start argument (see lavaan     documentation options ). case, also set     inits=\"simple\", aware starting values     used chain. convergence Useful target=\"jags\". \"auto\", parameters   sampled convergence achieved (via autorun.jags()).   case, arguments burnin sample passed   autorun.jags() startburnin startsample,   respectively. Otherwise, parameters   sampled specified user (run.jags   defaults). target Desired MCMC sampling, \"stan\" (pre-compiled   marginal approach)   default. Also available \"vb\", calls rstan function   vb(). options include \"jags\", \"stancond\",   \"stanclassic\", sample latent variables provide   greater functionality (syntax written \"fly\").   slower less efficient. save.lvs sampled latent variables (factor scores)   saved? Logical; defaults FALSE wiggle Labels equality-constrained parameters   \"approximately\" equal. Can also \"intercepts\", \"loadings\",   \"regressions\", \"means\". wiggle.sd prior sd (normal distribution) used approximate equality   constraints. Can one value, (target=\"stan\") numeric vector   values length wiggle. prisamp samples drawn prior, instead   posterior (target=\"stan\" )? Logical; defaults FALSE jags.ic DIC computed JAGS way, addition BUGS way? Logical; defaults FALSE seed vector length n.chains (target   \"jags\") integer (target \"stan\") containing random   seeds MCMC run. NULL, seeds chosen randomly. bcontrol list containing additional parameters passed     run.jags (autorun.jags) stan.  See manpage functions     overview additional parameters can set.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"bcfa function wrapper general     blavaan function, using following default     lavaan arguments:     int.ov.free = TRUE, int.lv.free = FALSE,     auto.fix.first = TRUE (unless std.lv = TRUE),     auto.fix.single = TRUE, auto.var = TRUE,     auto.cov.lv.x = TRUE,     auto.th = TRUE, auto.delta = TRUE,     auto.cov.y = TRUE.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"object class lavaan, several methods   available, including summary method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"","code":"if (FALSE) { # The Holzinger and Swineford (1939) example HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939) summary(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit Growth Curve Models — bgrowth","title":"Fit Growth Curve Models — bgrowth","text":"Fit Growth Curve model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit Growth Curve Models — bgrowth","text":"","code":"bgrowth(..., cp = \"srs\", dp = NULL, n.chains = 3, burnin, sample, adapt, mcmcfile = FALSE, mcmcextra = list(),  inits = \"simple\", convergence = \"manual\", target = \"stan\", save.lvs = FALSE, wiggle = NULL, wiggle.sd = 0.1, prisamp = FALSE, jags.ic = FALSE, seed = NULL, bcontrol = list())"},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit Growth Curve Models — bgrowth","text":"... Default lavaan arguments.  See lavaan. cp Handling prior distributions covariance parameters:   possible values \"srs\" (default) \"fa\". Option \"fa\" available target=\"jags\". dp Default prior distributions different types     parameters, typically result call dpriors().     See dpriors() help file information. n.chains Number desired MCMC chains. burnin Number burnin/warmup iterations (including adaptive   iterations, target=\"jags\"). Defaults 4000 target=\"jags\"   500 Stan targets. sample total number samples take burnin. Defaults 10000 target=\"jags\" 1000 Stan targets. adapt target=\"jags\", number adaptive iterations use start   sampling. Defaults 1000. mcmcfile TRUE, JAGS/Stan model written file   (lavExport directory). Can also supply character   string, serves name directory files written. mcmcextra list potential names syntax (unavailable   target=\"stan\"),   monitor, data, llnsamp. syntax object text string containing extra   code insert JAGS/Stan model syntax. data object   list extra data send JAGS/Stan model.    moment_match_k_threshold specified within data looic    model calculated using moment matching. monitor object   character vector containing extra JAGS/Stan parameters   monitor. llnsamp object relevant models ordinal   variables, specifies number samples drawn approximate   model log-likelihood (larger numbers imply higher accuracy   longer time). log-likelihood specifically used compute   information criteria. inits character string, options currently     \"simple\" (default), \"Mplus\", \"prior\", \"jags\".  first two     cases, parameter values set though estimated via     ML (see lavaan).  starting parameter value     chain perturbed original values     addition random uniform noise.  \"prior\" used, starting     parameter values obtained based prior distributions     (also trying ensure starting values crash     model estimation).  \"jags\", starting values     specified JAGS choose values (probably     crash Stan targets). can also supply     list starting values chain, list format can     obtained , e.g., blavInspect(fit, \"inits\"). Finally,     can specify starting values similar way lavaan,     using lavaan start argument (see lavaan     documentation options ). case, also set     inits=\"simple\", aware starting values     used chain. convergence Useful target=\"jags\". \"auto\", parameters   sampled convergence achieved (via autorun.jags()).   case, arguments burnin sample passed   autorun.jags() startburnin startsample,   respectively. Otherwise, parameters   sampled specified user (run.jags   defaults). target Desired MCMC sampling, \"stan\" (pre-compiled   marginal approach)   default. Also available \"vb\", calls rstan function   vb(). options include \"jags\", \"stancond\",   \"stanclassic\", sample latent variables provide   greater functionality (syntax written \"fly\").   slower less efficient. save.lvs sampled latent variables (factor scores)   saved? Logical; defaults FALSE wiggle Labels equality-constrained parameters   \"approximately\" equal. Can also \"intercepts\", \"loadings\",   \"regressions\", \"means\". wiggle.sd prior sd (normal distribution) used approximate equality   constraints. Can one value, (target=\"stan\") numeric vector   values length wiggle. prisamp samples drawn prior, instead   posterior (target=\"stan\" )? Logical; defaults FALSE jags.ic DIC computed JAGS way, addition BUGS way? Logical; defaults FALSE seed vector length n.chains (target   \"jags\") integer (target \"stan\") containing random   seeds MCMC run. NULL, seeds chosen randomly. bcontrol list containing additional parameters passed     run.jags (autorun.jags) stan.  See manpage functions     overview additional parameters can set.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit Growth Curve Models — bgrowth","text":"bgrowth function wrapper general       blavaan function, using following default       lavaan arguments:     meanstructure = TRUE,      int.ov.free = FALSE, int.lv.free = TRUE,     auto.fix.first = TRUE (unless std.lv = TRUE),     auto.fix.single = TRUE, auto.var = TRUE,     auto.cov.lv.x = TRUE,      auto.th = TRUE, auto.delta = TRUE,     auto.cov.y = TRUE.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit Growth Curve Models — bgrowth","text":"object class blavaan, several methods   available, including summary method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit Growth Curve Models — bgrowth","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit Growth Curve Models — bgrowth","text":"","code":"if (FALSE) { ## linear growth model with a time-varying covariate model.syntax <- '   # intercept and slope with fixed coefficients     i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4     s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4    # regressions     i ~ x1 + x2     s ~ x1 + x2    # time-varying covariates     t1 ~ c1     t2 ~ c2     t3 ~ c3     t4 ~ c4 '  fit <- bgrowth(model.syntax, data=Demo.growth) summary(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":null,"dir":"Reference","previous_headings":"","what":"Bayesian model comparisons — blavCompare","title":"Bayesian model comparisons — blavCompare","text":"Bayesian model comparisons, including WAIC, LOO, Bayes factor approximation.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bayesian model comparisons — blavCompare","text":"","code":"blavCompare(object1, object2, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bayesian model comparisons — blavCompare","text":"object1 object class blavaan. object2 second object class blavaan. ... arguments (unused now).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Bayesian model comparisons — blavCompare","text":"function approximates log-Bayes factor two candidate models using Laplace approximation model's marginal log-likelihood.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bayesian model comparisons — blavCompare","text":"log-Bayes factor approximation, along model's approximate marginal log-likelihood.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Bayesian model comparisons — blavCompare","text":"Raftery, . E. (1993). Bayesian model selection structural equation models. K. . Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 163-180). Beverly Hills, CA: Sage.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bayesian model comparisons — blavCompare","text":"","code":"if (FALSE) { hsm1 <- ' visual  =~ x1 + x2 + x3 + x4           textual =~ x4 + x5 + x6           speed   =~ x7 + x8 + x9 '  fit1 <- bcfa(hsm1, data=HolzingerSwineford1939)  hsm2 <- ' visual  =~ x1 + x2 + x3           textual =~ x4 + x5 + x6 + x7           speed   =~ x7 + x8 + x9 '  fit2 <- bcfa(hsm2, data=HolzingerSwineford1939)  blavCompare(fit1, fit2) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":null,"dir":"Reference","previous_headings":"","what":"SEM Fit Indices for Bayesian SEM — blavFitIndices","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"function provides posterior distribution \\(\\chi^2\\)-based fit indices assess global fit latent variable model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"","code":"blavFitIndices(object, thin = 1L, pD = c(\"loo\",\"waic\",\"dic\"),                rescale = c(\"devM\",\"ppmc\",\"mcmc\"),                fit.measures = \"all\", baseline.model = NULL)  ## S4 method for signature 'blavFitIndices' # S4 method for blavFitIndices summary(object, ...)  # S3 method for bfi summary(object, central.tendency = c(\"mean\",\"median\",\"mode\"),         hpd = TRUE, prob = .90)"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"object object class blavaan. thin Optional integer indicating much thin chain.     Default 1L, indicating thin chains. pD character indicating information criterion     returned fitMeasures(object) use estimated number     parameters. default leave-one-information criterion     (LOO-IC), highly recommended Vehtari et al. (2017). rescale character indicating method used calculate     fit indices. rescale = \"devM\" (default), Bayesian analog     \\(\\chi^2\\) statistic (deviance evaluated posterior mean     model parameters) approximated rescaling deviance     iteration subtracting estimated number parameters.     rescale = \"PPMC\", deviance iteration rescaled     subtracting deviance data simulated posterior predictive     distribution (posterior predictive model checking; see Hoofs et al.,     2017). rescale = \"MCMC\", fit measures simply calculated     using fitMeasures iteration Markov     chain(s), based model-implied moments iteration (advised     model includes informative priors, case model's     estimated pD deviate number parameters used     calculate df fitMeasures). fit.measures \"\", fit measures available     returned. single fit measures specified name,     computed returned. rescale = \"devM\"     \"PPMC\", currently available indices \"BRMSEA\",     \"BGammaHat\", \"adjBGammaHat\", \"BMc\", \"BCFI\",     \"BTLI\", \"BNFI\". rescale = \"MCMC\", user may     request indices returned fitMeasures     objects class lavaan. baseline.model NULL, object class     blavaan, representing user-specified baseline model.     baseline.model provided, incremental fit indices (BCFI,     BTLI, BNFI) can requested fit.measures. Ignored     rescale = \"MCMC\". ... Additional arguments summary method: central.tendency Takes values \"mean\", \"median\", \"mode\", indicating statistics     used characterize location posterior distribution.     default, 3 statistics returned. posterior mean labeled     EAP expected posteriori estimate, mode     labeled MAP modal posteriori     estimate. hpd logical indicating whether calculate highest     posterior density (HPD) credible interval fit     index (defaults TRUE). prob \"confidence\" level   credible interval(s) (defaults 0.9).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"S4 object class blavFitIndices consisting 2 slots: @details list containing choices made user     (defaults; e.g., values pD rescale set),     well posterior distribution \\(\\chi^2\\) (deviance)     statistic (rescaled, rescale = \"devM\" \"PPMC\"). @indices list containing posterior distribution     requested fit.measure. summary() method returns data.frame containing one row   requested fit.measure, columns containing specified   measure(s) central.tendency, posterior SD,   (requested) HPD credible-interval limits.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"Mauricio Garnier-Villareal (Vrije Universiteit Amsterdam; mgv@pm.) Terrence D. Jorgensen (University Amsterdam; TJorgensen314@gmail.com)","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"rescale = \"PPMC\" based : Hoofs, H., van de Schoot, R., Jansen, N. W., & Kant, . (2017).   Evaluating model fit Bayesian confirmatory factor analysis large   samples: Simulation study introducing BRMSEA.   Educational Psychological Measurement. doi:10.1177/0013164417709314 rescale = \"devM\" based : Garnier-Villarreal, M., & Jorgensen, T. D. (2020).  Adapting Fit Indices Bayesian Structural Equation Modeling: Comparison Maximum Likelihood.  Psychological Methods, 25(1), 46--70. https://doi.org/dx.doi.org/10.1037/met0000224   (See also https://osf.io/afkcw/) references: Vehtari, ., Gelman, ., & Gabry, J. (2017). Practical Bayesian model   evaluation using leave-one-cross-validation WAIC.   Statistics Computing, 27(5), 1413--1432.   doi:10.1007/s11222-016-9696-4","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"","code":"if (FALSE) { HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 ' ## fit target model fit1 <- bcfa(HS.model, data = HolzingerSwineford1939,               n.chains = 2, burnin = 1000, sample = 1000)  ## fit null model to calculate CFI, TLI, and NFI null.model <- c(paste0(\"x\", 1:9, \" ~~ x\", 1:9), paste0(\"x\", 1:9, \" ~ 1\")) fit0 <- bcfa(null.model, data = HolzingerSwineford1939,               n.chains = 2, burnin = 1000, sample = 1000)  ## calculate posterior distributions of fit indices  ## The default method mimics fit indices derived from ML estimation ML <- blavFitIndices(fit1, baseline.model = fit0) ML summary(ML)  ## other options:  ## - use Hoofs et al.'s (2017) PPMC-based method ## - use the estimated number of parameters from WAIC instead of LOO-IC PPMC <- blavFitIndices(fit1, baseline.model = fit0,                        pD = \"waic\", rescale = \"PPMC\") ## issues a warning about using rescale=\"PPMC\" with N < 1000 (see Hoofs et al.)  ## - specify only the desired measures of central tendency ## - specify a different \"confidence\" level for the credible intervals summary(PPMC, central.tendency = c(\"mean\",\"mode\"), prob = .95)    ## Access the posterior distributions for further investigation head(distML <- data.frame(ML@indices))  ## For example, diagnostic plots using the bayesplot package:  ## distinguish chains nChains <- blavInspect(fit1, \"n.chains\") distML$Chain <- rep(1:nChains, each = nrow(distML) / nChains)  library(bayesplot) mcmc_pairs(distML, pars = c(\"BRMSEA\",\"BMc\",\"BGammaHat\",\"BCFI\",\"BTLI\"),            diag_fun = \"hist\") ## Indices are highly correlated across iterations in both chains  ## Compare to PPMC method distPPMC <- data.frame(PPMC@indices) distPPMC$Chain <- rep(1:nChains, each = nrow(distPPMC) / nChains) mcmc_pairs(distPPMC, pars = c(\"BRMSEA\",\"BMc\",\"BGammaHat\",\"BCFI\",\"BTLI\"),            diag_fun = \"dens\") ## nonlinear relation between BRMSEA, related to the floor effect of BRMSEA ## that Hoofs et al. found for larger (12-indicator) models  }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":null,"dir":"Reference","previous_headings":"","what":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"blavInspect() blavTech() functions can used inspect/extract information stored inside (can computed ) fitted blavaan object. similar lavaan's lavInspect() function.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"","code":"blavInspect(blavobject, what, ...)  blavTech(blavobject, what, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"blavobject object class blavaan. Character. needs inspected/extracted? See Details Bayes-specific options, see lavaan's lavInspect() additional options. Note: argument case-sensitive (everything converted lower case.) ... lavaan arguments supplied lavInspect(); see lavaan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"list Bayesian-specific values argument; additional values can found lavInspect() documentation. \"start\": list starting values chain, unless inits=\"jags\" used model estimation. Aliases: \"starting.values\", \"inits\". \"rhat\": parameter's potential scale reduction     factor convergence assessment. Can also use \"psrf\" instead \"rhat\" \"ac.10\": parameter's estimated lag-10 autocorrelation. \"neff\": parameters effective sample size, taking account autocorrelation. \"mcmc\": object class mcmc containing individual parameter draws MCMC run. Aliases: \"draws\", \"samples\". \"mcobj\": underlying run.jags stan object resulted MCMC run. \"n.chains\": number chains sampled. \"cp\": approach used estimating covariance     parameters (\"srs\" \"fa\"); relevant     using JAGS. \"dp\": Default prior distributions used type model parameter. \"postmode\": Estimated posterior mode free parameter. \"postmean\": Estimated posterior mean free parameter. \"postmedian\": Estimated posterior median free parameter. \"lvs\": object class mcmc containing latent variable (factor score) draws. two-level models, use level = 1 level = 2 specify factor scores want. \"lvmeans\": matrix mean factor scores (rows observations, columns variables). Use additional level argument way. \"hpd\": HPD interval free parameter. case, prob argument can used specify number (0,1) reflecting desired percentage interval.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"","code":"if (FALSE) { # The Holzinger and Swineford (1939) example HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data = HolzingerSwineford1939,             bcontrol = list(method = \"rjparallel\"))  # extract information blavInspect(fit, \"psrf\") blavInspect(fit, \"hpd\", prob = .9) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":null,"dir":"Reference","previous_headings":"","what":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"purpose blavPredict() function compute various   types model predictions, conditioned observed data. differs   somewhat lavPredict() lavaan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"","code":"blavPredict(object, newdata = NULL, type = \"lv\", level = 1L)"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"object object class blavaan. newdata Currently unused. (optional data.frame, containing variables data.frame used fitting model object.) type character string. \"lv\", estimated values latent variables model computed. \"ov\" \"yhat\", predicted means observed variables model computed. \"ypred\" \"ydist\", predicted values observed variables (including residual noise) computed. \"ymis\" \"ovmis\", model predicted values (\"imputations\") missing data computed. See details information. level type = \"lv\", used specify whether one desires level 1 latent variables level 2 latent variables.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"predict() function calls blavPredict() function default options. , provide information type option. options work target=\"stan\", \"number samples\" defined number posterior samples across chains. type=\"lv\": posterior distribution latent variables conditioned observed variables. Returns list \"number samples\" entries, entry matrix rows  observations columns latent variables. type=\"yhat\": posterior expected value observed variables conditioned sampled latent variables. Returns list \"number samples\" entries, entry matrix rows observations columns observed variables. type=\"ypred\": posterior predictive distribution observed variables conditioned sampled latent variables (including residual variances). Returns list \"number samples\" entries, entry data frame rows observations columns observed variables. type=\"ymis\": posterior predictive distribution missing values conditioned observed variables. Returns matrix \"number samples\" rows \"number missing variables\" columns.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"","code":"if (FALSE) { data(HolzingerSwineford1939)  ## fit model HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data = HolzingerSwineford1939, save.lvs = TRUE) lapply(blavPredict(fit)[1:2], head) # first 6 rows of first 10 posterior samples head(blavPredict(fit, type = \"yhat\")[[1]]) # top of first posterior sample  ## multigroup models return a list of factor scores (one per group) mgfit <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\",               group.equal = c(\"loadings\",\"intercepts\"), save.lvs = TRUE)  lapply(blavPredict(fit)[1:2], head) head(blavPredict(fit, type = \"ypred\")[[1]]) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blav_internal.html","id":null,"dir":"Reference","previous_headings":"","what":"blavaan internal functions — blav_internal","title":"blavaan internal functions — blav_internal","text":"Internal functions related Bayesian model estimation.   called user.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":null,"dir":"Reference","previous_headings":"","what":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"blavaan class contains lavaan   class, representing (fitted) Bayesian latent variable   model. contains description model specified user,   summary data, internal matrix representation, model   fitted, fitting results.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"objects-from-the-class","dir":"Reference","previous_headings":"","what":"Objects from the Class","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"Objects can created via   bcfa, bsem, bgrowth   blavaan functions.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"slots","dir":"Reference","previous_headings":"","what":"Slots","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"version: lavaan package version used create objects call: function call returned match.call(). timing: elapsed time (user+system) various parts       program list, including total time. Options: Named list options provided       user, filled-automatically. ParTable: Named list describing model parameters. Can coerced data.frame. documentation, called `parameter table'. pta: Named list containing parameter table attributes. Data: Object internal class \"Data\": information data. SampleStats: Object internal class \"SampleStats\": sample       statistics Model: Object internal class \"Model\":       internal (matrix) representation model Cache: List using objects try compute , reuse many times. Fit: Object internal class \"Fit\":       results fitting model. longer used. boot: List. Unused Bayesian models. optim: List. Information optimization. loglik: List. Information loglikelihood model (maximum likelihood used). implied: List. Model implied statistics. vcov: List. Information variance matrix (vcov) model parameters. test: List. Different test statistics. h1: List. Information unrestricted h1 model (available). baseline: List. Information baseline model (often independence model) (available). external: List. Includes Stan JAGS objects used MCMC.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"methods","dir":"Reference","previous_headings":"","what":"Methods","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"coef signature(object = \"blavaan\", type = \"free\"): Returns       estimates parameters model named numeric vector.       type=\"free\", free parameters returned.       type=\"user\", parameters listed parameter table       returned, including constrained fixed parameters. vcov signature(object = \"lavaan\"): returns       covariance matrix estimated parameters. show signature(object = \"blavaan\"): Print short summary       model fit summary signature(object = \"blavaan\", header = TRUE,      fit.measures = FALSE, estimates = TRUE, ci = TRUE,       standardized = FALSE, rsquare = FALSE, std.nox = FALSE,      psrf = TRUE, neff = FALSE, postmedian = FALSE, postmode = FALSE,      priors = TRUE, bf = FALSE, nd = 3L):       Print nice summary model estimates.       header = TRUE, header section (including fit measures)       printed.       fit.measures = TRUE, additional fit measures added       header section.       estimates = TRUE, print parameter estimates section.       ci = TRUE, add confidence intervals parameter estimates       section.       standardized = TRUE,       standardized solution also printed.  Note SEs       tests still based unstandardized estimates. Use       standardizedSolution obtain SEs test       statistics standardized estimates.       rsquare=TRUE, R-Square values dependent variables       model printed.       std.nox = TRUE, std.column contains       std.nox column parameterEstimates() output.       psrf = TRUE, potential scale reduction factors (Rhats)       printed.       neff = TRUE, effective sample sizes printed.       postmedian postmode TRUE, posterior       medians modes printed instead posterior means.       priors = TRUE, parameter prior distributions       printed.       bf = TRUE, Savage-Dickey approximations Bayes       factor printed certain parameters.       Nothing returned (use       lavInspect another extractor function       extract information fitted model).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"","code":"if (FALSE) { HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939)  summary(fit, standardized=TRUE, fit.measures=TRUE, rsquare=TRUE) coef(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit a Bayesian Latent Variable Model — blavaan","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"Fit Bayesian latent variable model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"","code":"blavaan(..., cp = \"srs\",     dp = NULL, n.chains = 3, burnin, sample,     adapt, mcmcfile = FALSE, mcmcextra = list(), inits = \"simple\",     convergence = \"manual\", target = \"stan\", save.lvs = FALSE,     wiggle = NULL, wiggle.sd = 0.1, prisamp = FALSE, jags.ic = FALSE,     seed = NULL, bcontrol = list())"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"... Default lavaan arguments.  See lavaan. cp Handling prior distributions covariance parameters:   possible values \"srs\" (default) \"fa\".  Option   \"fa\" available target=\"jags\". dp Default prior distributions different types     parameters, typically result call dpriors().     See dpriors() help file information. n.chains Number desired MCMC chains. burnin Number burnin/warmup iterations (including adaptive   iterations, target=\"jags\"). Defaults 4000 target=\"jags\"   500 Stan targets. sample total number samples take burnin. Defaults 10000 target=\"jags\" 1000 Stan targets. adapt target=\"jags\", number adaptive iterations use start   sampling. Defaults 1000. mcmcfile TRUE, JAGS/Stan model data written   files (lavExport directory). Can also supply character   string, serves name directory files written. mcmcextra list potential names syntax (unavailable   target=\"stan\"),   monitor, data, llnsamp. syntax object text string containing extra   code insert JAGS/Stan model syntax. data object   list extra data send JAGS/Stan model.    moment_match_k_threshold specified within data looic    model calculated using moment matching. monitor object   character vector containing extra JAGS/Stan parameters   monitor. llnsamp object relevant models ordinal   variables, specifies number samples drawn approximate   model log-likelihood (larger numbers imply higher accuracy   longer time). log-likelihood specifically used compute   information criteria. inits character string, options currently     \"simple\" (default), \"Mplus\", \"prior\", \"jags\".  first two     cases, parameter values set though estimated via     ML (see lavaan).  starting parameter value     chain perturbed original values     addition random uniform noise.  \"prior\" used, starting     parameter values obtained based prior distributions     (also trying ensure starting values crash     model estimation).  \"jags\", starting values     specified JAGS choose values (probably     crash Stan targets). can also supply     list starting values chain, list format can     obtained , e.g., blavInspect(fit, \"inits\"). Finally,     can specify starting values similar way lavaan,     using lavaan start argument (see lavaan     documentation options ). case, also set     inits=\"simple\", aware starting values     used chain. convergence Useful target=\"jags\". \"auto\", parameters   sampled convergence achieved (via autorun.jags()).   case, arguments burnin sample passed   autorun.jags() startburnin startsample,   respectively. Otherwise, parameters   sampled specified user (run.jags   defaults). target Desired MCMC sampling, \"stan\" (pre-compiled   marginal approach)   default. Also available \"vb\", calls rstan function   vb(). options include \"jags\", \"stancond\",   \"stanclassic\", sample latent variables provide   greater functionality (syntax written \"fly\").   slower less efficient. save.lvs sampled latent variables (factor scores)   saved? Logical; defaults FALSE wiggle Labels equality-constrained parameters   \"approximately\" equal. Can also \"intercepts\", \"loadings\",   \"regressions\", \"means\". wiggle.sd prior sd (normal distribution) used approximate equality   constraints. Can one value, (target=\"stan\") numeric vector   values length wiggle. prisamp samples drawn prior, instead   posterior (target=\"stan\" )? Logical; defaults FALSE jags.ic DIC computed JAGS way, addition BUGS way? Logical; defaults FALSE seed vector length n.chains (target   \"jags\") integer (target \"stan\") containing random   seeds MCMC run. NULL, seeds chosen randomly. bcontrol list containing additional parameters passed     run.jags (autorun.jags) stan.  See manpage functions     overview additional parameters can set.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"object inherits class lavaan, several methods   available, including summary method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"","code":"if (FALSE) { # The Holzinger and Swineford (1939) example HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- blavaan(HS.model, data=HolzingerSwineford1939,                auto.var=TRUE, auto.fix.first=TRUE,                auto.cov.lv.x=TRUE) summary(fit) coef(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit Structural Equation Models — bsem","title":"Fit Structural Equation Models — bsem","text":"Fit Structural Equation Model (SEM).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit Structural Equation Models — bsem","text":"","code":"bsem(..., cp = \"srs\",      dp = NULL, n.chains = 3, burnin, sample,      adapt, mcmcfile = FALSE, mcmcextra = list(), inits = \"simple\",      convergence = \"manual\", target = \"stan\", save.lvs = FALSE,      wiggle = NULL, wiggle.sd = 0.1, prisamp = FALSE, jags.ic = FALSE,      seed = NULL, bcontrol = list())"},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit Structural Equation Models — bsem","text":"... Default lavaan arguments.  See lavaan. cp Handling prior distributions covariance parameters:   possible values \"srs\" (default) \"fa\". Option \"fa\" available target=\"jags\". dp Default prior distributions different types     parameters, typically result call dpriors().     See dpriors() help file information. n.chains Number desired MCMC chains. burnin Number burnin/warmup iterations (including adaptive   iterations, target=\"jags\"). Defaults 4000 target=\"jags\"   500 Stan targets. sample total number samples take burnin. Defaults 10000 target=\"jags\" 1000 Stan targets. adapt target=\"jags\", number adaptive iterations use start   sampling. Defaults 1000. mcmcfile TRUE, JAGS/Stan model written file   (lavExport directory). Can also supply character   string, serves name directory files written. mcmcextra list potential names syntax (unavailable   target=\"stan\"),   monitor, data, llnsamp. syntax object text string containing extra   code insert JAGS/Stan model syntax. data object   list extra data send JAGS/Stan model.    moment_match_k_threshold specified within data looic    model calculated using moment matching. monitor object   character vector containing extra JAGS/Stan parameters   monitor. llnsamp object relevant models ordinal   variables, specifies number samples drawn approximate   model log-likelihood (larger numbers imply higher accuracy   longer time). log-likelihood specifically used compute   information criteria. inits character string, options currently     \"simple\" (default), \"Mplus\", \"prior\", \"jags\".  first two     cases, parameter values set though estimated via     ML (see lavaan).  starting parameter value     chain perturbed original values     addition random uniform noise.  \"prior\" used, starting     parameter values obtained based prior distributions     (also trying ensure starting values crash     model estimation).  \"jags\", starting values     specified JAGS choose values (probably     crash Stan targets). can also supply     list starting values chain, list format can     obtained , e.g., blavInspect(fit, \"inits\"). Finally,     can specify starting values similar way lavaan,     using lavaan start argument (see lavaan     documentation options ). case, also set     inits=\"simple\", aware starting values     used chain. convergence Useful target=\"jags\". \"auto\", parameters   sampled convergence achieved (via autorun.jags()).   case, arguments burnin sample passed   autorun.jags() startburnin startsample,   respectively. Otherwise, parameters   sampled specified user (run.jags   defaults). target Desired MCMC sampling, \"stan\" (pre-compiled   marginal approach)   default. Also available \"vb\", calls rstan function   vb(). options include \"jags\", \"stancond\",   \"stanclassic\", sample latent variables provide   greater functionality (syntax written \"fly\").   slower less efficient. save.lvs sampled latent variables (factor scores) saved? Logical; defaults FALSE wiggle Labels equality-constrained parameters   \"approximately\" equal. Can also \"intercepts\", \"loadings\",   \"regressions\", \"means\". wiggle.sd prior sd (normal distribution) used approximate equality   constraints. Can one value, (target=\"stan\") numeric vector   values length wiggle. prisamp samples drawn prior, instead   posterior (target=\"stan\" )? Logical; defaults FALSE jags.ic DIC computed JAGS way, addition BUGS way? Logical; defaults FALSE seed vector length n.chains (target   \"jags\") integer (target \"stan\") containing random   seeds MCMC run. NULL, seeds chosen randomly. bcontrol list containing additional parameters passed     run.jags (autorun.jags) stan.  See manpage functions     overview additional parameters can set.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit Structural Equation Models — bsem","text":"bsem function wrapper general     blavaan function, using following default     lavaan arguments:     int.ov.free = TRUE, int.lv.free = FALSE,     auto.fix.first = TRUE (unless std.lv = TRUE),     auto.fix.single = TRUE, auto.var = TRUE,     auto.cov.lv.x = TRUE,     auto.th = TRUE, auto.delta = TRUE,     auto.cov.y = TRUE.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit Structural Equation Models — bsem","text":"object class lavaan, several methods   available, including summary method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit Structural Equation Models — bsem","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit Structural Equation Models — bsem","text":"","code":"if (FALSE) { ## The industrialization and Political Democracy Example ## Bollen (1989), page 332 model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ y1 + a*y2 + b*y3 + c*y4      dem65 =~ y5 + a*y6 + b*y7 + c*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  ## unique priors for mv intercepts; parallel chains fit <- bsem(model, data=PoliticalDemocracy,             dp=dpriors(nu=\"normal(5,10)\")) summary(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":null,"dir":"Reference","previous_headings":"","what":"Specify Default Prior Distributions — dpriors","title":"Specify Default Prior Distributions — dpriors","text":"Specify \"default\" prior distributions classes model parameters.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Specify Default Prior Distributions — dpriors","text":"","code":"dpriors(..., target = \"stan\")"},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Specify Default Prior Distributions — dpriors","text":"... Parameter names paired desired priors (see example     ). target priors jags, stan (default), stanclassic?","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Specify Default Prior Distributions — dpriors","text":"prior distributions always use JAGS/Stan syntax parameterizations.   example, normal distribution JAGS parameterized via   precision, whereas normal distribution Stan parameterized   via standard deviation. User-specified prior distributions specific parameters   (using prior() operator within model syntax) always   override prior distributions set using dpriors(). parameter names : nu: Observed variable intercept parameters. alpha: Latent variable intercept parameters. lambda: Loading parameters. beta: Regression parameters. itheta: Observed variable precision parameters. ipsi: Latent variable precision parameters. rho: Correlation parameters (associated covariance parameters). ibpsi: Inverse covariance matrix     blocks latent variables (used target=\"jags\"). tau: Threshold parameters (ordinal data ). delta: Delta parameters (ordinal data ).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Specify Default Prior Distributions — dpriors","text":"character vector containing prior distribution type parameter.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Specify Default Prior Distributions — dpriors","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Specify Default Prior Distributions — dpriors","text":"","code":"dpriors(nu = \"normal(0,10)\", lambda = \"normal(0,1)\", rho = \"beta(3,3)\") #>                nu             alpha            lambda              beta  #>    \"normal(0,10)\"    \"normal(0,10)\"     \"normal(0,1)\"    \"normal(0,10)\"  #>             theta               psi               rho             ibpsi  #> \"gamma(1,.5)[sd]\" \"gamma(1,.5)[sd]\"       \"beta(3,3)\" \"wishart(3,iden)\"  #>               tau  #>   \"normal(0,1.5)\""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":null,"dir":"Reference","previous_headings":"","what":"blavaan Diagnostic Plots — plot.blavaan","title":"blavaan Diagnostic Plots — plot.blavaan","text":"Convenience functions create plots blavaan objects, via bayesplot package.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"blavaan Diagnostic Plots — plot.blavaan","text":"","code":"# S3 method for blavaan plot(x, pars = NULL, plot.type = \"trace\", showplot = TRUE, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"blavaan Diagnostic Plots — plot.blavaan","text":"x object class blavaan. pars Parameter numbers plot, numbers correspond order parameters reported coef() (also shown 'free' column parTable). numbers provided, free parameters plotted. plot.type type plot desired. name MCMC function, without mcmc_ prefix. showplot plot sent graphic device? Defaults TRUE. ... arguments sent bayesplot function.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"blavaan Diagnostic Plots — plot.blavaan","text":"previous versions blavaan, plotting functionality   handled separately JAGS Stan (using plot functionality   packages runjags rstan, respectively). uniformity,   plotting functionality now handled bayesplot. users desire   additional functionality immediately available, can extract matrix MCMC draws via .matrix(blavInspect(x, 'mcmc')).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"blavaan Diagnostic Plots — plot.blavaan","text":"invisible ggplot object , desired, can customized.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"blavaan Diagnostic Plots — plot.blavaan","text":"","code":"if (FALSE) { HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939)  # trace plots of free loadings plot(fit, pars = 1:6) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":null,"dir":"Reference","previous_headings":"","what":"Posterior Predictive Model Checks — ppmc","title":"Posterior Predictive Model Checks — ppmc","text":"function allows users conduct posterior predictive model check assess global local fit latent variable model using discrepancy function can applied lavaan model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Posterior Predictive Model Checks — ppmc","text":"","code":"ppmc(object, thin = 1, fit.measures = c(\"srmr\",\"chisq\"), discFUN = NULL,      conditional = FALSE)  # S4 method for blavPPMC summary(object, ...)  # S3 method for ppmc summary(object, discFUN, dist = c(\"obs\",\"sim\"),         central.tendency = c(\"mean\",\"median\",\"mode\"),         hpd = TRUE, prob = .95, to.data.frame = FALSE, diag = TRUE,         sort.by = NULL, decreasing = FALSE)  # S3 method for blavPPMC plot(x, ..., discFUN, element, central.tendency = \"\",      hpd = TRUE, prob = .95, nd = 3)  # S3 method for blavPPMC hist(x, ..., discFUN, element, hpd = TRUE, prob = .95,      printLegend = TRUE, legendArgs = list(x = \"topleft\"),      densityArgs = list(), nd = 3)  # S3 method for blavPPMC pairs(x, discFUN, horInd = 1:DIM, verInd = 1:DIM,       printLegend = FALSE, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Posterior Predictive Model Checks — ppmc","text":"object,x object class blavaan. thin Optional integer indicating much thin chain.     Default 1L, indicating thin chains object. fit.measures character vector indicating names global     discrepancy measures returned fitMeasures. Ignored     unless discFUN NULL, users may include     fitMeasures list discrepancy functions     discFUN. ordinal models, \"logl\" \"chisq\"     computations done via lavaan. discFUN function, list functions, can     called object class lavaan. function     must return object whose mode numeric, may     vector, matrix, multidimensional array.     summary plot methods, discFUN     character indicating discrepancy function     summarize. conditional logical indicating whether , artificial data     generation, condition estimated latent   variables. Requires model estimated save.lvs = TRUE. element numeric character indicating index (    dimension discFUN output, multiple) plot. horInd,verInd Similar element, numeric     character vector indicating indices matrix plot     scatterplot matrix. horInd==verInd, histograms     plotted upper triangle. dist character indicating whether summarize distribution     discFUN either observed simulated data. central.tendency character indicating statistics     used characterize location posterior (predictive)     distribution. default, 3 statistics returned     summary method, none plot method. posterior     mean labeled EAP expected posteriori estimate,     mode labeled MAP modal posteriori estimate. hpd logical indicating whether calculate highest     posterior density (HPD) credible interval discFUN. prob \"confidence\" level credible interval(s). nd number digits print scatterplot. .data.frame logical indicating whether summary     symmetric 2-dimensional matrix returned discFUN     unique elements stored rows data.frame can sorted     convenience identifying large discrepancies. discFUN     returns asymmetric 2-dimensional matrix, list matrices     returned summary can also converted data.frame. diag Passed lower.tri .data.frame=TRUE. sort.character. summary returns data.frame,     can sorted column name using order. Note     discFUN returns asymmetric 2-dimensional matrix,     data.frame returned list sorted     independently, rows unlikely consistent across     summary statistics. decreasing Passed order     !.null(sort.). ... Additional graphical parameters     passed plot.default. printLegend logical. TRUE (default), legend     printed histogram legendArgs list arguments passed     legend function.  default argument list     placing legend top-left figure. densityArgs list arguments passed     density function, used obtain densities     hist method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Posterior Predictive Model Checks — ppmc","text":"S4 object class blavPPMC consisting 5 list slots: @discFUN user-supplied discFUN, call     fitMeasures returns fit.measures. @dims dimensions object returned     discFUN. @PPP posterior predictive p value     discFUN element. @obsDist posterior distribution realize values     discFUN applied observed data. @simDist posterior predictive distribution values     discFUN applied data simulated posterior samples. summary() method returns numeric vector discFUN returns scalar, data.frame one discrepancy function per row     discFUN returns numeric vector, list     one summary statistic per element discFUN returns matrix multidimensional array. plot pairs methods invisibly return NULL,   printing plot (scatterplot matrix) current device. hist method invisibly returns list arguments can   passed function list element named.  Users   can edit arguments list customize histograms.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Posterior Predictive Model Checks — ppmc","text":"Terrence D. Jorgensen (University Amsterdam; TJorgensen314@gmail.com)","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Posterior Predictive Model Checks — ppmc","text":"Levy, R. (2011). Bayesian data--model fit assessment structural equation   modeling. Structural Equation Modeling, 18(4), 663--685.   doi:10.1080/10705511.2011.607723","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Posterior Predictive Model Checks — ppmc","text":"","code":"if (FALSE) { HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 ' ## fit single-group model fit <- bcfa(HS.model, data = HolzingerSwineford1939,              n.chains = 2, burnin = 1000, sample = 500) ## fit multigroup model fitg <- bcfa(HS.model, data = HolzingerSwineford1939,              n.chains = 2, burnin = 1000, sample = 500, group = \"school\")   ## Use fit.measures as a shortcut for global fitMeasures only ## - Note that indices calculated from the \"df\" are only appropriate under ##   noninformative priors, such that pD approximates the number of estimated ##   parameters counted under ML estimation; incremental fit indices ##   introduce further complications)  AFIs <- ppmc(fit, thin = 10, fit.measures = c(\"srmr\",\"chisq\",\"rmsea\",\"cfi\")) summary(AFIs)                 # summarize the whole vector in a data.frame hist(AFIs, element = \"rmsea\") # only plot one discrepancy function at a time plot(AFIs, element = \"srmr\")   ## define a list of custom discrepancy functions ## - (global) fit measures ## - (local) standardized residuals  discFUN <- list(global = function(fit) {                   fitMeasures(fit, fit.measures = c(\"cfi\",\"rmsea\",\"srmr\",\"chisq\"))                 },                 std.cov.resid = function(fit) lavResiduals(fit, zstat = FALSE,                                                            summary = FALSE)$cov,                 std.mean.resid = function(fit) lavResiduals(fit, zstat = FALSE,                                                             summary = FALSE)$mean) out1g <- ppmc(fit, discFUN = discFUN)  ## summarize first discrepancy by default (fit indices) summary(out1g) ## some model-implied correlations look systematically over/underestimated summary(out1g, discFUN = \"std.cov.resid\", central.tendency = \"EAP\") hist(out1g, discFUN = \"std.cov.resid\", element = c(1, 7)) plot(out1g, discFUN = \"std.cov.resid\", element = c(\"x1\",\"x7\")) ## For ease of investigation, optionally export summary as a data.frame, ## sorted by size of average residual summary(out1g, discFUN = \"std.cov.resid\", central.tendency = \"EAP\",         to.data.frame = TRUE, sort.by = \"EAP\") ## or sorted by size of PPP summary(out1g, discFUN = \"std.cov.resid\", central.tendency = \"EAP\",         to.data.frame = TRUE, sort.by = \"PPP_sim_LessThan_obs\")  ## define a list of custom discrepancy functions for multiple groups ## (return each group's numeric output using a different function)  disc2g <- list(global = function(fit) {                  fitMeasures(fit, fit.measures = c(\"cfi\",\"rmsea\",\"mfi\",\"srmr\",\"chisq\"))                },                cor.resid1 = function(fit) lavResiduals(fit, zstat = FALSE,                                                        type = \"cor.bollen\",                                                        summary = FALSE)[[1]]$cov,                cor.resid2 = function(fit) lavResiduals(fit, zstat = FALSE,                                                        type = \"cor.bollen\",                                                        summary = FALSE)[[2]]$cov) out2g <- ppmc(fitg, discFUN = disc2g, thin = 2) ## some residuals look like a bigger problem in one group than another pairs(out2g, discFUN = \"cor.resid1\", horInd = 1:3, verInd = 7:9) # group 1 pairs(out2g, discFUN = \"cor.resid2\", horInd = 1:3, verInd = 7:9) # group 2  ## print all to file: must be a LARGE picture. First group 1 ... png(\"cor.resid1.png\", width = 1600, height = 1200) pairs(out2g, discFUN = \"cor.resid1\") dev.off() ## ... then group 2 png(\"cor.resid2.png\", width = 1600, height = 1200) pairs(out2g, discFUN = \"cor.resid2\") dev.off() }"},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":null,"dir":"Reference","previous_headings":"","what":"Standardized Posterior — standardizedPosterior","title":"Standardized Posterior — standardizedPosterior","text":"Standardized posterior distribution latent variable model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Standardized Posterior — standardizedPosterior","text":"","code":"standardizedPosterior(object, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Standardized Posterior — standardizedPosterior","text":"object object class blavaan. ... Additional arguments passed lavaan's   standardizedSolution()","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Standardized Posterior — standardizedPosterior","text":"allowed standardizedSolution() arguments type, cov.std, remove.eq, remove.ineq, remove.def. arguments immediately suited posterior distributions.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Standardized Posterior — standardizedPosterior","text":"matrix containing standardized posterior draws, rows draws   columns parameters.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Standardized Posterior — standardizedPosterior","text":"","code":"if (FALSE) { model <- '    # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ y1 + a*y2 + b*y3 + c*y4      dem65 =~ y5 + a*y6 + b*y7 + c*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit <- bsem(model, data=PoliticalDemocracy,             dp=dpriors(nu=\"dnorm(5,1e-2)\"),             bcontrol=list(method=\"rjparallel\"))  standardizedPosterior(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-05-2","dir":"Changelog","previous_headings":"","what":"Version 0.5-2","title":"Version 0.5-2","text":"CRAN release: 2023-09-25","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-5-2","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.5-2","text":"maintenance release, primarily adding new array declaration syntax Stan models (syntax became available new version rstan).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-5-2","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.5-2","text":"blavCompare() work models meanstructure = FALSE (reported Pedro Ribeiro).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-05-1","dir":"Changelog","previous_headings":"","what":"Version 0.5-1","title":"Version 0.5-1","text":"CRAN release: 2023-08-29","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-5-1","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.5-1","text":"Two-level models now supported (complete, continuous data) via cluster argument.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-5-1","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.5-1","text":"two-level model specification, levels labeled “within” “”. restrictive lavaan specification. target=“jags”, latent variable extraction via blavInspect(, “lvs”) fails (reported Joseph Saraceno).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-8","dir":"Changelog","previous_headings":"","what":"Version 0.4-8","title":"Version 0.4-8","text":"CRAN release: 2023-06-12","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-8","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-8","text":"maintenance release bug fixes changes compiler settings","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-8","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-8","text":"certain models residual correlations /correlated factors, initial values target=‘stan’ lead non-positive definite matrices (reported Yuanyuan Hu). models latent variable regressed observed variable (lv ~ ov), latent variable samples account mean observed variable (centered around 0 constant).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-7","dir":"Changelog","previous_headings":"","what":"Version 0.4-7","title":"Version 0.4-7","text":"CRAN release: 2023-03-01","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-7","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-7","text":"primarily update address C++14 vs C++17 compilation issue identified CRAN bugs 0.4-6 also fixed","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-7","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-7","text":"Sampling priors (prisamp = TRUE) fails models meanstructure = FALSE; posterior still estimated (reported Armel Brizuela Rodríguez). target = “jags”, models single-indicator latent variable, latent variable regressed variables, return incorrect parameter estimates (reported Brad Cosentino).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-6","dir":"Changelog","previous_headings":"","what":"Version 0.4-6","title":"Version 0.4-6","text":"CRAN release: 2023-02-11","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-6","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-6","text":"target = “stan”, meanstructure=FALSE allowed, along use sample.cov sample.nobs instead raw data Users warned priors covariance matrices neither diagonal unrestricted models observed variable intercepts appear latent intercept vector (alpha), default priors come observed intercept vector nu (user expect) inits = “simple” now default (instead “prior”), address convergence problems stan targets, “:=” can now used identity function target = “stan”, fix missing data issue 0.4-3 (complete data one group ) Column names added blavPredict(, type=“lv”)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-6","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-6","text":"blavFitIndices() save.lvs = TRUE work correctly models without meanstructure. Workaround use meanstructure = TRUE model estimation command (reported Charles Hofacker). lavaan summary() method sometimes called instead blavaan summary() method (reported multiple users, Shu Fai Cheung providing helpful examples).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-3","dir":"Changelog","previous_headings":"","what":"Version 0.4-3","title":"Version 0.4-3","text":"CRAN release: 2022-05-11","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-3","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-3","text":"target = “stan”, models run faster earlier versions (use sufficient statistics) Posterior summaries faster ordinal models (using mnormt::sadmvn() default) Variational Bayes option added: target=“vb”, uses rstan::vb() cmdstanr functionality added: target=“cmdstanr”, uses model target=“stan” Fix blavInspect(., “lvs”/“lvmeans”) multiple groups + missing data Fixes ppmc() ordinal models; blavFitIndices() turned ordinal models (research needed) loo() moment matching available passing mcmcextra = list(data = list(moment_match_k_threshold))","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-3","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-3","text":"target = “stan” fails complete data one group missing data another group (reported Ronja Runge). blavPredict(, type=“ymis”) still available models ordinal variables","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-1","dir":"Changelog","previous_headings":"","what":"Version 0.4-1","title":"Version 0.4-1","text":"CRAN release: 2022-01-27","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-1","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-1","text":"Functionality ordinal observed variables now available. models missing data, posterior summaries sped (log-likelihood computations now done Stan).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-1","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-1","text":"blavPredict(, type=“ymis”) working models ordinal variables blavInspect(, ‘lvs’) (, ‘lvmeans’) can fail models combination multiple groups, missing values, excluded cases blavFitIndices() ppmc() working models ordinal variables, may indicate excessively bad fit blavFitIndices(, rescale=“mcmc”) fails","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-18","dir":"Changelog","previous_headings":"","what":"Version 0.3-18","title":"Version 0.3-18","text":"CRAN release: 2021-11-27","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-18","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-18","text":"version adds reference new JSS paper, including DOI, corrects inconsistent version dependency. changes compared 0.3-17.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-17","dir":"Changelog","previous_headings":"","what":"Version 0.3-17","title":"Version 0.3-17","text":"CRAN release: 2021-07-19","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-17","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-17","text":"maintenance release correct major bugs previous version.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-16","dir":"Changelog","previous_headings":"","what":"Version 0.3-16","title":"Version 0.3-16","text":"CRAN release: 2021-07-11","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-16","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-16","text":"blavPredict() function added predicting latent variables missing data. posterior summaries sped . (fitMeasures available test=“none”) bug fixes previous version.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-16","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-16","text":"certain models missing data, ppp-values incorrect (sometimes equaling 1.0). target=“stan”, multiple group models fail cases missing observed variables (reported DeAnne Hunter).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-15","dir":"Changelog","previous_headings":"","what":"Version 0.3-15","title":"Version 0.3-15","text":"CRAN release: 2021-02-19","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-15","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-15","text":"Added S3 summary() method ppmc Posterior intervals summary() bug fixed","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-15","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-15","text":"summary() method ppmc() fitIndices() always work correctly. Jacobian incorrect target=“stan”, (non-default) priors placed precisions variances instead standard deviations. impact estimates posterior variability (reported Roy Levy).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-14","dir":"Changelog","previous_headings":"","what":"Version 0.3-14","title":"Version 0.3-14","text":"CRAN release: 2021-01-20 (version 0.3-13 violated CRAN policy)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-14","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-14","text":"maintenance release response change package Matrix.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-14","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-14","text":"Posterior intervals NA summary(). Workarounds use parameterEstimates() (intervals assuming posterior normality) compute using posterior samples (`blavInspect(fit, “mcmc”)’)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-12","dir":"Changelog","previous_headings":"","what":"Version 0.3-12","title":"Version 0.3-12","text":"CRAN release: 2020-11-12 (version 0.3-11 failed Windows CRAN checks)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-12","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-12","text":"vector values wiggle.sd allowed different priors approximate equality constraints logical argument “prisamp” added, sampling model’s prior target=“stan”, lkj prior used unrestricted lv correlation matrices default priors conditional approaches (targets jags stanclassic) revert placed precisions (opposed SDs), improvement sampling efficiency","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-10","dir":"Changelog","previous_headings":"","what":"Version 0.3-10","title":"Version 0.3-10","text":"CRAN release: 2020-08-03","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-10","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-10","text":"save.lvs=TRUE works missing data target=“stan” new arguments “wiggle” “wiggle.sd” approximate equality constraints target=“stan”","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-10","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-10","text":"plot labels target=“stan” sometimes incorrect (displaying parameter different panel label). complex equality constraints sometimes ignored (target=“jags” “stanclassic”) equality constraints std.lv=TRUE sometimes fail (target=“stan”) placing priors variances precisions yields incorrect results (target=“stan”; reported Roy Levy)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-9","dir":"Changelog","previous_headings":"","what":"Version 0.3-9","title":"Version 0.3-9","text":"CRAN release: 2020-03-09","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-9","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-9","text":"improvements save.lvs=TRUE target=“stan”. target=“stancond” added, experimental, noncentered Stan approach. bug fixes prior settings std.lv target=“stan”, defined parameters.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-9","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-9","text":"target=“stan”, problems sampling lvs multiple groups missing data. Errors blavCompare() blavFitIndices() due version updates packages. target=“stan”, models std.lv=TRUE converge.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-8","dir":"Changelog","previous_headings":"","what":"Version 0.3-8","title":"Version 0.3-8","text":"CRAN release: 2019-11-19","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-8","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-8","text":"post-estimation, posterior predictive computations sped considerably. 0.3-7 bugs fixed.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-8","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-8","text":"target=“stan” std.lv=TRUE, estimation fails certain (growth) models (reported Mauricio Garnier-Villareal). defined variables fail target=“jags” “stanclassic” (reported Mariëlle Zondervan-Zwijnenburg). User-specified priors sometimes placed wrong parameter, related 0.3-7 bug (reported Mauricio Garnier-Villareal). dpriors() issue 0.3-3 remains.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-7","dir":"Changelog","previous_headings":"","what":"Version 0.3-7","title":"Version 0.3-7","text":"CRAN release: 2019-09-27","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-7","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-7","text":"target=“stan”, gamma priors can now placed user’s choice variances, standard deviations, precisions. plot() now works uniformly across Stan JAGS, relying bayesplot. post-MCMC parallelization now handled via future.apply package (requires extra “plan” command user, works windows). 0.3-6 bugs fixed.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-7","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-7","text":"blavInspect(, ‘lvmeans’) returns rows wrong order target=“stan” (reported Mehdi Momen). User-specified priors sometimes placed wrong parameter, target=“stan” (reported Enrico Toffalini). dpriors() issue 0.3-3 remains.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-6","dir":"Changelog","previous_headings":"","what":"Version 0.3-6","title":"Version 0.3-6","text":"CRAN release: 2019-08-08","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-6","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-6","text":"fixes stan plot bug 0.3-5.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-6","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-6","text":"user-specified priors correlation parameters silently ignored target=“stan” (reported James Uanhoro). save.lvs=TRUE work target=“stan” (reported Mauricio Garnier-Villareal). dpriors() issue 0.3-3 remains.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-5","dir":"Changelog","previous_headings":"","what":"Version 0.3-5","title":"Version 0.3-5","text":"CRAN release: 2019-08-03","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-5","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-5","text":"target=“stan” now default, using pre-compiled Stan model instead “fly” code. ppmc() function added Terrence Jorgensen, facilitating posterior predictive checks. default priors changed gamma precisions gamma standard deviations.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-5","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-5","text":"Stan plot method silently fails (reported Matt Yalch). dpriors() issue 0.3-3 remains.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-4","dir":"Changelog","previous_headings":"","what":"Version 0.3-4","title":"Version 0.3-4","text":"CRAN release: 2019-01-11","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-4","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-4","text":"Add function standardizedPosterior() standardizing posterior draws. Turn posterior modes target=“jags”, due conflict current versions runjags modeest. Rearrange posterior predictive internals.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-4","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-4","text":"dpriors() issue 0.3-3 remains. target=“jags”, lv means obtained blavInspect() (via argument ‘lvmeans’) incorrect. (reported Mauricio Garnier-Villareal) Use plot() target=“stan” causes problems future blavInspect() calls.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-3","dir":"Changelog","previous_headings":"","what":"Version 0.3-3","title":"Version 0.3-3","text":"CRAN release: 2018-10-31","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-3","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-3","text":"convergence=“auto”, max time previously 5 min (undocumented). now Inf. Axis labels (parameter names) now sensible convergence plots. Relative effective sample size now used compute loo/waic SEs, SEs now returned via fitMeasures(). Added unit testing via package testthat. Fixed bugs 0.3-2 (exception identity assignments using ‘:=’)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-3","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-3","text":"Use ‘dpriors()’: observed variable precisions assigned latent precision (ipsi) prior; latent means assigned observed mean (nu) prior.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-2","dir":"Changelog","previous_headings":"","what":"Version 0.3-2","title":"Version 0.3-2","text":"CRAN release: 2018-06-10","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-2","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-2","text":"Conditional (latent variables) information criteria available save.lvs = TRUE. Experimental function ‘blavFitIndices()’ added Bayesian versions SEM metrics, contributed Terrence Jorgensen. blavaan “intelligently” chooses target, either runjags rstan () installed. Fixed bugs 0.3-1, especially related missing data Stan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-2","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-2","text":"Errors Stan models std.lv=TRUE, observed variable regressed latent variable (reported Bo Zhang). Error identity assignments using ‘:=’ (reported Marco Tullio Liuzza). Explicitly adding argument ‘.fit=TRUE’ fails (reported Esteban Montenegro).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-1","dir":"Changelog","previous_headings":"","what":"Version 0.3-1","title":"Version 0.3-1","text":"CRAN release: 2018-01-12","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-1","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-1","text":"Stan export now supported; use target=“stan”. Improved handling complex models, including growth/change models. Sampling factor scores (lvs) available via ‘save.lvs=TRUE’. Samples/means can obtained supplying arguments ‘lvs’ ‘lvmeans’ ‘blavInspect()’. Fixed bugs 0.2-4.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-1","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-1","text":"Errors Stan models missing data, exogenous (“x”) variables. Errors multi-group Stan models std.lv=TRUE.","code":""}]
+[{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Approximate fit indices","text":"SEM, one first steps evaluate model’s global fit. commonly done presenting multiple fit indices, common based model’s \\(\\chi^2\\). developed Bayesian versions indices (Garnier-Villarreal Jorgensen 2020) can computed blavaan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"noncentrality-based-fit-indices","dir":"Articles","previous_headings":"","what":"Noncentrality-Based Fit Indices","title":"Approximate fit indices","text":"group indices compares hypothesized model perfect saturated model. specifically uses noncentrality parameter \\(\\hat{\\lambda} = \\chi^2 - df\\), df adjusted different model/data characterictics. Specific indices include Root Mean Square Error approximation (RMSEA), McDonald’s centrality index (Mc), gamma-hat (\\(\\hat{\\Gamma}\\)), adjusted gamma-hat (\\(\\hat{\\Gamma}_{adj}\\)). show example Holzinger Swineford (1939) example. first estimate SEM/CFA model usual need pass model blavFitIndices() function Finally, can describe posterior distribution indices summary() function. call, see 3 central tendency measures (mean median, mode), standard deviation, 90% Credible Interval","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939, std.lv=TRUE) gl_fits <- blavFitIndices(fit) summary(gl_fits, central.tendency = c(\"mean\",\"median\",\"mode\"), prob = .90) ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for devm-based fit indices: ##  ##                EAP Median   MAP    SD lower upper ## BRMSEA       0.097  0.096 0.095 0.005 0.088 0.105 ## BGammaHat    0.957  0.957 0.958 0.004 0.950 0.964 ## adjBGammaHat 0.910  0.911 0.913 0.009 0.896 0.925 ## BMc          0.903  0.904 0.906 0.010 0.889 0.919"},{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"incremental-fit-indices","dir":"Articles","previous_headings":"","what":"Incremental Fit Indices","title":"Approximate fit indices","text":"Another group fit indices compares hypothesized model worst possible model, called incremental indices. indices compare model’s \\(\\chi^2_H\\) null model’s \\(\\chi^2_0\\) different ways. Indices include Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), Normed Fit Index (NFI). estimate indices need defined estimate respective null model. standard null model used default frequentist SEM programs (like lavaan) includes indicators variances intercepts, covariances items. can specify null model including respective indicator variances model syntax, hypothesized null models, pass blavFitIndices function, now provide types fit indices summary() method now presents central tendicy measure asked , standard deviation, credible interval noncentrality incremental fit indices.","code":"HS.model_null <- ' x1 ~~ x1  x2 ~~ x2  x3 ~~ x3 x4 ~~ x4 x5 ~~ x5 x6 ~~ x6 x7 ~~ x7 x8 ~~ x8 x9 ~~ x9 '  fit_null <- bcfa(HS.model_null, data=HolzingerSwineford1939) gl_fits_all <- blavFitIndices(fit, baseline.model = fit_null)  summary(gl_fits_all, central.tendency = c(\"mean\",\"median\",\"mode\"), prob = .90) ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for devm-based fit indices: ##  ##                EAP Median   MAP    SD lower upper ## BRMSEA       0.097  0.096 0.095 0.005 0.088 0.105 ## BGammaHat    0.957  0.957 0.958 0.004 0.950 0.964 ## adjBGammaHat 0.910  0.911 0.913 0.009 0.896 0.925 ## BMc          0.903  0.904 0.906 0.010 0.889 0.919 ## BCFI         0.930  0.931 0.933 0.007 0.919 0.942 ## BTLI         0.887  0.888 0.891 0.012 0.869 0.906 ## BNFI         0.910  0.910 0.912 0.007 0.899 0.921"},{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"access-the-indices-posterior-distributions","dir":"Articles","previous_headings":"","what":"Access the indices posterior distributions","title":"Approximate fit indices","text":"can also extract posterior distributions respective indices, way can explore details. example, diagnostic plots using bayesplot package. saved posterior distributions, can explore histogram scatterplots indices.","code":"dist_fits <- data.frame(gl_fits_all@indices) head(dist_fits) ##       BRMSEA BGammaHat adjBGammaHat       BMc      BCFI      BTLI      BNFI ## 1 0.10222768 0.9522573    0.9004844 0.8933233 0.9232277 0.8750093 0.9026881 ## 2 0.09272435 0.9603860    0.9174279 0.9113684 0.9363476 0.8963694 0.9151496 ## 3 0.09481637 0.9586530    0.9138157 0.9075169 0.9340132 0.8925688 0.9130789 ## 4 0.09097977 0.9618062    0.9203882 0.9145267 0.9387426 0.9002686 0.9174598 ## 5 0.09824281 0.9557453    0.9077548 0.9010598 0.9291252 0.8846109 0.9083685 ## 6 0.11322189 0.9420630    0.8792351 0.8707717 0.9050757 0.8454565 0.8850777 mcmc_pairs(dist_fits, pars = c(\"BRMSEA\",\"BGammaHat\",\"BCFI\",\"BTLI\"),            diag_fun = \"hist\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/approx_fi.html","id":"summary","dir":"Articles","previous_headings":"","what":"Summary","title":"Approximate fit indices","text":"can estimate posterior distributions \\(\\chi^2\\) based global fit indices. Notice presented fit indices based recommended method devM recommended number parameters metric loo. can adjusted user desired. general recommendation prefer \\(\\hat{\\Gamma}\\) CFI, shown less sensitive model data characteristics. defaults recommendations made based previous simulation research. details fit indices please see Garnier-Villarreal Jorgensen (2020).","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_efficiency.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Convergence and Efficiency Evaluation","text":"Bayesian models estimated Markov-Chain Monte Carlo (MCMC) sampler, model estimation doesn’t stop achieved convergence criteria. run long desired (determined burnin sample arguments), need evaluate convergence efficiency estimated posterior distributions. analyze results convergence achieved, judged metrics described . example use Industrialization Political Democracy example (Bollen 1989).","code":"model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000)"},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_efficiency.html","id":"convergence","dir":"Articles","previous_headings":"","what":"Convergence","title":"Convergence and Efficiency Evaluation","text":"primary convergence diagnostic \\(\\hat{R}\\), compares - within-chain samples model parameters univariate quantities interest (Vehtari et al. 2021). chains mixed well (ie, - within-chain estimates don’t agree), \\(\\hat{R}\\) larger 1. recommend running least three chains default using posterior samples \\(\\hat{R} < 1.05\\) parameters. blavaan presents \\(\\hat{R}\\) reported underlying MCMC program, either Stan JAGS (Stan default). can obtain \\(\\hat{R}\\) summary() function, can also extract blavInspect() function large models can cumbersome look entries. can instead find largest \\(\\hat{R}\\) see less \\(1.05\\) \\(\\hat{R} < 1.05\\) can establish MCMC chains converged stable solution. model converged, might increase number burnin iterations /change model priors dpriors() function. address issues model failed converge due needing iterations due model misspecification (bad priors). rule thumb, seldom see model require 1,000 burnin samples Stan. model converging 1,000 burnin samples, likely default prior distributions clash data. can happen, e.g., variables contain values 100s 1000s.","code":"blavInspect(fit, \"rhat\") ##   ind60=~x1   ind60=~x2   ind60=~x3           a           b           c  ##   1.0018687   1.0011498   1.0019669   1.0010774   1.0035505   1.0009847  ##           d           a           b           c           d dem60~ind60  ##   1.0037108   1.0010774   1.0035505   1.0009847   1.0037108   1.0025700  ## dem65~ind60 dem65~dem60      y1~~y5      y2~~y4      y2~~y6      y3~~y7  ##   0.9992636   1.0013518   1.0004050   0.9999044   0.9996021   0.9997691  ##      y4~~y8      y6~~y8      x1~~x1      x2~~x2      x3~~x3      y1~~y1  ##   0.9993516   1.0003211   0.9992072   1.0001601   1.0013318   1.0006956  ##      y2~~y2      y3~~y3      y4~~y4      y5~~y5      y6~~y6      y7~~y7  ##   1.0009872   1.0000227   0.9997030   1.0005515   0.9992962   1.0018510  ##      y8~~y8        x1~1        x2~1        x3~1        y1~1        y2~1  ##   1.0000982   1.0011787   1.0012383   1.0013904   1.0017004   1.0011649  ##        y3~1        y4~1        y5~1        y6~1        y7~1        y8~1  ##   1.0013353   1.0025494   1.0054546   1.0041114   1.0031621   1.0043085 max(blavInspect(fit, \"psrf\")) ## [1] 1.005455 fit <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=1000, sample=1000)"},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_efficiency.html","id":"efficiency","dir":"Articles","previous_headings":"","what":"Efficiency","title":"Convergence and Efficiency Evaluation","text":"also evaluate efficiency posterior samples. Effective sample size (ESS) useful measure sampling efficiency, well defined even chains finite mean variance (Vehtari et al. 2021). short, posterior samples produced MCMC autocorrelated. means , draw 500 posterior samples, 500 independent pieces information posterior distribution, samples autocorlated. ESS metric like currency conversion, telling much autocorrelated samples worth convert indepndent samples. blavaan can print summary function neff argument can also extract blavInspect() function ESS sample size, least 100 (optimally, much 100) times number chains order reliable indicate estimates posterior quantiles reliable. example, 3 chains, want see least neff=300 every parameter. can easily find lowest ESS min() function:","code":"summary(fit, neff=T) blavInspect(fit, \"neff\") ##   ind60=~x1   ind60=~x2   ind60=~x3           a           b           c  ##    1676.611    1626.443    1861.550    1413.085    1591.407    1675.781  ##           d           a           b           c           d dem60~ind60  ##    1240.096    1413.085    1591.407    1675.781    1240.096    2218.345  ## dem65~ind60 dem65~dem60      y1~~y5      y2~~y4      y2~~y6      y3~~y7  ##    2401.326    2458.749    1664.306    1924.265    2945.089    2255.887  ##      y4~~y8      y6~~y8      x1~~x1      x2~~x2      x3~~x3      y1~~y1  ##    2026.768    1394.098    2632.528    2022.808    2820.950    2514.076  ##      y2~~y2      y3~~y3      y4~~y4      y5~~y5      y6~~y6      y7~~y7  ##    2726.223    2835.621    1920.701    1780.442    2433.502    1597.422  ##      y8~~y8        x1~1        x2~1        x3~1        y1~1        y2~1  ##    1278.782    1212.542    1200.562    1368.136    1367.420    1712.215  ##        y3~1        y4~1        y5~1        y6~1        y7~1        y8~1  ##    1608.132    1305.350    1199.165    1284.532    1220.148    1130.688 min(blavInspect(fit, \"neff\")) ## [1] 1130.688"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_loop.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Convergence loop","text":"many cases need run BSEM models multiple times converged. can take might want R . tutorial shows use loop increase number burnin samples model converges, can let run without adjust every time","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_loop.html","id":"convergence-loop","dir":"Articles","previous_headings":"","what":"Convergence loop","title":"Convergence loop","text":"start writing model syntax always. instead running blavaan functions usual, run inside loop follows. loop starts need define starting BURN <- 0 number iterations, convergence value higher desired rhat <- 20. loop set sto stop convergence criteria (rhat) lower desired value, like \\(\\hat{R} < 1.05\\), specify (rhat > 1.05), meaning loop continue long rhat higher 1.05. Thn inside loop increase number BURN iterations 1000 example. estimating model, evaluate convergence getting highest estimated \\(\\hat{R}\\), printing screen see far model converging. Note increasing number burnin iterations, keeping number saved samples (1000 case). want can increase decrease number saved iterations according case. can visualize convergence trace plots","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  BURN <- 0 rhat <- 20 while(rhat > 1.05) {      BURN <- BURN + 1000 ### increase burn in by 1000 iterations every time      fit <- bcfa(HS.model, std.lv=T,                data=HolzingerSwineford1939,                n.chains = 3, burnin = BURN,               sample=1000)   rhat <- max(blavInspect(fit, \"psrf\"), na.rm=T)   print(paste0(\"Rhat=\",rhat))   } print(paste0(\"Rhat=\",rhat)) ## [1] \"Rhat=1.00250742312635\" plot(fit, pars = 1:9, plot.type = \"trace\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/convergence_loop.html","id":"convergence-criteria","dir":"Articles","previous_headings":"","what":"Convergence criteria","title":"Convergence loop","text":"example use \\(\\hat{R} < 1.05\\) convergence criteria. recommend use \\(\\hat{R} < 1.01\\) convergence criteria, higher. \\(\\hat{R}\\) approximates 1, can argue model converged estimates achieve stability within chains (Gelman et al. 2014)","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/cross_loadings_strong_priors.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Cross-loadings with strong priors","text":"advantage BSEM can use priors set soft constraints model, estimating parameter strong prior. way parameter estimated, prior restrict possible values. suggested Muthén Asparouhov (2012), way estimate possible cross-loadings CFA. way, posterior distribution restricted parameters includes values outside strong prior, can interpreted model modification. means parameters less restricted, prior distribution relaxed. tutorial present estimate CFA possible cross-loadings restricted strong priors.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/cross_loadings_strong_priors.html","id":"cross-loadings","dir":"Articles","previous_headings":"","what":"Cross-loadings","title":"Cross-loadings with strong priors","text":"show example Holzinger Swineford (1939) data. First estimate regular model cross-loadings default priors. can see overall model results summary() function, looking posterior distribution factor loadings, correlations, intercepts variances. Next, add possible cross-loadings strong prior \\(N(0, \\sigma = 0.08)\\). prior centers loadings around 0 allows little space move. can look summary() model evaluate cross-loadings. can specifically see whether cross-loadings seem large enough suggest kept model, looking posterior mean (Estimate) credible interval. suggest simply look whether CI excludes 0 (similar null hypothesis), evaluate whether minimum value CI (value closer 0) far enough away 0 relavant instead just different 0.","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit_df <- bcfa(HS.model, data=HolzingerSwineford1939,              std.lv=TRUE, meanstructure=T) summary(fit_df) ## blavaan 0.5.2.1191 ended normally after 1000 iterations ##  ##   Estimator                                      BAYES ##   Optimization method                             MCMC ##   Number of model parameters                        30 ##  ##   Number of observations                           301 ##  ##   Statistic                                 MargLogLik         PPP ##   Value                                      -3870.865       0.000 ##  ## Parameter Estimates: ##  ##  ## Latent Variables: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##   visual =~                                                                     ##     x1                0.908    0.089    0.735    1.085    1.000    normal(0,10) ##     x2                0.502    0.082    0.344    0.664    0.999    normal(0,10) ##     x3                0.661    0.082    0.502    0.821    1.000    normal(0,10) ##   textual =~                                                                    ##     x4                1.002    0.058    0.893    1.117    1.000    normal(0,10) ##     x5                1.116    0.065    0.994    1.245    1.000    normal(0,10) ##     x6                0.929    0.056    0.821    1.041    1.000    normal(0,10) ##   speed =~                                                                      ##     x7                0.619    0.077    0.465    0.769    1.002    normal(0,10) ##     x8                0.735    0.078    0.580    0.887    1.000    normal(0,10) ##     x9                0.680    0.080    0.531    0.848    1.001    normal(0,10) ##  ## Covariances: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##   visual ~~                                                                     ##     textual           0.450    0.064    0.315    0.570    0.999     lkj_corr(1) ##     speed             0.460    0.086    0.284    0.619    1.001     lkj_corr(1) ##   textual ~~                                                                    ##     speed             0.276    0.073    0.129    0.414    0.999     lkj_corr(1) ##  ## Intercepts: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##    .x1                4.937    0.067    4.810    5.072    0.999    normal(0,32) ##    .x2                6.088    0.065    5.959    6.217    1.000    normal(0,32) ##    .x3                2.251    0.066    2.121    2.381    1.000    normal(0,32) ##    .x4                3.061    0.068    2.932    3.195    1.000    normal(0,32) ##    .x5                4.341    0.075    4.196    4.483    1.000    normal(0,32) ##    .x6                2.186    0.065    2.061    2.314    1.000    normal(0,32) ##    .x7                4.187    0.063    4.064    4.311    0.999    normal(0,32) ##    .x8                5.528    0.059    5.412    5.639    1.000    normal(0,32) ##    .x9                5.375    0.060    5.257    5.493    0.999    normal(0,32) ##     visual            0.000                                                     ##     textual           0.000                                                     ##     speed             0.000                                                     ##  ## Variances: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##    .x1                0.557    0.131    0.278    0.800    1.000 gamma(1,.5)[sd] ##    .x2                1.152    0.108    0.954    1.381    1.000 gamma(1,.5)[sd] ##    .x3                0.859    0.102    0.664    1.065    1.000 gamma(1,.5)[sd] ##    .x4                0.379    0.050    0.286    0.482    1.001 gamma(1,.5)[sd] ##    .x5                0.455    0.059    0.342    0.572    1.000 gamma(1,.5)[sd] ##    .x6                0.362    0.047    0.277    0.462    1.000 gamma(1,.5)[sd] ##    .x7                0.819    0.092    0.652    1.009    1.002 gamma(1,.5)[sd] ##    .x8                0.500    0.094    0.328    0.682    1.002 gamma(1,.5)[sd] ##    .x9                0.570    0.095    0.373    0.750    1.001 gamma(1,.5)[sd] ##     visual            1.000                                                     ##     textual           1.000                                                     ##     speed             1.000 HS.model.cl<-' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9                     ## Cross-loadings               visual =~  prior(\"normal(0,.08)\")*x4 + prior(\"normal(0,.08)\")*x5 + prior(\"normal(0,.08)\")*x6 + prior(\"normal(0,.08)\")*x7 + prior(\"normal(0,.08)\")*x8 + prior(\"normal(0,.08)\")*x9               textual =~ prior(\"normal(0,.08)\")*x1 + prior(\"normal(0,.08)\")*x2 + prior(\"normal(0,.08)\")*x3 + prior(\"normal(0,.08)\")*x7 + prior(\"normal(0,.08)\")*x8 + prior(\"normal(0,.08)\")*x9                speed =~ prior(\"normal(0,.08)\")*x1 + prior(\"normal(0,.08)\")*x2 + prior(\"normal(0,.08)\")*x3 + prior(\"normal(0,.08)\")*x4 + prior(\"normal(0,.08)\")*x5 + prior(\"normal(0,.08)\")*x6'  fit_cl <- bcfa(HS.model.cl, data=HolzingerSwineford1939,              std.lv=TRUE, meanstructure=T) summary(fit_cl) ## blavaan 0.5.2.1191 ended normally after 1000 iterations ##  ##   Estimator                                      BAYES ##   Optimization method                             MCMC ##   Number of model parameters                        48 ##  ##   Number of observations                           301 ##  ##   Statistic                                 MargLogLik         PPP ##   Value                                      -3858.783       0.134 ##  ## Parameter Estimates: ##  ##  ## Latent Variables: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##   visual =~                                                                     ##     x1                0.761    0.099    0.574    0.959    1.001    normal(0,10) ##     x2                0.567    0.093    0.390    0.751    1.000    normal(0,10) ##     x3                0.769    0.097    0.586    0.964    1.000    normal(0,10) ##   textual =~                                                                    ##     x4                0.983    0.064    0.861    1.110    1.000    normal(0,10) ##     x5                1.155    0.071    1.014    1.298    1.000    normal(0,10) ##     x6                0.894    0.060    0.781    1.018    1.000    normal(0,10) ##   speed =~                                                                      ##     x7                0.728    0.086    0.554    0.892    1.003    normal(0,10) ##     x8                0.792    0.085    0.636    0.973    1.008    normal(0,10) ##     x9                0.542    0.076    0.394    0.695    1.004    normal(0,10) ##   visual =~                                                                     ##     x4                0.032    0.058   -0.080    0.148    0.999   normal(0,.08) ##     x5               -0.073    0.062   -0.193    0.050    0.999   normal(0,.08) ##     x6                0.063    0.055   -0.047    0.171    1.000   normal(0,.08) ##     x7               -0.130    0.065   -0.259   -0.004    1.003   normal(0,.08) ##     x8               -0.005    0.067   -0.138    0.124    0.999   normal(0,.08) ##     x9                0.193    0.060    0.075    0.309    1.000   normal(0,.08) ##   textual =~                                                                    ##     x1                0.111    0.065   -0.019    0.237    1.000   normal(0,.08) ##     x2                0.007    0.059   -0.110    0.130    0.999   normal(0,.08) ##     x3               -0.084    0.063   -0.212    0.037    1.000   normal(0,.08) ##     x7                0.015    0.062   -0.111    0.135    1.000   normal(0,.08) ##     x8               -0.039    0.062   -0.161    0.082    0.999   normal(0,.08) ##     x9                0.032    0.054   -0.077    0.135    1.000   normal(0,.08) ##   speed =~                                                                      ##     x1                0.042    0.065   -0.081    0.172    1.000   normal(0,.08) ##     x2               -0.048    0.063   -0.172    0.076    1.000   normal(0,.08) ##     x3                0.027    0.064   -0.097    0.149    1.000   normal(0,.08) ##     x4               -0.006    0.056   -0.116    0.104    1.001   normal(0,.08) ##     x5                0.005    0.061   -0.114    0.123    1.000   normal(0,.08) ##     x6               -0.001    0.053   -0.103    0.106    1.000   normal(0,.08) ##  ## Covariances: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##   visual ~~                                                                     ##     textual           0.374    0.095    0.186    0.549    1.000     lkj_corr(1) ##     speed             0.353    0.111    0.125    0.559    1.000     lkj_corr(1) ##   textual ~~                                                                    ##     speed             0.259    0.103    0.044    0.451    1.000     lkj_corr(1) ##  ## Intercepts: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##    .x1                4.937    0.068    4.804    5.070    0.999    normal(0,32) ##    .x2                6.087    0.066    5.961    6.213    0.999    normal(0,32) ##    .x3                2.251    0.067    2.119    2.385    1.000    normal(0,32) ##    .x4                3.063    0.066    2.931    3.191    1.000    normal(0,32) ##    .x5                4.342    0.074    4.193    4.481    1.000    normal(0,32) ##    .x6                2.188    0.063    2.061    2.307    0.999    normal(0,32) ##    .x7                4.187    0.064    4.060    4.312    1.000    normal(0,32) ##    .x8                5.529    0.060    5.410    5.649    0.999    normal(0,32) ##    .x9                5.374    0.060    5.257    5.492    1.000    normal(0,32) ##     visual            0.000                                                     ##     textual           0.000                                                     ##     speed             0.000                                                     ##  ## Variances: ##                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior        ##    .x1                0.677    0.107    0.457    0.885    1.001 gamma(1,.5)[sd] ##    .x2                1.090    0.107    0.897    1.307    1.000 gamma(1,.5)[sd] ##    .x3                0.718    0.114    0.497    0.938    1.000 gamma(1,.5)[sd] ##    .x4                0.388    0.051    0.289    0.490    0.999 gamma(1,.5)[sd] ##    .x5                0.411    0.065    0.291    0.543    1.000 gamma(1,.5)[sd] ##    .x6                0.372    0.044    0.290    0.461    0.999 gamma(1,.5)[sd] ##    .x7                0.714    0.099    0.524    0.914    1.002 gamma(1,.5)[sd] ##    .x8                0.434    0.100    0.218    0.609    1.015 gamma(1,.5)[sd] ##    .x9                0.589    0.067    0.461    0.726    1.003 gamma(1,.5)[sd] ##     visual            1.000                                                     ##     textual           1.000                                                     ##     speed             1.000"},{"path":"http://ecmerkle.github.io/blavaan/articles/cross_loadings_strong_priors.html","id":"caveats","dir":"Articles","previous_headings":"","what":"Caveats","title":"Cross-loadings with strong priors","text":"model possible cross-loadings kept final analysis model, used step make decisions model changes. two main reasons, (1) model overfitted present good overall fit just due inclusion lot nuisance parameters. example posterior predictive p-value goes ppp = 0 ppp = 0.134, model better theoretically inflating model fit. (2), addition small-variance priors can prevent detection important misspecifications Bayesian confirmatory factor analysis, can obscure underlying problems model diluting large number nuisance parameters (Jorgensen et al. 2019).","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/estimate.html","id":"primary-arguments","dir":"Articles","previous_headings":"","what":"Primary arguments","title":"Model Estimation","text":"Primary arguments model estimation commands include burnin, sample, n.chains, target. burnin sample arguments used specify desired number burn-iterations posterior samples n.chains chains (burnin argument controls warm-iterations Stan). target argument, hand, used specify MCMC strategy used estimation. default, target = \"stan\", tends fastest efficient. options slightly flexible, including target = \"stanclassic\" target = \"jags\". approaches sample latent variables model parameters, whereas target = \"stan\" marginalizes latent variables. detail approaches, see JSS paper.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/estimate.html","id":"secondary-arguments","dir":"Articles","previous_headings":"","what":"Secondary arguments","title":"Model Estimation","text":"Noteworthy secondary arguments include save.lvs, mcmcfile, mcmcextra, inits. save.lvs argument controls whether latent variables sampled model estimation. defaults FALSE latent variable sampling can take large amount memory, can slow post-estimation summaries. setting save.lvs = TRUE allows model summaries latent variables observed variable predictions using blavPredict() functions. setting mcmcfile = TRUE, users can obtain Stan (JAGS) code data specified model. files written lavExport folder within user’s working directory. One file extension .jag .stan, second file R data file (extension .rda). rda file can loaded R (via load()) list including elements data, monitors, inits. elements can supplied stan() model estimation outside blavaan. mcmcextra argument used supply extra information Stan JAGS. Users can supply list element names monitor, data, syntax, llnsamp. elements respectively used specify extra parameters monitor, extra data pass model estimation, extra syntax include model file (JAGS ), number importance samples likelihood approximation (relevant models ordinal variables). inits argument used control starting values MCMC estimation. can sometimes salvage model immediately crashes. default, inits = \"simple\", initializes model parameters 0 1 fashion similar lavaan’s use argument. second option, inits = \"prior\", draws initial values prior distributions. user can also specify list initial values via argument, though required list format somewhat cumbersome. recommend exporting model data using mcmcfile = TRUE, loading resulting rda file, looking format initial values blavaan created .","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/estimate.html","id":"parallelization","dir":"Articles","previous_headings":"","what":"Parallelization","title":"Model Estimation","text":"Speed always issue sample via MCMC, especially using software like Stan JAGS. computers multiple cores, estimation can sped sending MCMC chain separate core. accomplished bcontrol argument, list whose elements correspond stan() run.jags() arguments. parallelizing chains Stan, want use argument bcontrol = list(cores = 3). Many arguments available control aspects estimation; see ?stan ?run.jags possibilities. Parallelization can also helpful speed post-estimation computations. future package controls parallelization, requires extra command prior estimation. common commands ","code":"library(\"future\") plan(\"multicore\") ## mac or linux plan(\"multisession\") ## windows"},{"path":"http://ecmerkle.github.io/blavaan/articles/invariance.html","id":"model-estimation","dir":"Articles","previous_headings":"","what":"Model Estimation","title":"Measurement Invariance","text":"Consider measurement invariance study Holzinger Swineford (1939) data. lavaan, may first estimate two models: examine absolute fit fit1. also compare fit2 fit1 via Likelihood Ratio Test. Instead , wish something similar via Bayesian methods. accomplish via blavaan, can fit Bayesian versions fit1 fit2 using similar syntax. Model fit comparison statistics available via fitMeasures() blavCompare() functions:","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit1 <- cfa(HS.model, data = HolzingerSwineford1939, group = \"school\")  fit2 <- cfa(HS.model, data = HolzingerSwineford1939, group = \"school\",             group.equal = \"loadings\") bfit1 <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\")  bfit2 <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\",                group.equal = \"loadings\") fitMeasures(bfit1)  fitMeasures(bfit2)  blavCompare(bfit1, bfit2)"},{"path":"http://ecmerkle.github.io/blavaan/articles/invariance.html","id":"approximate-invariance","dir":"Articles","previous_headings":"","what":"Approximate Invariance","title":"Measurement Invariance","text":"approximate measurement invariance studies, replace hard equality constraints soft constraints using informative prior distributions. wiggle argument can used invoke types constraints. example: constrains loadings associated x2 x3 approximately equal across groups, informative priors associated constraints normal standard deviations 0.05. Using strategy, syntax can become cumbersome. many cases, group.equal argument can help . example: example, model intercepts loadings across-group constraints. loadings approximately equal across groups, due argument wiggle = \"loadings\". intercepts constrained exactly equal across groups. way, becomes easy use exact approximate equality constraints model, desired.","code":"HS.model <- ' visual  =~ x1 + c(\"a\", \"a\")*x2 + c(\"b\", \"b\")*x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  bfit3 <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\", wiggle = c(\"a\", \"b\"),               wiggle.sd = 0.05) HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '       bfit4 <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\",               group.equal = c(\"intercepts\", \"loadings\"), wiggle = \"loadings\",               wiggle.sd = 0.05)"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/mod_indices.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Modification indices","text":"SEM, one first steps evaluate model’s global fit. global fit, need evaluate local fit model, meaning model reproduces specific correlations observed variables. couple common methods , () testing high residual correlations, (b) modification indices. tutorial focuses second. Modification indices test likely change model fit single parameter added model originally included. test can carried every possible parameter included (Bentler 1990).","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/mod_indices.html","id":"modification-indices","dir":"Articles","previous_headings":"","what":"Modification Indices","title":"Modification indices","text":"Modification indices present different indices quantify effect parameter, focus two . () modification index (MI) Lagrange multiplier, estimates extent model’s chi-square (\\(\\chi^2\\)) test statistic decrease parameter added model freely estimated, (b) standardized expected parameter change (SEPC), approximated standardized value parameter estimated model (Whittaker 2012). MI presents possible effect overall model, SEPC presents effect size missed parameter. show example Holzinger Swineford (1939) model. first estimate SEM/CFA model usual need write discrepancy function collect modification indices. list contains two functions estimate save MI SEPC. pass function ppmc() function blavaan. function, MI SEPC computed posterior sample, leading posterior distributions . view top 5 parameters arrange posterior mean (EAP) MI, case shows parameter highest impact overall model fit (according EAP) visual=~x9, cross-loading Visual factor item x9. according posterior median, parameter highest impact residual correlation indicators x7 x8 MI still recommended best metric indicate parameter best include next, can use SEPC evaluate likely effect size respective parameters. see 2 highest parameters, likely SEPC x7~~x8 = 0.799229902211115 visual=~x9 = 0.518551878229323. information can decide include one new parameters model (one time). example, factor loadings larger impact model-implied covariance matrix, choose visual=~x9 can check added parameter expected impact overall fit blavFitIndices() summary() functions. important consider also theoretical relevance suggested parameters, ensure make sense, instead just adding parameters good fit.","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939, std.lv=TRUE) discFUN <- list(   mod.ind_mi = function(object){     temp <- modificationindices(object, free.remove = F)     mods <- temp$mi     names(mods) <- paste0(temp$lhs, temp$op, temp$rhs)     return(mods)   },   mod.ind_sepc.all = function(object){     temp <- modificationindices(object, free.remove = F)     sepc.all <- temp$sepc.all     names(sepc.all) <- paste0(temp$lhs, temp$op, temp$rhs)     return(sepc.all)   } ) out <- ppmc(fit, discFUN = discFUN) summary(out, prob=.9, discFUN = \"mod.ind_mi\", sort.by=\"EAP\", decreasing=T)[1:5,] ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for the posterior distribution of realized discrepancy-function values based on observed data, along with posterior predictive p values to test hypotheses in either direction: ##  ##  ##               EAP Median    MAP     SD  lower  upper PPP_sim_GreaterThan_obs ## visual=~x9 35.353 35.458 35.495 10.624 17.727 52.239                   0.013 ## x7~~x8     32.891 35.539 39.626 14.716  4.604 52.733                   0.084 ## x8~~x9     27.117 12.160  2.726 42.978  0.000 70.495                   0.320 ## x4~~x6     19.784  7.015  1.388 36.713  0.000 52.503                   0.468 ## visual=~x7 18.162 16.144 12.432  9.849  4.183 33.098                   0.015 ##            PPP_sim_LessThan_obs ## visual=~x9                0.987 ## x7~~x8                    0.916 ## x8~~x9                    0.680 ## x4~~x6                    0.532 ## visual=~x7                0.985 summary(out, prob=.9, discFUN = \"mod.ind_mi\", sort.by=\"Median\", decreasing=T)[1:5,] ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for the posterior distribution of realized discrepancy-function values based on observed data, along with posterior predictive p values to test hypotheses in either direction: ##  ##  ##                EAP Median    MAP     SD  lower  upper PPP_sim_GreaterThan_obs ## x7~~x8      32.891 35.539 39.626 14.716  4.604 52.733                   0.084 ## visual=~x9  35.353 35.458 35.495 10.624 17.727 52.239                   0.013 ## visual=~x7  18.162 16.144 12.432  9.849  4.183 33.098                   0.015 ## x8~~x9      27.117 12.160  2.726 42.978  0.000 70.495                   0.320 ## textual=~x1 11.011  9.976  5.705  8.318  0.000 22.179                   0.222 ##             PPP_sim_LessThan_obs ## x7~~x8                     0.916 ## visual=~x9                 0.987 ## visual=~x7                 0.985 ## x8~~x9                     0.680 ## textual=~x1                0.778 summary(out, prob=.9, discFUN = \"mod.ind_sepc.all\", sort.by=\"EAP\", decreasing=T)[1:5,] ##  ## Posterior summary statistics and highest posterior density (HPD) 90% credible intervals for the posterior distribution of realized discrepancy-function values based on observed data, along with posterior predictive p values to test hypotheses in either direction: ##  ##  ##               EAP Median   MAP    SD lower upper PPP_sim_GreaterThan_obs ## x7~~x8      0.799  0.790 0.742 0.383 0.487 1.274                   0.047 ## visual=~x9  0.519  0.494 0.466 0.132 0.334 0.688                   0.007 ## textual=~x1 0.272  0.298 0.314 0.175 0.036 0.513                   0.120 ## x1~~x9      0.247  0.247 0.248 0.037 0.198 0.299                   0.018 ## x2~~x3      0.223  0.223 0.219 0.037 0.171 0.282                   0.026 ##             PPP_sim_LessThan_obs ## x7~~x8                     0.953 ## visual=~x9                 0.993 ## textual=~x1                0.880 ## x1~~x9                     0.982 ## x2~~x3                     0.974 HS.model <- ' visual  =~ x1 + x2 + x3 + x9               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit2 <- bcfa(HS.model, data=HolzingerSwineford1939, std.lv=TRUE)"},{"path":"http://ecmerkle.github.io/blavaan/articles/mod_indices.html","id":"summary","dir":"Articles","previous_headings":"","what":"Summary","title":"Modification indices","text":"tutorial show calculate MI SEPC across posterior distributions, evaluate parameters can added. ppmc() function able calculate relevant information model estimation, build posterior distributions . general recommendations use MI identify likely parameter add, SEPC effect size new parameter.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Model Comparison","text":"traditional method model comparison frequentist SEM (fSEM) \\(\\chi^2\\) (Likelihood Ratio Test) variations. BSEM, take Bayesian model comparison methods, apply SEM. Specifically, focus two information criteria, (1) Widely Applicable Information Criterion (WAIC), (2) Leave-One-cross-validation (LOO). methods intend evaluate --sample predictive accuracy models, compare performance. ability predict datapoint hasn’t used training model (McElreath 2020) example use Industrialization Political Democracy example (Bollen 1989).","code":"model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit1 <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000)"},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"widely-applicable-information-criterion","dir":"Articles","previous_headings":"","what":"Widely Applicable Information Criterion","title":"Model Comparison","text":"WAIC (Watanabe 2010) can seen fully Bayesian generalization Akaike Information Criteria (AIC), measure uncertainty/information model prediction row data across posterior draws. Log-Pointwise-Predictive-Density (lppd). WAIC defined \\[\\begin{equation} WAIC= -2lppd + 2efp_{WAIC}, \\end{equation}\\] first term involves log-likelihoods observed data (marginal latent variables) second term effective number parameters. first term, \\(lppd\\), estimated : \\[\\begin{equation} \\widehat{lppd} = \\sum^{n}_{= 1} log \\Bigg(\\frac{1}{S}\\sum^{S}_{S=1}f(y_{}|\\theta^{S}) \\Bigg) \\end{equation}\\] \\(S\\) number posterior draws \\(f(y_{}|\\theta^{S})\\) density observation \\(\\) respect parameter sampled iteration \\(s\\). effective number parameter (\\(efp_{WAIC}\\)) calculated : \\[\\begin{equation}\\label{eq:efpWAIC} efp_{WAIC} = \\sum^n_{=1}var_{s}(logf(y_{}|\\theta)) \\end{equation}\\] separate variance estimated observation \\(\\) across \\(S\\) posterior draws.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"leave-one-out-cross-validation","dir":"Articles","previous_headings":"","what":"Leave-One-Out cross-validation","title":"Model Comparison","text":"LOO measures predictive density observation holding one observation time use rest observations update prior. estimation calculated via (Vehtari, Gelman, Gabry 2017): \\[\\begin{equation}     LOO = -2\\sum_{=1}^{n} log \\Bigg(\\frac{\\sum^{S}_{s =1} w^{s}_{}f(y_{}|\\theta^{s})}{\\sum^{s}_{s=1} w^{s}_{}}\\Bigg) \\end{equation}\\] \\(w^s_{}\\) Pareto-smoothed sampling weights based relative magnitude individual \\(\\) density function across \\(S\\) posterior samples. LOO effective number parameters involves \\(lppd\\) term WAIC: \\[\\begin{equation}     efp_{LOO} = lppd + LOO/2 \\end{equation}\\]","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"model-comparison","dir":"Articles","previous_headings":"","what":"Model comparison","title":"Model Comparison","text":"WAIC LOO approximate models’ performance across posterior draws, able calculate standard error model comparisons involving . model differences estimate differences across Expected Log-Pointwise-Predictive-Density (elpd), standard error respective difference. clear cutoff rules interpret present comparisons, researchers need use expert knowledge part decision process. best recommendation present differences elpd \\(\\Delta elpd\\), standard error, ratio . ratio least 2 can consider evidence differences models, ratio 4 considered stronger evidence. first example, compare standard political democracy model, model factor regressions fixed 0. 2 models, can compare blavCompare looking comparison object, can see WAIC, LOO, estimates, respective differences . information criteria, best model one lowest value case can see model 1 lower LOOIC, ratio shows LOO differences 5 SE magnitude. indicates model estimated regressions better Now, lets look example smaller difference models, smallest regression (dem65~ind60) fixed 0. see LOOIC, see difference two models minimal, ratio 0.21. indicates models functionally equivalent. case like , researchers decide model better representation, theoretically stronger. Lets one last model, largest regression (dem65~dem60) fixed 0. case, looking LOOIC, see model one better (lower value), ratio difference shows model 5 SE magnitude. Indicating evidence model predictive differences","code":"model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ 0*ind60     dem65 ~ 0*ind60 + 0*dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit2 <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000) bc12 <- blavCompare(fit1, fit2) bc12 ## $bf ##   bf mll1 mll2  ##   NA   NA   NA  ##  ## $loo ## $loo[[1]] ##             Estimate        SE ## elpd_loo -1606.11441 19.535855 ## p_loo       37.57331  2.931881 ## looic     3212.22882 39.071710 ##  ## $loo[[2]] ##             Estimate        SE ## elpd_loo -1646.98380 18.865450 ## p_loo       34.72419  2.768238 ## looic     3293.96759 37.730900 ##  ##  ## $diff_loo ##  elpd_diff    se_diff  ## -40.869388   7.883331  ##  ## $waic ## $waic[[1]] ##              Estimate        SE ## elpd_waic -1605.82594 19.502689 ## p_waic       37.28485  2.892072 ## waic       3211.65189 39.005379 ##  ## $waic[[2]] ##              Estimate       SE ## elpd_waic -1646.68503 18.82321 ## p_waic       34.42542  2.70925 ## waic       3293.37005 37.64643 ##  ##  ## $diff_waic ##  elpd_diff    se_diff  ## -40.859084   7.870287 abs(bc12$diff_loo[1] / bc12$diff_loo[2]) ## elpd_diff  ##  5.184279 model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ 0*ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit3 <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000) bc13 <- blavCompare(fit1, fit3) bc13 ## $bf ##   bf mll1 mll2  ##   NA   NA   NA  ##  ## $loo ## $loo[[1]] ##             Estimate        SE ## elpd_loo -1606.11441 19.535855 ## p_loo       37.57331  2.931881 ## looic     3212.22882 39.071710 ##  ## $loo[[2]] ##             Estimate        SE ## elpd_loo -1606.72727 19.416513 ## p_loo       37.59722  2.921451 ## looic     3213.45454 38.833026 ##  ##  ## $diff_loo ##  elpd_diff    se_diff  ## -0.6128641  0.9821245  ##  ## $waic ## $waic[[1]] ##              Estimate        SE ## elpd_waic -1605.82594 19.502689 ## p_waic       37.28485  2.892072 ## waic       3211.65189 39.005379 ##  ## $waic[[2]] ##            Estimate        SE ## elpd_waic -1606.447 19.387422 ## p_waic       37.317  2.880573 ## waic       3212.894 38.774843 ##  ##  ## $diff_waic ##  elpd_diff    se_diff  ## -0.6211150  0.9806277 abs(bc13$diff_loo[1] / bc13$diff_loo[2]) ## elpd_diff  ## 0.6240187 model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + 0*dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit4 <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T, n.chains=3,             burnin=500, sample=1000) bc14 <- blavCompare(fit1, fit4) bc14 ## $bf ##   bf mll1 mll2  ##   NA   NA   NA  ##  ## $loo ## $loo[[1]] ##             Estimate        SE ## elpd_loo -1606.11441 19.535855 ## p_loo       37.57331  2.931881 ## looic     3212.22882 39.071710 ##  ## $loo[[2]] ##             Estimate        SE ## elpd_loo -1629.39258 19.862092 ## p_loo       37.75678  2.984498 ## looic     3258.78516 39.724184 ##  ##  ## $diff_loo ## elpd_diff   se_diff  ## -23.27817   3.98061  ##  ## $waic ## $waic[[1]] ##              Estimate        SE ## elpd_waic -1605.82594 19.502689 ## p_waic       37.28485  2.892072 ## waic       3211.65189 39.005379 ##  ## $waic[[2]] ##              Estimate        SE ## elpd_waic -1629.01598 19.814740 ## p_waic       37.38018  2.925757 ## waic       3258.03196 39.629480 ##  ##  ## $diff_waic ##  elpd_diff    se_diff  ## -23.190036   3.968117 abs(bc14$diff_loo[1] / bc14$diff_loo[2]) ## elpd_diff  ##  5.847892"},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"bayes-factor","dir":"Articles","previous_headings":"","what":"Bayes factor","title":"Model Comparison","text":"Bayesian literature use Bayes factor (BF) compare models. number criticisms related use BF BSEM, including (1) BF unstable large models (like SEMs), (2) highly sensitive model priors, (3) requires strong priors stable estimation , (4) can require large number posterior draws, (5) estimation using marginal likelihood ignores lot information posterior distributions. details discussion please see Tendeiro Kiers (2019) Schad et al. (2022). criticisms lead us recommend use BF everyday BSEM estimation. researchers commit prior distributions commit exploring noise computations, BF can used describe relative odds one model another, intuitive model comparison metrics.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/model_comparison.html","id":"summary","dir":"Articles","previous_headings":"","what":"Summary","title":"Model Comparison","text":"recommend use LOO WAIC general model comparison metrics BSEM. allow us estimate models’ --sample predictive accuracies, respective differences across posterior draws. also provide us uncertainty estimates comparison. cases LOO WAIC lead similar results, LOO recommended stable metric (Vehtari, Gelman, Gabry 2017). general, \\(\\Delta elpd\\) least 2 standard errors preferably 4 standard errors can interpreted evidence differential predictive accuracy.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/multilevel.html","id":"blavaan-coverage","dir":"Articles","previous_headings":"","what":"blavaan Coverage","title":"Two-level SEM","text":"version 0.5-1, blavaan handles two-level, random intercept models complete, continuous data. Handling missing data (assuming missingness random) come future release. meantime, multiple imputation might used combination current blavaan functionality (though currently automatic way ). Alternatively, much missing data occurs lower-level units, listwise deletion work. blavaan approach model estimation mimics lavaan approach, uses matrix results (see Rosseel 2021) enable us efficiently evaluate multilevel SEM likelihood. often lead efficient MCMC estimation, compared sampling level 1 level 2 latent variables working conditional likelihoods (see Merkle et al. 2021 discussion marginal vs conditional likelihoods). Similar single-level models, users can sample latent variables using save.lvs = TRUE argument bcfa/bsem/bgrowth/blavaan commands. Marginal information criteria (marginal latent variables) also automatically computed, information criteria generally preferred condition latent variables (see Merkle, Furr, Rabe-Hesketh 2019 detail context single-level models).","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/multilevel.html","id":"bayes-specific-options","dir":"Articles","previous_headings":"","what":"Bayes-specific Options","title":"Two-level SEM","text":"Bayesian models require prior distributions. previous blavaan defaults single-level models now used two-level models. can continue use commands like dpriors(lambda = \"normal(1,.5)\") specify Normal(1,.5) prior factor loadings , two-level models, specification apply level 1 level 2 loadings. Depending model, may also useful specify priors individual parameters via prior() argument inside model specification syntax. default prior distributions always work well observed variables whose values far 0. continue encourage users consider prior distributions, possibly using prisamp = TRUE option draw samples prior (used prior predictive checking). Model checking also differs Bayesian frequentist methods. Just like one-level models, blavaan reports posterior predictive p-value general model assessment. computed comparing marginal likelihood observed data (marginal latent variables) marginal likelihood artificial data, iteration MCMC sampling. finer-grained model assessment, encourage users try ppmc(). allows compute posterior predictive p-value using , custom model assessment (defined R function).","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/multilevel.html","id":"concluding-thoughts","dir":"Articles","previous_headings":"","what":"Concluding Thoughts","title":"Two-level SEM","text":"think new blavaan functionality provides viable option Bayesian two-level SEM, provide solid base future model developments. always, underlying Stan files supporting data available via mcmcfile = TRUE argument, blavaan code available Github. Bug reports appreciated, either blavaan Google group Github issue.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Ordinal Models in blavaan","text":"Structural equation models ordinal observed variables supported starting blavaan 0.4-1 (target=\"stan\" ). document describes overall approach, includes model estimation, threshold parameters, log-likelihood calculation, posterior predictive p-values, Jacobians. assume somewhat familiar layout SEM; , technical detail examples found Merkle Rosseel (2018) , recently, Merkle et al. (2021) (links papers references section). aim provide enough detail elucidate new blavaan features, informal enough get () bored.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"estimation","dir":"Articles","previous_headings":"","what":"Estimation","title":"Ordinal Models in blavaan","text":"Ordinal observed variables handled via data augmentation, style Chib Greenberg (1998). might already know , phrase data augmentation imprecise context SEM. many possible things augmented, can make model estimation easier. augmenting observed data predictions missing data, related multiple imputation methods. augmenting observed data latent variables, can simplify likelihood calculation (leading sometimes called conditional likelihood, though conditional also many meanings). augmenting categorical observed variables underlying, latent continuous variables. last type augmentation . testing, found faster efficient approaches sample latent variables alongside model parameters (latent variables integrated likelihoods ; similar description Merkle et al. (2021)). data augmentation implementation, ordinal observation (e.g., \\(y\\)) used generate continuous, underlying counterpart (e.g., \\(y^\\ast\\)). \\(y^\\ast\\) must obey model’s threshold parameters (commonly denoted \\(\\mathbf{\\tau}\\)), based value observed data. example, ignoring subscripts \\(y^\\ast\\) assuming ordinal variable 4 categories, \\[\\begin{align*} y^* < \\tau_1 &\\text{ }y = 1 \\\\ \\tau_1 <\\ y^* < \\tau_2 &\\text{ }y = 2 \\\\ \\tau_2 <\\ y^* < \\tau_3 &\\text{ }y = 3 \\\\ y^* >\\ \\tau_3 &\\text{ }y = 4 \\end{align*}\\] require \\(\\tau_1 < \\tau_2 < \\tau_3\\). generate \\(y^*\\) separately ordinal observation dataset. become additional, bounded parameters Stan file. Stan User’s Guide helpful example multivariate probit regression using related approach; see https://mc-stan.org/docs/2_27/stan-users-guide/multivariate-outcomes.html. trickiest parts involve enforcing boundaries \\(y^*\\) variables, ensuring threshold parameters ordinal variable ordered correctly (allowing possibility different ordinal variables different numbers thresholds). require Jacobian adjustments took good deal time code correctly (detail appears later section). parameters defined generated, remainder model estimation similar simpler situation observed variables continuous. terms Stan file, ordinal overhead comes transformed parameters block. get model block, things operate continuous data.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"thresholds-priors","dir":"Articles","previous_headings":"","what":"Thresholds & Priors","title":"Ordinal Models in blavaan","text":"prior distributions threshold (\\(\\tau\\)) parameters involved may appear. , described previous section, threshold parameters single variable must ordered. say, example, thresholds normal(0,1) prior distribution, ignoring fact one threshold’s value influences size thresholds’ values. Michael Betancourt describes Stan Discourse, prior “interacts (ordering) constraint enforce sort uniform repulsion interior points, resulting rigid differences.” quote https://discourse.mc-stan.org/t/prior-choice--ordered-inverse-transformed-parameters/16378/3 address issue, first define unconstrained, unordered parameter vector whose length equals number thresholds model. Call vector \\(\\mathbf{\\tau}^*\\). obtain ordered thresholds exponentiating unordered parameter vector specific manner. manner works exactly Stan defines parameter type ordered. See https://mc-stan.org/docs/2_28/reference-manual/ordered-vector.html. Additionally, similar idea independently developed signal detection models Paulewicz Blaut (2020) (see bhsdtr package). idea easily shown via example. Say ordinal variable 4 categories. three thresholds variable obtained via: \\[\\begin{align*} \\tau_1 &= \\tau^*_1 \\\\ \\tau_2 &= \\tau^*_1 + \\exp(\\tau^*_2) \\\\ \\tau_3 &= \\tau^*_1 + \\exp(\\tau^*_2) + \\exp(\\tau^*_3). \\end{align*}\\] place normal prior distributions unordered \\(\\tau^*\\) parameters, opposed placing priors ordered \\(\\tau\\) parameters. normal priors imply lowest threshold (\\(\\tau_1\\) ) normal prior, differences successive \\(\\tau\\)’s log-normal priors. blavaan, priors can specified usual two ways. First, add dp argument model estimation command follows. assign prior unordered \\(\\tau^*\\) parameters model. Second, specify priors specific threshold parameters model specification syntax. example, say 4-category observed variable called x1. unique priors three thresholds specified model syntax via clear time priors \\(\\tau^*\\) parameters best option. 2019 paper, Michael Betancourt describes Dirichlet prior regularizes thresholds ordinal regression model. strategy seem work SEM, especially useful datasets categories ordinal variable sparse. issues warrant study. https://betanalpha.github.io/assets/case_studies/ordinal_regression.html","code":"dp = dpriors(tau = \"normal(0, .5)\") x1 | prior(\"normal(-1, 1)\") * t1 + prior(\"normal(0, .5)\") * t2 + prior(\"normal(0, 1)\") * t3"},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"likelihood-computations","dir":"Articles","previous_headings":"","what":"Likelihood Computations","title":"Ordinal Models in blavaan","text":"get continuous data model block, seems reasonable expect simple likelihood computations. depends likelihood want compute. likelihood used sampling Stan simple multivariate normal \\(y^*\\) observations, combined continuous observed variables model. indeed simple compute. likelihood want use model comparison. one thing, \\(y^*\\) parameters associated ordinal data involved likelihood, quantities like effective number parameters become inflated. number parameters involved likelihood also increases sample size, generally bad land model comparison metrics. See Merkle, Furr, Rabe-Hesketh (2019) detail . means , quantities like WAIC PSIS-LOO, must compute second model likelihood involves observed, ordinal \\(y\\) variables integrates latent \\(y^*\\) variables. difficult problem amounts evaluating CDF sometimes-high-dimensional, multivariate normal distribution (see Chib Greenberg 1998, Equation 11). multiple possibilities approximating CDF. currently rely sadmvn() function mnormt package (Azzalini Genz 2020), uses subregion adaptive integration method Genz (1992) fast accurate (15 fewer ordinal variables model). second possibility involves Monte Carlo simulation, implemented tmvnsim package (Bhattacjarjee 2016). case, generate many random samples appropriate truncated multivariate normal average resulting importance sampling weights. procedure computationally intensive also time intensive, balance number random samples drawn amount time takes. users wish use tmvnsim(), must declare number importance samples draw. accomplished setting llnsamp within mcmcextra$data argument. example, draw 100 samples approximation, call bsem() similar functions include argument Beyond two methods, also possible use quadrature latent variables. Many people consider quadrature gold standard , quadrature reduce dimension integration many models (usually fewer latent variables observed variables). quadrature specific SEM, fast, efficient, open implementations method appear currently exist (implementations hidden blavaan, pure R implementations fairly slow). hand, approximation multivariate normal CDF general problem multiple fast, efficient, open implementations, long many ordinal variables model. also exists relatively new method Z. . Botev (2017) evaluating CDF multivariate normal, implementation method appearing package TruncatedNormal (Z. Botev Belzile 2021). method especially useful evaluating high-dimensional normal distributions (case, 15 ordinal variables), may incorporated future versions blavaan.","code":"mcmcextra = list(data = list(llnsamp = 100))"},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"comparison-to-lavaan","dir":"Articles","previous_headings":"","what":"Comparison to lavaan","title":"Ordinal Models in blavaan","text":"Ordinal SEM associated two types model parameterizations: delta theta. refer different scale parameterizations \\(y^*\\) variables: delta refers total standard deviation \\(y^*\\) (including variability due latent variables), theta refers residual standard deviation \\(y^*\\). blavaan, theta parameterization implemented. , want compare lavaan results blavaan results, need use argument parameterization = \"theta\" estimate lavaan model. Also, default lavaan estimator ordinal models multiple-step procedure involves weighted least squares discrepancy function. resulting parameter estimates sometimes far posterior means reported blavaan. blavaan estimates usually closer estimator=\"PML\" lavaan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"posterior-predictive-p-values","dir":"Articles","previous_headings":"","what":"Posterior Predictive p-values","title":"Ordinal Models in blavaan","text":"Posterior predictive p-value (ppp) computations receive speed boost 0.4 series. computations now occur Stan, whereas previously occurred R model estimation. discussed Asparouhov Muthén (2021), ppp computations needed models missing data can excessively slow, requiring us run EM algorithm posterior sample order find “H1” (“saturated”) model covariance matrix. solution Asparouhov Muthén (2021) involves realization need use fully-optimized H1 covariance matrix order compute ppp. blavaan, consequently run EM algorithm fixed number iterations order compute H1 covariance matrix “good enough” ppp. default number iterations set 20, users can change default supplying emiter value via mcmcextra argument. example,","code":"mcmcextra = list(data = list(emiter = 50))"},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"jacobians","dir":"Articles","previous_headings":"","what":"Jacobians","title":"Ordinal Models in blavaan","text":"(section likely relevant editing/writing Stan models.) Stan model underlying blavaan currently requires Jacobian adjustments two places. section briefly reviews ideas underneath adjustments, future self may wish remember. need Jacobian adjustment place prior something appear Stan parameters block. Jacobian tells us implied priors things parameters block, based priors appear model block. Jacobian comes statistics literature “change variables”: applying function random variables, finding distribution function based original distribution random variables. comes Stan models, means starting priors model block finding implied priors parameters block. confused long time , Stan file, functions naturally go opposite direction: starting parameters block, moving model block. fact functions go model parameters convenient, though, Jacobian adjustments require inverse functions. inverse functions move us parameters model, already exist Stan model. just need find appropriate derivatives functions, lead Jacobian. example, consider fact blavaan allows users choose whether priors go standard deviation, variance, precision parameters. standard deviations appear parameters block regardless user chooses (Stan model precompiled time package installation). Say user wants priors precisions. transform standard deviations precisions model block, put prior precision. addition prior, need Jacobian function starts standard deviation (call \\(\\sigma\\)) transforms precision (\\(\\sigma^{-2}\\)). derivative \\(\\sigma^{-2}\\) respect \\(\\sigma\\) \\(-2 \\sigma^{-3}\\). simple function mapping single parameter different value, Jacobian absolute value derivative, \\(2 \\sigma^{-3}\\). Stan file, add log Jacobian target: examples discussion can found : https://mc-stan.org/users/documentation/case-studies/mle-params.html","code":"target += log(2) - 3*log(sigma)"},{"path":"http://ecmerkle.github.io/blavaan/articles/ordinal.html","id":"summary","dir":"Articles","previous_headings":"","what":"Summary","title":"Ordinal Models in blavaan","text":"blavaan 0.4 series offers enhanced functionality variety areas. computational decisions made reflect balance estimation precision estimation speed. case software defaults behave poorly situations. example, default prior distributions can problematic certain situations, likelihood approximations ordinal models may precise desired, new ppp computations may behave differently previous computations. encourage users carry sensitivity analyses, also report bugs!","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/plotting.html","id":"basics","dir":"Articles","previous_headings":"","what":"Basics","title":"Plot Functionality","text":"many blavaan models many parameters, users generally need specify parameters wish plot. accomplished supplying numbers pars argument, numbers correspond order parameters coef() command (numbers also appear free column parameter table). Users must also specify type plot desire via plot.type argument. , example, trace plot first four model parameters looks like  Many plot types available, coming bayesplot package. general, bayesplot functions begin mcmc_, corresponding plot.type remainder function name without leading mcmc_. Examples many plots can found bayesplot vignette.","code":"plot(fit, pars = 1:4, plot.type = \"trace\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/plotting.html","id":"customization","dir":"Articles","previous_headings":"","what":"Customization","title":"Plot Functionality","text":"Users may wish customize aspects resulting plots. , plot() function output ggplot object. makes possible modify plot ggplot object, allows many possibilities. One starting point exploring ggplot2 .  Alternatively, users may wish create plot entirely different available via plot(). can facilitated extracting posterior samples Stan model, via blavInspect():","code":"p <- plot(fit, pars = 1:4, plot.type = \"trace\", showplot = FALSE)  p + facet_text(size=15) + legend_none() ## list of draws ## (one list entry per chain): draws <- blavInspect(fit, \"mcmc\")  ## convert the list to a matrix ## (each row is a sample, ##  each column is a parameter) draws <- do.call(\"rbind\", draws)  ## Stan (or JAGS) model modobj <- blavInspect(fit, \"mcobj\")"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/prior.html","id":"defaults","dir":"Articles","previous_headings":"","what":"Defaults","title":"Specifying Prior Distributions","text":"default priors can seen via important note prior distributions correspond Stan parameterizations. similar R parameterizations necessarily exactly . Greek(ish) names correspond following parameter types (MV manifest/observed variable LV latent variable): information priors thresholds, see ordinal modeling details. target = \"stan\" (default), priors currently restricted one distribution per parameter type. can change prior distribution parameters (example, mean standard deviation normal), change prior distribution type. exceptions “theta” “psi” parameters: , can use modifiers “[sd]”, “[var]”, “[prec]” specify whether want priors apply standard deviation, variance, precision. require flexibility prior specification, change target either \"stanclassic\" (old Stan approach) \"jags\" (JAGS approach). Alternatively, can export Stan model via mcmcfile = TRUE, edit file needed, fit via rstan package. modify prior distributions, simply supply new text string dpriors() like : default prior loadings now normal mean 1 standard deviation 2, rest parameters remain original defaults. next time estimate model (via bsem(), bcfa(), bgrowth(), blavaan()), add argument dp=mydp use new set default priors.","code":"dpriors() ##                nu             alpha            lambda              beta  ##    \"normal(0,32)\"    \"normal(0,10)\"    \"normal(0,10)\"    \"normal(0,10)\"  ##             theta               psi               rho             ibpsi  ## \"gamma(1,.5)[sd]\" \"gamma(1,.5)[sd]\"       \"beta(1,1)\" \"wishart(3,iden)\"  ##               tau  ##   \"normal(0,1.5)\" ##                  nu               alpha              lambda                beta  ##      \"MV intercept\"      \"LV intercept\"           \"Loading\"        \"Regression\"  ##               theta                 psi                 rho               ibpsi  ##      \"MV precision\"      \"LV precision\"       \"Correlation\" \"Covariance matrix\"  ##                 tau  ##         \"Threshold\" mydp <- dpriors(lambda=\"normal(1,2)\") mydp ##                nu             alpha            lambda              beta  ##    \"normal(0,32)\"    \"normal(0,10)\"     \"normal(1,2)\"    \"normal(0,10)\"  ##             theta               psi               rho             ibpsi  ## \"gamma(1,.5)[sd]\" \"gamma(1,.5)[sd]\"       \"beta(1,1)\" \"wishart(3,iden)\"  ##               tau  ##   \"normal(0,1.5)\""},{"path":"http://ecmerkle.github.io/blavaan/articles/prior.html","id":"individual-parameters","dir":"Articles","previous_headings":"","what":"Individual Parameters","title":"Specifying Prior Distributions","text":"addition setting prior one type model parameter, user may wish set prior specific model parameter. accomplished using prior() modifier within model specification. example, consider following syntax Holzinger Swineford (1939) confirmatory factor model: loading visual x2 now normal prior mean 1 standard deviation 2, loading textual x6 normal prior mean 3 standard deviation 1.5. loadings default prior distribution. syntax, additionally specified gamma(3,3) prior associated residual x1. [sd] text end distribution says prior goes residual standard deviation, opposed residual precision residual variance. exist two options : [var] option residual variance, brackets precision (also use [prec]). bracketed text can used model variance/SD/precision parameter also used default prior specification desired.","code":"HS.model <- ' visual  =~ x1 + prior(\"normal(1,2)\")*x2 + x3               textual =~ x4 + x5 + prior(\"normal(3,1.5)\")*x6               speed   =~ x7 + x8 + x9                x1 ~~ prior(\"gamma(3,3)[sd]\")*x1 '"},{"path":"http://ecmerkle.github.io/blavaan/articles/prior.html","id":"covariance-parameters","dir":"Articles","previous_headings":"","what":"Covariance Parameters","title":"Specifying Prior Distributions","text":"One additional note covariance parameters defined model syntax: prior() syntax specifies prior correlation associated covariance parameter, opposed covariance . specified distribution support (0,1), blavaan automatically translates prior equivalent distribution support (-1,1). safest stick beta priors . example, syntax places Beta(1,1) (uniform) prior correlation visual textual factors. desired, also specify priors standard deviations (variances precisions) visual textual factors. Together prior correlation, priors imply prior covariance visual textual.","code":"HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9                visual ~~ prior(\"beta(1,1)\")*textual '"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/prior_pred_checks.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Prior Predictive Checks","text":"Bayesian models need specify priors model parameters. Priors distribution think parameters follow, even data. can represent high low uncertainty, diffuse prior indicates don know lot parameter behave, informative prior means quite certain expected distribution.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/prior_pred_checks.html","id":"prior-predictive-checks","dir":"Articles","previous_headings":"","what":"Prior Predictive Checks","title":"Prior Predictive Checks","text":"Prior predictive checks (PPC) generate data according prior order asses whether prior appropriate (Gabry et al. 2019). posterior predictive check generates replicated data according posterior predictive distribution. contrast, prior predictive check generates data according prior predictive distribution \\(y^{sim} ∼ p(y)\\). prior predictive distribution just like posterior predictive distribution observed data, prior predictive check nothing limiting case posterior predictive check data. easy carry mechanically simulating parameters \\(θ^{sim}∼p(\\theta)\\) according priors, simulating data \\(y^{sim}∼p(y∣ \\theta^{sim})\\) according sampling distribution given simulated parameters. result simulation joint distribution, \\((y^{sim},θ^{sim})∼p(y,\\theta)\\) thus \\(y^{sim}∼p(y)\\) simulation prior predictive distribution. blavaan can get PPC use argument prisamp=TRUE , tell blavaan ignore data buil distributions priors. start adjusting priors, instead using default priors.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/prior_pred_checks.html","id":"weakly-informative-priors","dir":"Articles","previous_headings":"Prior Predictive Checks","what":"Weakly informative priors","title":"Prior Predictive Checks","text":"show example Holzinger Swineford (1939) data, first case weakly informative priors. stpecifying observeded variable intercepts prior \\(N(3, 2)\\), factor loadings prior \\(N(0.4, 2)\\), residual standard deviation prior \\(\\Gamma(1,1)\\). estimate BSEM model respective priors dp argument, prisamp=TRUE, getting PPC instead posterior distributions. might get warning messages either divergent /failed convergence. ignore messages likely issues evaluations prior predictions. now blavaan object prior predictive distributions, can use package functions describe , see parameters within expected ranges. example can get PPC density distributions first 9 parameters (factor loadings case). basic plot() method calls functions bayesplot package (Gabry Mahr 2021) plot.type = \"dens\" argument can plot density distributions  can also pick parameters plot, like factor correlations chossing parameters 19:21 case  factor loadings distributions see first loading factor bounded 0, due modeling identification constraint blavaan, maximum values aroun 6. distributions range -6 6 -4 4, priors likely value around 0. described weakly informative priors allows range begative positive values without allowing crazy high/low values Note realistic range dependen parameter, model specification, data. , consider priors function characterictics. factor correlations kept deafult diffuse priors, allowed high low correlation, prior distributions flat across possible correlation values.","code":"priors <- dpriors(nu=\"normal(3,2)\",                   lambda=\"normal(0.4, 2)\",                   theta=\"gamma(1,1)[sd]\") HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit_wi <- bcfa(HS.model, data=HolzingerSwineford1939,              std.lv=TRUE, meanstructure=T, test = \"none\",             dp=priors, prisamp = T) plot(fit_wi, pars=1:9, plot.type = \"dens\") plot(fit_wi, pars=19:21, plot.type = \"dens\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/prior_pred_checks.html","id":"default-priors","dir":"Articles","previous_headings":"Prior Predictive Checks","what":"Default priors","title":"Prior Predictive Checks","text":"next example, estimate PPC package default priors, consider diffuse priors. can see blavaan default priors function dpriors() estimate BSEM model ignore dp argument letting run default priors, prisamp=TRUE, getting PPC instead posterior distributions. can plot density distributions compare . see default diffuse priors, model allows high values -30 30  way can see diffuse priors allows higher range values. researcher decide range priors better present expectations. important note PPC allows see expected distributions based priors, might priors used estimation process, priors interact model specification constraints (o bound constraint first factor loading) (Merkle et al. 2023)","code":"dpriors() ##                nu             alpha            lambda              beta  ##    \"normal(0,32)\"    \"normal(0,10)\"    \"normal(0,10)\"    \"normal(0,10)\"  ##             theta               psi               rho             ibpsi  ## \"gamma(1,.5)[sd]\" \"gamma(1,.5)[sd]\"       \"beta(1,1)\" \"wishart(3,iden)\"  ##               tau  ##   \"normal(0,1.5)\" fit_df <- bcfa(HS.model, data=HolzingerSwineford1939,              std.lv=TRUE, meanstructure=T, test = \"none\",              prisamp = T) plot(fit_df, pars=1:9, plot.type = \"dens\")"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Probability of Direction","text":"Probability Direction (pd) index effect existence, ranging 0% 100%, representing certainty effect goes particular direction (.e., positive negative) (Makowski et al. 2019). Beyond simplicity interpretation, understanding computation, index also presents interesting properties: independent model: solely based posterior distributions require additional information data model. robust scale response variable predictors. *strongly correlated frequentist p-value, can thus used draw parallels give reference readers non-familiar Bayesian statistics. Can interpreted probability parameter (described posterior distribution) chosen cutoff, explicit hypothesis. mathematically defined proportion posterior distribution satisfies specified hypothesis. Although differently expressed, index fairly similar (.e., strongly correlated) frequentist p-value.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"probability-of-direction-pd","dir":"Articles","previous_headings":"","what":"Probability of Direction (pd)","title":"Probability of Direction","text":"example use Industrialization Political Democracy example (Bollen 1989). first estimate latent regression model can look overall model results summary function, case also asking standardized estimates, \\(R^2\\) calculate probability direction use function package brms (Bürkner 2017) Ans need extract posterior draws matrix, also important note parameters posterior draws named Stan underlying object names, instead (b)lavaan parameter names. can see parameter name equates partable() function, follows example focus regressions factors Now, can calculate pd, hypothesis() function brms can ask specific question posterior distributions, example want know proportion regression dem65~ind60 higher 0. function requires 2 arguments, posterior draws (mc_out) hypothesis (bet_sign[2] > 0), also adding ``alpha``` argument specifies size credible intervals estimate presents mean posterior distribution, respective measures variability (deviation credible interval). Post.Prob pd stated hypothesis, example can say 91% posterior distribution dem65~ind60 lower 0. equivalent one-tail test. Evid.Ratio evidence ratio hypothesis, hypothesis form \\(> b\\), evidence ratio ratio posterior probability \\(> b\\) posterior probability \\(< b\\) another example, want know proportion regression dem60~ind60 higher 0. can see 100% posterior probability higher 0, case Evid.Ratio = Inf, happens whole distribution fulfills hypothesis. another possible case interest, use test equalities parameters, example can test dem60~ind60 higher dem65~ind60. see 97% posteriors state dem60~ind60 higher dem65~ind60, mean difference (dem60~ind60 - dem65~ind60) Estimate=0.46","code":"model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ a*y1 + b*y2 + c*y3 + d*y4      dem65 =~ a*y5 + b*y6 + c*y7 + d*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit <- bsem(model, data=PoliticalDemocracy,             std.lv=T, meanstructure=T) summary(fit, standardize=T, rsquare=T) ## blavaan 0.5.2.1191 ended normally after 1000 iterations ##  ##   Estimator                                      BAYES ##   Optimization method                             MCMC ##   Number of model parameters                        42 ##   Number of equality constraints                     4 ##  ##   Number of observations                            75 ##  ##   Statistic                                 MargLogLik         PPP ##   Value                                             NA       0.023 ##  ## Parameter Estimates: ##  ##  ## Latent Variables: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##   ind60 =~                                                               ##     x1                0.708    0.075    0.578    0.866    0.708    0.923 ##     x2                1.543    0.146    1.291    1.854    1.543    0.973 ##     x3                1.280    0.149    1.013    1.601    1.280    0.872 ##   dem60 =~                                                               ##     y1         (a)    1.466    0.171    1.138    1.806    1.794    0.764 ##     y2         (b)    1.738    0.229    1.300    2.199    2.127    0.585 ##     y3         (c)    1.816    0.201    1.435    2.227    2.223    0.701 ##     y4         (d)    1.951    0.195    1.577    2.344    2.388    0.790 ##   dem65 =~                                                               ##     y5         (a)    1.466    0.171    1.138    1.806    2.314    0.814 ##     y6         (b)    1.738    0.229    1.300    2.199    2.743    0.771 ##     y7         (c)    1.816    0.201    1.435    2.227    2.867    0.837 ##     y8         (d)    1.951    0.195    1.577    2.344    3.080    0.871 ##      Rhat    Prior        ##                           ##     1.001    normal(0,10) ##     1.001    normal(0,10) ##     1.001    normal(0,10) ##                           ##     1.001    normal(0,10) ##     0.999    normal(0,10) ##     1.001    normal(0,10) ##     1.000    normal(0,10) ##                           ##     1.001                 ##     0.999                 ##     1.001                 ##     1.000                 ##  ## Regressions: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##   dem60 ~                                                                ##     ind60             0.705    0.172    0.384    1.065    0.576    0.576 ##   dem65 ~                                                                ##     ind60             0.250    0.173   -0.094    0.596    0.158    0.158 ##     dem60             0.866    0.129    0.624    1.124    0.672    0.672 ##      Rhat    Prior        ##                           ##     1.001    normal(0,10) ##                           ##     0.999    normal(0,10) ##     1.000    normal(0,10) ##  ## Covariances: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##  .y1 ~~                                                                  ##    .y5                0.737    0.440   -0.022    1.689    0.737    0.295 ##  .y2 ~~                                                                  ##    .y4                1.784    0.829    0.350    3.686    1.784    0.326 ##    .y6                2.222    0.853    0.713    4.068    2.222    0.332 ##  .y3 ~~                                                                  ##    .y7                1.319    0.675    0.116    2.760    1.319    0.312 ##  .y4 ~~                                                                  ##    .y8                0.381    0.493   -0.515    1.411    0.381    0.118 ##  .y6 ~~                                                                  ##    .y8                1.092    0.691   -0.186    2.550    1.092    0.277 ##      Rhat    Prior        ##                           ##     1.000       beta(1,1) ##                           ##     1.000       beta(1,1) ##     1.000       beta(1,1) ##                           ##     1.000       beta(1,1) ##                           ##     1.000       beta(1,1) ##                           ##     1.001       beta(1,1) ##  ## Intercepts: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##    .x1                5.053    0.091    4.872    5.226    5.053    6.588 ##    .x2                4.789    0.188    4.411    5.153    4.789    3.022 ##    .x3                3.554    0.175    3.200    3.886    3.554    2.423 ##    .y1                5.461    0.276    4.913    6.000    5.461    2.326 ##    .y2                4.251    0.433    3.422    5.143    4.251    1.170 ##    .y3                6.556    0.372    5.822    7.282    6.556    2.069 ##    .y4                4.451    0.348    3.757    5.116    4.451    1.472 ##    .y5                5.133    0.330    4.462    5.776    5.133    1.806 ##    .y6                2.970    0.413    2.142    3.769    2.970    0.834 ##    .y7                6.190    0.407    5.393    6.979    6.190    1.807 ##    .y8                4.038    0.412    3.193    4.813    4.038    1.142 ##     ind60             0.000                               0.000    0.000 ##    .dem60             0.000                               0.000    0.000 ##    .dem65             0.000                               0.000    0.000 ##      Rhat    Prior        ##     1.005    normal(0,32) ##     1.003    normal(0,32) ##     1.002    normal(0,32) ##     1.001    normal(0,32) ##     1.000    normal(0,32) ##     1.001    normal(0,32) ##     1.002    normal(0,32) ##     1.001    normal(0,32) ##     1.000    normal(0,32) ##     1.000    normal(0,32) ##     1.002    normal(0,32) ##                           ##                           ##                           ##  ## Variances: ##                    Estimate  Post.SD pi.lower pi.upper   Std.lv  Std.all ##    .x1                0.088    0.023    0.048    0.138    0.088    0.149 ##    .x2                0.132    0.081    0.001    0.305    0.132    0.052 ##    .x3                0.514    0.105    0.338    0.745    0.514    0.239 ##    .y1                2.295    0.589    1.266    3.588    2.295    0.416 ##    .y2                8.687    1.621    5.949   12.160    8.687    0.658 ##    .y3                5.102    1.037    3.353    7.429    5.102    0.508 ##    .y4                3.444    0.922    1.872    5.473    3.444    0.377 ##    .y5                2.724    0.648    1.652    4.118    2.724    0.337 ##    .y6                5.148    1.082    3.170    7.515    5.148    0.406 ##    .y7                3.515    0.852    2.089    5.450    3.515    0.300 ##    .y8                3.014    0.885    1.324    4.874    3.014    0.241 ##     ind60             1.000                               1.000    1.000 ##    .dem60             1.000                               0.668    0.668 ##    .dem65             1.000                               0.401    0.401 ##      Rhat    Prior        ##     1.000 gamma(1,.5)[sd] ##     1.003 gamma(1,.5)[sd] ##     1.000 gamma(1,.5)[sd] ##     1.000 gamma(1,.5)[sd] ##     1.000 gamma(1,.5)[sd] ##     1.000 gamma(1,.5)[sd] ##     1.000 gamma(1,.5)[sd] ##     1.001 gamma(1,.5)[sd] ##     1.000 gamma(1,.5)[sd] ##     0.999 gamma(1,.5)[sd] ##     1.000 gamma(1,.5)[sd] ##                           ##                           ##                           ##  ## R-Square: ##                    Estimate ##     x1                0.851 ##     x2                0.948 ##     x3                0.761 ##     y1                0.584 ##     y2                0.342 ##     y3                0.492 ##     y4                0.623 ##     y5                0.663 ##     y6                0.594 ##     y7                0.700 ##     y8                0.759 ##     dem60             0.332 ##     dem65             0.599 library(brms) mc_out <- as.matrix(blavInspect(fit, \"mcmc\")) dim(mc_out) ## [1] 3000   42 colnames(mc_out) ##  [1] \"ly_sign[1]\"    \"ly_sign[2]\"    \"ly_sign[3]\"    \"ly_sign[4]\"    ##  [5] \"ly_sign[5]\"    \"ly_sign[6]\"    \"ly_sign[7]\"    \"ly_sign[4]\"    ##  [9] \"ly_sign[5]\"    \"ly_sign[6]\"    \"ly_sign[7]\"    \"bet_sign[1]\"   ## [13] \"bet_sign[2]\"   \"bet_sign[3]\"   \"Theta_cov[1]\"  \"Theta_cov[2]\"  ## [17] \"Theta_cov[3]\"  \"Theta_cov[4]\"  \"Theta_cov[5]\"  \"Theta_cov[6]\"  ## [21] \"Theta_var[1]\"  \"Theta_var[2]\"  \"Theta_var[3]\"  \"Theta_var[4]\"  ## [25] \"Theta_var[5]\"  \"Theta_var[6]\"  \"Theta_var[7]\"  \"Theta_var[8]\"  ## [29] \"Theta_var[9]\"  \"Theta_var[10]\" \"Theta_var[11]\" \"Nu_free[1]\"    ## [33] \"Nu_free[2]\"    \"Nu_free[3]\"    \"Nu_free[4]\"    \"Nu_free[5]\"    ## [37] \"Nu_free[6]\"    \"Nu_free[7]\"    \"Nu_free[8]\"    \"Nu_free[9]\"    ## [41] \"Nu_free[10]\"   \"Nu_free[11]\" pt <- partable(fit)[,c(\"lhs\",\"op\",\"rhs\",\"pxnames\")] pt ##      lhs op   rhs       pxnames ## 1  ind60 =~    x1    ly_sign[1] ## 2  ind60 =~    x2    ly_sign[2] ## 3  ind60 =~    x3    ly_sign[3] ## 4  dem60 =~    y1    ly_sign[4] ## 5  dem60 =~    y2    ly_sign[5] ## 6  dem60 =~    y3    ly_sign[6] ## 7  dem60 =~    y4    ly_sign[7] ## 8  dem65 =~    y5    ly_sign[4] ## 9  dem65 =~    y6    ly_sign[5] ## 10 dem65 =~    y7    ly_sign[6] ## 11 dem65 =~    y8    ly_sign[7] ## 12 dem60  ~ ind60   bet_sign[1] ## 13 dem65  ~ ind60   bet_sign[2] ## 14 dem65  ~ dem60   bet_sign[3] ## 15    y1 ~~    y5  Theta_cov[1] ## 16    y2 ~~    y4  Theta_cov[2] ## 17    y2 ~~    y6  Theta_cov[3] ## 18    y3 ~~    y7  Theta_cov[4] ## 19    y4 ~~    y8  Theta_cov[5] ## 20    y6 ~~    y8  Theta_cov[6] ## 21    x1 ~~    x1  Theta_var[1] ## 22    x2 ~~    x2  Theta_var[2] ## 23    x3 ~~    x3  Theta_var[3] ## 24    y1 ~~    y1  Theta_var[4] ## 25    y2 ~~    y2  Theta_var[5] ## 26    y3 ~~    y3  Theta_var[6] ## 27    y4 ~~    y4  Theta_var[7] ## 28    y5 ~~    y5  Theta_var[8] ## 29    y6 ~~    y6  Theta_var[9] ## 30    y7 ~~    y7 Theta_var[10] ## 31    y8 ~~    y8 Theta_var[11] ## 32 ind60 ~~ ind60          <NA> ## 33 dem60 ~~ dem60          <NA> ## 34 dem65 ~~ dem65          <NA> ## 35    x1 ~1          Nu_free[1] ## 36    x2 ~1          Nu_free[2] ## 37    x3 ~1          Nu_free[3] ## 38    y1 ~1          Nu_free[4] ## 39    y2 ~1          Nu_free[5] ## 40    y3 ~1          Nu_free[6] ## 41    y4 ~1          Nu_free[7] ## 42    y5 ~1          Nu_free[8] ## 43    y6 ~1          Nu_free[9] ## 44    y7 ~1         Nu_free[10] ## 45    y8 ~1         Nu_free[11] ## 46 ind60 ~1                <NA> ## 47 dem60 ~1                <NA> ## 48 dem65 ~1                <NA> ## 49  .p4. ==  .p8.          <NA> ## 50  .p5. ==  .p9.          <NA> ## 51  .p6. == .p10.          <NA> ## 52  .p7. == .p11.          <NA> pt[pt$op==\"~\",] ##      lhs op   rhs     pxnames ## 12 dem60  ~ ind60 bet_sign[1] ## 13 dem65  ~ ind60 bet_sign[2] ## 14 dem65  ~ dem60 bet_sign[3] hypothesis(mc_out, \"bet_sign[2] > 0\", alpha = 0.05) ## New names: ## • `ly_sign[4]` -> `ly_sign[4]...4` ## • `ly_sign[5]` -> `ly_sign[5]...5` ## • `ly_sign[6]` -> `ly_sign[6]...6` ## • `ly_sign[7]` -> `ly_sign[7]...7` ## • `ly_sign[4]` -> `ly_sign[4]...8` ## • `ly_sign[5]` -> `ly_sign[5]...9` ## • `ly_sign[6]` -> `ly_sign[6]...10` ## • `ly_sign[7]` -> `ly_sign[7]...11` ## Hypothesis Tests for class : ##          Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob ## 1 (bet_sign[2]) > 0     0.25      0.17    -0.04     0.53      13.15      0.93 ##   Star ## 1      ## --- ## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses. ## '*': For one-sided hypotheses, the posterior probability exceeds 95%; ## for two-sided hypotheses, the value tested against lies outside the 95%-CI. ## Posterior probabilities of point hypotheses assume equal prior probabilities. hypothesis(mc_out, \"bet_sign[1] > 0\", alpha = 0.05) ## New names: ## • `ly_sign[4]` -> `ly_sign[4]...4` ## • `ly_sign[5]` -> `ly_sign[5]...5` ## • `ly_sign[6]` -> `ly_sign[6]...6` ## • `ly_sign[7]` -> `ly_sign[7]...7` ## • `ly_sign[4]` -> `ly_sign[4]...8` ## • `ly_sign[5]` -> `ly_sign[5]...9` ## • `ly_sign[6]` -> `ly_sign[6]...10` ## • `ly_sign[7]` -> `ly_sign[7]...11` ## Hypothesis Tests for class : ##          Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob ## 1 (bet_sign[1]) > 0     0.71      0.17     0.44     1.01        Inf         1 ##   Star ## 1    * ## --- ## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses. ## '*': For one-sided hypotheses, the posterior probability exceeds 95%; ## for two-sided hypotheses, the value tested against lies outside the 95%-CI. ## Posterior probabilities of point hypotheses assume equal prior probabilities. hypothesis(mc_out, \"bet_sign[1] - bet_sign[2] > 0\", alpha = 0.05) ## New names: ## • `ly_sign[4]` -> `ly_sign[4]...4` ## • `ly_sign[5]` -> `ly_sign[5]...5` ## • `ly_sign[6]` -> `ly_sign[6]...6` ## • `ly_sign[7]` -> `ly_sign[7]...7` ## • `ly_sign[4]` -> `ly_sign[4]...8` ## • `ly_sign[5]` -> `ly_sign[5]...9` ## • `ly_sign[6]` -> `ly_sign[6]...10` ## • `ly_sign[7]` -> `ly_sign[7]...11` ## Hypothesis Tests for class : ##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio ## 1 (bet_sign[1]-bet_... > 0     0.46      0.26     0.06     0.91      32.71 ##   Post.Prob Star ## 1      0.97    * ## --- ## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses. ## '*': For one-sided hypotheses, the posterior probability exceeds 95%; ## for two-sided hypotheses, the value tested against lies outside the 95%-CI. ## Posterior probabilities of point hypotheses assume equal prior probabilities."},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"region-of-practical-equivalence-rope","dir":"Articles","previous_headings":"","what":"Region of Practical Equivalence (ROPE)","title":"Probability of Direction","text":"Note far tested hypothesis 0, equivalent frequentist null hypothesis tests. can test . Bayesian inference based statistical significance, effects tested “zero”. Indeed, Bayesian framework offers probabilistic view parameters, allowing assessment uncertainty related . Thus, rather concluding effect present simply differs zero, conclude probability outside specific range can considered “practically effect” (.e., negligible magnitude) sufficient. range called region practical equivalence (ROPE). Indeed, statistically, probability posterior distribution different 0 make much sense (probability different single point infinite). Therefore, idea underlining ROPE let user define area around null value enclosing values equivalent null value practical purposes (Kruschke Liddell 2018) examples, change value tested, common recommendations use |0.1| minimally relevant value standardized regressions, case find 0.79 proportion posterior 0.1","code":"hypothesis(mc_out, \"bet_sign[2] > .1\", alpha = 0.05) ## New names: ## • `ly_sign[4]` -> `ly_sign[4]...4` ## • `ly_sign[5]` -> `ly_sign[5]...5` ## • `ly_sign[6]` -> `ly_sign[6]...6` ## • `ly_sign[7]` -> `ly_sign[7]...7` ## • `ly_sign[4]` -> `ly_sign[4]...8` ## • `ly_sign[5]` -> `ly_sign[5]...9` ## • `ly_sign[6]` -> `ly_sign[6]...10` ## • `ly_sign[7]` -> `ly_sign[7]...11` ## Hypothesis Tests for class : ##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio ## 1 (bet_sign[2])-(.1) > 0     0.15      0.17    -0.14     0.43        4.3 ##   Post.Prob Star ## 1      0.81      ## --- ## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses. ## '*': For one-sided hypotheses, the posterior probability exceeds 95%; ## for two-sided hypotheses, the value tested against lies outside the 95%-CI. ## Posterior probabilities of point hypotheses assume equal prior probabilities."},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"vs--95-ci","dir":"Articles","previous_headings":"","what":"89% vs. 95% CI","title":"Probability of Direction","text":"commonly frequentist tradition see use 95% Credible interval. Using 89% another popular choice, used default long time. start? Naturally, came choosing CI level report default, people started using 95%, arbitrary convention used frequentist world. However, authors suggested 95% might appropriate Bayesian posterior distributions, potentially lacking stability enough posterior samples drawn (McElreath 2020). proposition use 90% instead 95%. However, recently, McElreath (2020) suggested use arbitrary thresholds first place, use 89%? Moreover, 89 highest prime number exceed already unstable 95% threshold. anything? Nothing, reminds us total arbitrariness conventions (McElreath 2020). can use argument alpha argument hypothesis function, interpretation values Post.Prob","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/probability_direction.html","id":"caveats","dir":"Articles","previous_headings":"","what":"Caveats","title":"Probability of Direction","text":"Although allows testing hypotheses similar manner frequentist null-hypothesis testing framework, strongly argue using arbitrary cutoffs (e.g., p < .05) determine ‘existence’ effect. ROPE sensitive scale, aware value interest representative respective scale. , standardize parameters useful commonly used scale","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/articles/start.html","id":"installation","dir":"Articles","previous_headings":"","what":"Installation","title":"Getting Started with blavaan","text":"blavaan can installed CRAN usual way: situations, may wish install blavaan GitHub. GitHub version sometimes contains bug fixes yet CRAN, though can also less stable. install GitHub, use following command. command requires system can compile Stan models, guaranteed usually install blavaan CRAN. trouble, may help look RStan Getting Started page.","code":"install.packages(\"blavaan\") remotes::install_github(\"ecmerkle/blavaan\", INSTALL_opts = \"--no-multiarch\")"},{"path":"http://ecmerkle.github.io/blavaan/articles/start.html","id":"commands-and-syntax","dir":"Articles","previous_headings":"","what":"Commands and Syntax","title":"Getting Started with blavaan","text":"blavaan package depends lavaan package model specification computations. means , already know lavaan, already able many things blavaan. particular, many blavaan commands add letter “b” start lavaan command. example, sem() becomes bsem(), lavInspect() becomes blavInspect(). also sometimes possible use lavaan command blavaan object, though results may always expect. details mind, look lavaan tutorial many examples models. can translate many examples blavaan adding “b” start commands. look pages , learn additional blavaan arguments specific Bayesian methods.","code":""},{"path":"http://ecmerkle.github.io/blavaan/articles/summaries.html","id":"convergence","dir":"Articles","previous_headings":"","what":"Convergence","title":"Model Summaries","text":"Following model estimation, immediately wish look “goodness” posterior samples, including convergence stationary distribution autocorrelation. Popular convergence metrics available via blavInspect() function: R-hat values near 1.00 indicate convergence, large effective sample sizes (hundreds ) preferred. details metrics, see, e.g., Posterior Analysis section Stan Reference Manual. model definitely converged (judged Rhat), blavaan issue multiple warnings. Lack convergence sometimes caused bad initial values chain strays extreme region posterior space. cases, can helpful re-estimate model second time. also helpful specify mildly-informative priors loading parameters, chains wander extreme loading values. example, expect variables positively correlated loadings fixed 1 identification, Normal(1,.5) often mildly-informative prior. Otherwise, lack convergence may imply prior distributions severely conflict data, ill-defined model. sometimes helpful try fit model lavaan, observe whether errors occur .","code":"blavInspect(fit, 'rhat') blavInspect(fit, 'neff')"},{"path":"http://ecmerkle.github.io/blavaan/articles/summaries.html","id":"model-fit-comparison","dir":"Articles","previous_headings":"","what":"Model Fit & Comparison","title":"Model Summaries","text":"Next, may wish examine model fit metrics. many metrics available summary() output, available fitMeasures() function: judging absolute fit, blavaan supplies posterior predictive p-value based likelihood ratio statistic. Good-fitting models values near 0.5 metric. examining models’ relative fits, blavaan supplies DIC, WAIC, LOOIC. latter two metrics computed help loo package (Vehtari et al. 2020). Comparison multiple models criteria facilitated via blavCompare(), provides standard errors difference two criteria. notable functions include blavFitIndices() alternative measures absolute fit ppmc() general posterior predictive checks.","code":"summary(fit) fitMeasures(fit)"},{"path":"http://ecmerkle.github.io/blavaan/articles/summaries.html","id":"latent-variables-standardization","dir":"Articles","previous_headings":"","what":"Latent Variables & Standardization","title":"Model Summaries","text":"often-discussed advantage Bayesian models abilities describe uncertainty “random” parameters, including random effects latent variables. access functionality blavaan, users must set save.lvs = TRUE model estimation, done top page. model estimation, uses can access information via blavInspect() blavPredict(). Relevant arguments blavInspect() include lvmeans lvs. former returns posterior means latent variables, similar predictions supplied frequentist models. latter returns posterior samples latent variables, users summarize uncertainties functions latent variables. posterior samples returned list length n.chains, list entry row per posterior sample (number columns total number latent variables model): related, different, information can obtained blavPredict(). function also return posterior samples latent variables, matrix instead list: blavPredict() function also return predictions observed variables conditioned sampled latent variables. type = \"yhat\" argument returns expected values observed variables conditioned latent variable samples; type = \"ypred\" argument returns posterior predictions observed variables including residual noise (essentially yhat + error); type = \"ymis\" argument returns posterior predictions missing variables conditioned observed. expected values predictions returned list format; matrix, see last line code . Finally, fully related latent variables: standardizedPosterior() function return standardized posterior draws. calls lavaan function standardizedSolution() background function’s flexibility.","code":"postmns <- blavInspect(fit, what = \"lvmeans\") postsamps <- blavInspect(fit, what = \"lvs\") postsamps <- blavPredict(fit, type = \"lv\") evpreds <- blavPredict(fit, type = \"yhat\") postpreds <- blavPredict(fit, type = \"ypred\") mispreds <- blavPredict(fit, type = \"ymis\")  ## convert to matrix from list: evpreds <- do.call(\"rbind\", evpreds)"},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Edgar Merkle. Author, maintainer. Yves Rosseel. Author. Ben Goodrich. Author. Mauricio Garnier-Villarreal. Contributor.            R/blav_compare.RR/ctr_bayes_fit.Rvignettes Terrence D. Jorgensen. Contributor.            R/ctr_bayes_fit.RR/ctr_ppmc.RR/blav_predict.R Huub Hoofs. Contributor.            R/ctr_bayes_fit.R Rens van de Schoot. Contributor.            R/ctr_bayes_fit.R Andrew Johnson. Contributor.            Makevars Matthew Emery. Contributor.            loo moment_match","code":""},{"path":"http://ecmerkle.github.io/blavaan/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Merkle EC, Fitzsimmons E, Uanhoro J, Goodrich B (2021). “Efficient Bayesian Structural Equation Modeling Stan.” Journal Statistical Software, 100(6), 1–22. doi:10.18637/jss.v100.i06. Merkle EC, Rosseel Y (2018). “blavaan: Bayesian Structural Equation Models via Parameter Expansion.” Journal Statistical Software, 85(4), 1–30. doi:10.18637/jss.v085.i04.","code":"@Article{,   title = {Efficient {Bayesian} Structural Equation Modeling in {Stan}},   author = {Edgar C. Merkle and Ellen Fitzsimmons and James Uanhoro and Ben Goodrich},   journal = {Journal of Statistical Software},   year = {2021},   volume = {100},   number = {6},   pages = {1--22},   doi = {10.18637/jss.v100.i06}, } @Article{,   title = {{blavaan: Bayesian} Structural Equation Models via Parameter Expansion},   author = {Edgar C. Merkle and Yves Rosseel},   journal = {Journal of Statistical Software},   year = {2018},   volume = {85},   number = {4},   pages = {1--30},   doi = {10.18637/jss.v085.i04}, }"},{"path":"http://ecmerkle.github.io/blavaan/index.html","id":"blavaan","dir":"","previous_headings":"","what":"Bayesian Latent Variable Analysis","title":"Bayesian Latent Variable Analysis","text":"blavaan free, open source R package Bayesian latent variable analysis. relies JAGS Stan estimate models via MCMC. blavaan functions syntax similar lavaan. example, consider Political Democracy example Bollen (1989): development version blavaan (containing updates yet CRAN) can installed via command . Compilation required; may problem users currently rely binary version blavaan CRAN. information, see: Merkle, E. C., Fitzsimmons, E., Uanhoro, J., & Goodrich, B. (2021). Efficient Bayesian structural equation modeling Stan. Journal Statistical Software, 100(6), 1–22. Merkle, E. C., & Rosseel, Y. (2018). blavaan: Bayesian structural equation models via parameter expansion. Journal Statistical Software, 85(4), 1–30. blavaan supported Institute Education Sciences, U.S. Department Education, Grant R305D210044, well NSF grants SES-1061334 1460719.","code":"library(blavaan)  model <- '    # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ y1 + y2 + y3 + y4      dem65 =~ y5 + y6 + y7 + y8    # regressions      dem60 ~ ind60      dem65 ~ ind60 + dem60    # residual covariances      y1 ~~ y5      y2 ~~ y4 + y6      y3 ~~ y7      y4 ~~ y8      y6 ~~ y8 ' fit <- bsem(model, data = PoliticalDemocracy) summary(fit) remotes::install_github(\"ecmerkle/blavaan\", INSTALL_opts = \"--no-multiarch\")"},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit Confirmatory Factor Analysis Models — bcfa","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"Fit Confirmatory Factor Analysis (CFA) model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"","code":"bcfa(..., cp = \"srs\",      dp = NULL, n.chains = 3, burnin, sample,      adapt, mcmcfile = FALSE, mcmcextra = list(), inits = \"simple\",      convergence = \"manual\", target = \"stan\", save.lvs = FALSE,      wiggle = NULL, wiggle.sd = 0.1, prisamp = FALSE, jags.ic = FALSE,      seed = NULL, bcontrol = list())"},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"... Default lavaan arguments.  See lavaan. cp Handling prior distributions covariance parameters:   possible values \"srs\" (default)     \"fa\". Option \"fa\" available target=\"jags\". dp Default prior distributions different types     parameters, typically result call dpriors().     See dpriors() help file information. n.chains Number desired MCMC chains. burnin Number burnin/warmup iterations (including adaptive   iterations, target=\"jags\"). Defaults 4000 target=\"jags\"   500 Stan targets. sample total number samples take burnin. Defaults 10000 target=\"jags\" 1000 Stan targets. adapt target=\"jags\", number adaptive iterations use start   sampling. Defaults 1000. mcmcfile TRUE, JAGS/Stan model written file   (lavExport directory). Can also supply character   string, serves name directory files written. mcmcextra list potential names syntax (unavailable   target=\"stan\"),   monitor, data, llnsamp. syntax object text string containing extra   code insert JAGS/Stan model syntax. data object   list extra data send JAGS/Stan model.    moment_match_k_threshold specified within data looic    model calculated using moment matching. monitor object   character vector containing extra JAGS/Stan parameters   monitor. llnsamp object relevant models ordinal   variables, specifies number samples drawn approximate   model log-likelihood (larger numbers imply higher accuracy   longer time). log-likelihood specifically used compute   information criteria. inits character string, options currently     \"simple\" (default), \"Mplus\", \"prior\", \"jags\".  first two     cases, parameter values set though estimated via     ML (see lavaan).  starting parameter value     chain perturbed original values     addition random uniform noise.  \"prior\" used, starting     parameter values obtained based prior distributions     (also trying ensure starting values crash     model estimation).  \"jags\", starting values     specified JAGS choose values (probably     crash Stan targets). can also supply     list starting values chain, list format can     obtained , e.g., blavInspect(fit, \"inits\"). Finally,     can specify starting values similar way lavaan,     using lavaan start argument (see lavaan     documentation options ). case, also set     inits=\"simple\", aware starting values     used chain. convergence Useful target=\"jags\". \"auto\", parameters   sampled convergence achieved (via autorun.jags()).   case, arguments burnin sample passed   autorun.jags() startburnin startsample,   respectively. Otherwise, parameters   sampled specified user (run.jags   defaults). target Desired MCMC sampling, \"stan\" (pre-compiled   marginal approach)   default. Also available \"vb\", calls rstan function   vb(). options include \"jags\", \"stancond\",   \"stanclassic\", sample latent variables provide   greater functionality (syntax written \"fly\").   slower less efficient. save.lvs sampled latent variables (factor scores)   saved? Logical; defaults FALSE wiggle Labels equality-constrained parameters   \"approximately\" equal. Can also \"intercepts\", \"loadings\",   \"regressions\", \"means\". wiggle.sd prior sd (normal distribution) used approximate equality   constraints. Can one value, (target=\"stan\") numeric vector   values length wiggle. prisamp samples drawn prior, instead   posterior (target=\"stan\" )? Logical; defaults FALSE jags.ic DIC computed JAGS way, addition BUGS way? Logical; defaults FALSE seed vector length n.chains (target   \"jags\") integer (target \"stan\") containing random   seeds MCMC run. NULL, seeds chosen randomly. bcontrol list containing additional parameters passed     run.jags (autorun.jags) stan.  See manpage functions     overview additional parameters can set.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"bcfa function wrapper general     blavaan function, using following default     lavaan arguments:     int.ov.free = TRUE, int.lv.free = FALSE,     auto.fix.first = TRUE (unless std.lv = TRUE),     auto.fix.single = TRUE, auto.var = TRUE,     auto.cov.lv.x = TRUE,     auto.th = TRUE, auto.delta = TRUE,     auto.cov.y = TRUE.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"object class lavaan, several methods   available, including summary method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/bcfa.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit Confirmatory Factor Analysis Models — bcfa","text":"","code":"if (FALSE) { # The Holzinger and Swineford (1939) example HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939) summary(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit Growth Curve Models — bgrowth","title":"Fit Growth Curve Models — bgrowth","text":"Fit Growth Curve model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit Growth Curve Models — bgrowth","text":"","code":"bgrowth(..., cp = \"srs\", dp = NULL, n.chains = 3, burnin, sample, adapt, mcmcfile = FALSE, mcmcextra = list(),  inits = \"simple\", convergence = \"manual\", target = \"stan\", save.lvs = FALSE, wiggle = NULL, wiggle.sd = 0.1, prisamp = FALSE, jags.ic = FALSE, seed = NULL, bcontrol = list())"},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit Growth Curve Models — bgrowth","text":"... Default lavaan arguments.  See lavaan. cp Handling prior distributions covariance parameters:   possible values \"srs\" (default) \"fa\". Option \"fa\" available target=\"jags\". dp Default prior distributions different types     parameters, typically result call dpriors().     See dpriors() help file information. n.chains Number desired MCMC chains. burnin Number burnin/warmup iterations (including adaptive   iterations, target=\"jags\"). Defaults 4000 target=\"jags\"   500 Stan targets. sample total number samples take burnin. Defaults 10000 target=\"jags\" 1000 Stan targets. adapt target=\"jags\", number adaptive iterations use start   sampling. Defaults 1000. mcmcfile TRUE, JAGS/Stan model written file   (lavExport directory). Can also supply character   string, serves name directory files written. mcmcextra list potential names syntax (unavailable   target=\"stan\"),   monitor, data, llnsamp. syntax object text string containing extra   code insert JAGS/Stan model syntax. data object   list extra data send JAGS/Stan model.    moment_match_k_threshold specified within data looic    model calculated using moment matching. monitor object   character vector containing extra JAGS/Stan parameters   monitor. llnsamp object relevant models ordinal   variables, specifies number samples drawn approximate   model log-likelihood (larger numbers imply higher accuracy   longer time). log-likelihood specifically used compute   information criteria. inits character string, options currently     \"simple\" (default), \"Mplus\", \"prior\", \"jags\".  first two     cases, parameter values set though estimated via     ML (see lavaan).  starting parameter value     chain perturbed original values     addition random uniform noise.  \"prior\" used, starting     parameter values obtained based prior distributions     (also trying ensure starting values crash     model estimation).  \"jags\", starting values     specified JAGS choose values (probably     crash Stan targets). can also supply     list starting values chain, list format can     obtained , e.g., blavInspect(fit, \"inits\"). Finally,     can specify starting values similar way lavaan,     using lavaan start argument (see lavaan     documentation options ). case, also set     inits=\"simple\", aware starting values     used chain. convergence Useful target=\"jags\". \"auto\", parameters   sampled convergence achieved (via autorun.jags()).   case, arguments burnin sample passed   autorun.jags() startburnin startsample,   respectively. Otherwise, parameters   sampled specified user (run.jags   defaults). target Desired MCMC sampling, \"stan\" (pre-compiled   marginal approach)   default. Also available \"vb\", calls rstan function   vb(). options include \"jags\", \"stancond\",   \"stanclassic\", sample latent variables provide   greater functionality (syntax written \"fly\").   slower less efficient. save.lvs sampled latent variables (factor scores)   saved? Logical; defaults FALSE wiggle Labels equality-constrained parameters   \"approximately\" equal. Can also \"intercepts\", \"loadings\",   \"regressions\", \"means\". wiggle.sd prior sd (normal distribution) used approximate equality   constraints. Can one value, (target=\"stan\") numeric vector   values length wiggle. prisamp samples drawn prior, instead   posterior (target=\"stan\" )? Logical; defaults FALSE jags.ic DIC computed JAGS way, addition BUGS way? Logical; defaults FALSE seed vector length n.chains (target   \"jags\") integer (target \"stan\") containing random   seeds MCMC run. NULL, seeds chosen randomly. bcontrol list containing additional parameters passed     run.jags (autorun.jags) stan.  See manpage functions     overview additional parameters can set.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit Growth Curve Models — bgrowth","text":"bgrowth function wrapper general       blavaan function, using following default       lavaan arguments:     meanstructure = TRUE,      int.ov.free = FALSE, int.lv.free = TRUE,     auto.fix.first = TRUE (unless std.lv = TRUE),     auto.fix.single = TRUE, auto.var = TRUE,     auto.cov.lv.x = TRUE,      auto.th = TRUE, auto.delta = TRUE,     auto.cov.y = TRUE.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit Growth Curve Models — bgrowth","text":"object class blavaan, several methods   available, including summary method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit Growth Curve Models — bgrowth","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/bgrowth.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit Growth Curve Models — bgrowth","text":"","code":"if (FALSE) { ## linear growth model with a time-varying covariate model.syntax <- '   # intercept and slope with fixed coefficients     i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4     s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4    # regressions     i ~ x1 + x2     s ~ x1 + x2    # time-varying covariates     t1 ~ c1     t2 ~ c2     t3 ~ c3     t4 ~ c4 '  fit <- bgrowth(model.syntax, data=Demo.growth) summary(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":null,"dir":"Reference","previous_headings":"","what":"Bayesian model comparisons — blavCompare","title":"Bayesian model comparisons — blavCompare","text":"Bayesian model comparisons, including WAIC, LOO, Bayes factor approximation.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bayesian model comparisons — blavCompare","text":"","code":"blavCompare(object1, object2, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bayesian model comparisons — blavCompare","text":"object1 object class blavaan. object2 second object class blavaan. ... arguments (unused now).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Bayesian model comparisons — blavCompare","text":"function approximates log-Bayes factor two candidate models using Laplace approximation model's marginal log-likelihood.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Bayesian model comparisons — blavCompare","text":"log-Bayes factor approximation, along model's approximate marginal log-likelihood.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Bayesian model comparisons — blavCompare","text":"Raftery, . E. (1993). Bayesian model selection structural equation models. K. . Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 163-180). Beverly Hills, CA: Sage.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavCompare.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bayesian model comparisons — blavCompare","text":"","code":"if (FALSE) { hsm1 <- ' visual  =~ x1 + x2 + x3 + x4           textual =~ x4 + x5 + x6           speed   =~ x7 + x8 + x9 '  fit1 <- bcfa(hsm1, data=HolzingerSwineford1939)  hsm2 <- ' visual  =~ x1 + x2 + x3           textual =~ x4 + x5 + x6 + x7           speed   =~ x7 + x8 + x9 '  fit2 <- bcfa(hsm2, data=HolzingerSwineford1939)  blavCompare(fit1, fit2) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":null,"dir":"Reference","previous_headings":"","what":"SEM Fit Indices for Bayesian SEM — blavFitIndices","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"function provides posterior distribution \\(\\chi^2\\)-based fit indices assess global fit latent variable model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"","code":"blavFitIndices(object, thin = 1L, pD = c(\"loo\",\"waic\",\"dic\"),                rescale = c(\"devM\",\"ppmc\",\"mcmc\"),                fit.measures = \"all\", baseline.model = NULL)  ## S4 method for signature 'blavFitIndices' # S4 method for blavFitIndices summary(object, ...)  # S3 method for bfi summary(object, central.tendency = c(\"mean\",\"median\",\"mode\"),         hpd = TRUE, prob = .90)"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"object object class blavaan. thin Optional integer indicating much thin chain.     Default 1L, indicating thin chains. pD character indicating information criterion     returned fitMeasures(object) use estimated number     parameters. default leave-one-information criterion     (LOO-IC), highly recommended Vehtari et al. (2017). rescale character indicating method used calculate     fit indices. rescale = \"devM\" (default), Bayesian analog     \\(\\chi^2\\) statistic (deviance evaluated posterior mean     model parameters) approximated rescaling deviance     iteration subtracting estimated number parameters.     rescale = \"PPMC\", deviance iteration rescaled     subtracting deviance data simulated posterior predictive     distribution (posterior predictive model checking; see Hoofs et al.,     2017). rescale = \"MCMC\", fit measures simply calculated     using fitMeasures iteration Markov     chain(s), based model-implied moments iteration (advised     model includes informative priors, case model's     estimated pD deviate number parameters used     calculate df fitMeasures). fit.measures \"\", fit measures available     returned. single fit measures specified name,     computed returned. rescale = \"devM\"     \"PPMC\", currently available indices \"BRMSEA\",     \"BGammaHat\", \"adjBGammaHat\", \"BMc\", \"BCFI\",     \"BTLI\", \"BNFI\". rescale = \"MCMC\", user may     request indices returned fitMeasures     objects class lavaan. baseline.model NULL, object class     blavaan, representing user-specified baseline model.     baseline.model provided, incremental fit indices (BCFI,     BTLI, BNFI) can requested fit.measures. Ignored     rescale = \"MCMC\". ... Additional arguments summary method: central.tendency Takes values \"mean\", \"median\", \"mode\", indicating statistics     used characterize location posterior distribution.     default, 3 statistics returned. posterior mean labeled     EAP expected posteriori estimate, mode     labeled MAP modal posteriori     estimate. hpd logical indicating whether calculate highest     posterior density (HPD) credible interval fit     index (defaults TRUE). prob \"confidence\" level   credible interval(s) (defaults 0.9).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"S4 object class blavFitIndices consisting 2 slots: @details list containing choices made user     (defaults; e.g., values pD rescale set),     well posterior distribution \\(\\chi^2\\) (deviance)     statistic (rescaled, rescale = \"devM\" \"PPMC\"). @indices list containing posterior distribution     requested fit.measure. summary() method returns data.frame containing one row   requested fit.measure, columns containing specified   measure(s) central.tendency, posterior SD,   (requested) HPD credible-interval limits.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"Mauricio Garnier-Villareal (Vrije Universiteit Amsterdam; mgv@pm.) Terrence D. Jorgensen (University Amsterdam; TJorgensen314@gmail.com)","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"rescale = \"PPMC\" based : Hoofs, H., van de Schoot, R., Jansen, N. W., & Kant, . (2017).   Evaluating model fit Bayesian confirmatory factor analysis large   samples: Simulation study introducing BRMSEA.   Educational Psychological Measurement. doi:10.1177/0013164417709314 rescale = \"devM\" based : Garnier-Villarreal, M., & Jorgensen, T. D. (2020).  Adapting Fit Indices Bayesian Structural Equation Modeling: Comparison Maximum Likelihood.  Psychological Methods, 25(1), 46--70. https://doi.org/dx.doi.org/10.1037/met0000224   (See also https://osf.io/afkcw/) references: Vehtari, ., Gelman, ., & Gabry, J. (2017). Practical Bayesian model   evaluation using leave-one-cross-validation WAIC.   Statistics Computing, 27(5), 1413--1432.   doi:10.1007/s11222-016-9696-4","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavFitIndices.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"SEM Fit Indices for Bayesian SEM — blavFitIndices","text":"","code":"if (FALSE) { HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 ' ## fit target model fit1 <- bcfa(HS.model, data = HolzingerSwineford1939,               n.chains = 2, burnin = 1000, sample = 1000)  ## fit null model to calculate CFI, TLI, and NFI null.model <- c(paste0(\"x\", 1:9, \" ~~ x\", 1:9), paste0(\"x\", 1:9, \" ~ 1\")) fit0 <- bcfa(null.model, data = HolzingerSwineford1939,               n.chains = 2, burnin = 1000, sample = 1000)  ## calculate posterior distributions of fit indices  ## The default method mimics fit indices derived from ML estimation ML <- blavFitIndices(fit1, baseline.model = fit0) ML summary(ML)  ## other options:  ## - use Hoofs et al.'s (2017) PPMC-based method ## - use the estimated number of parameters from WAIC instead of LOO-IC PPMC <- blavFitIndices(fit1, baseline.model = fit0,                        pD = \"waic\", rescale = \"PPMC\") ## issues a warning about using rescale=\"PPMC\" with N < 1000 (see Hoofs et al.)  ## - specify only the desired measures of central tendency ## - specify a different \"confidence\" level for the credible intervals summary(PPMC, central.tendency = c(\"mean\",\"mode\"), prob = .95)    ## Access the posterior distributions for further investigation head(distML <- data.frame(ML@indices))  ## For example, diagnostic plots using the bayesplot package:  ## distinguish chains nChains <- blavInspect(fit1, \"n.chains\") distML$Chain <- rep(1:nChains, each = nrow(distML) / nChains)  library(bayesplot) mcmc_pairs(distML, pars = c(\"BRMSEA\",\"BMc\",\"BGammaHat\",\"BCFI\",\"BTLI\"),            diag_fun = \"hist\") ## Indices are highly correlated across iterations in both chains  ## Compare to PPMC method distPPMC <- data.frame(PPMC@indices) distPPMC$Chain <- rep(1:nChains, each = nrow(distPPMC) / nChains) mcmc_pairs(distPPMC, pars = c(\"BRMSEA\",\"BMc\",\"BGammaHat\",\"BCFI\",\"BTLI\"),            diag_fun = \"dens\") ## nonlinear relation between BRMSEA, related to the floor effect of BRMSEA ## that Hoofs et al. found for larger (12-indicator) models  }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":null,"dir":"Reference","previous_headings":"","what":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"blavInspect() blavTech() functions can used inspect/extract information stored inside (can computed ) fitted blavaan object. similar lavaan's lavInspect() function.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"","code":"blavInspect(blavobject, what, ...)  blavTech(blavobject, what, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"blavobject object class blavaan. Character. needs inspected/extracted? See Details Bayes-specific options, see lavaan's lavInspect() additional options. Note: argument case-sensitive (everything converted lower case.) ... lavaan arguments supplied lavInspect(); see lavaan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"list Bayesian-specific values argument; additional values can found lavInspect() documentation. \"start\": list starting values chain, unless inits=\"jags\" used model estimation. Aliases: \"starting.values\", \"inits\". \"rhat\": parameter's potential scale reduction     factor convergence assessment. Can also use \"psrf\" instead \"rhat\" \"ac.10\": parameter's estimated lag-10 autocorrelation. \"neff\": parameters effective sample size, taking account autocorrelation. \"mcmc\": object class mcmc containing individual parameter draws MCMC run. Aliases: \"draws\", \"samples\". \"mcobj\": underlying run.jags stan object resulted MCMC run. \"n.chains\": number chains sampled. \"cp\": approach used estimating covariance     parameters (\"srs\" \"fa\"); relevant     using JAGS. \"dp\": Default prior distributions used type model parameter. \"postmode\": Estimated posterior mode free parameter. \"postmean\": Estimated posterior mean free parameter. \"postmedian\": Estimated posterior median free parameter. \"lvs\": object class mcmc containing latent variable (factor score) draws. two-level models, use level = 1 level = 2 specify factor scores want. \"lvmeans\": matrix mean factor scores (rows observations, columns variables). Use additional level argument way. \"hpd\": HPD interval free parameter. case, prob argument can used specify number (0,1) reflecting desired percentage interval.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/blavInspect.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Inspect or Extract Information from a Fitted blavaan Object — blavInspect","text":"","code":"if (FALSE) { # The Holzinger and Swineford (1939) example HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data = HolzingerSwineford1939,             bcontrol = list(method = \"rjparallel\"))  # extract information blavInspect(fit, \"psrf\") blavInspect(fit, \"hpd\", prob = .9) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":null,"dir":"Reference","previous_headings":"","what":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"purpose blavPredict() function compute various   types model predictions, conditioned observed data. differs   somewhat lavPredict() lavaan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"","code":"blavPredict(object, newdata = NULL, type = \"lv\", level = 1L)"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"object object class blavaan. newdata Currently unused. (optional data.frame, containing variables data.frame used fitting model object.) type character string. \"lv\", estimated values latent variables model computed. \"ov\" \"yhat\", predicted means observed variables model computed. \"ypred\" \"ydist\", predicted values observed variables (including residual noise) computed. \"ymis\" \"ovmis\", model predicted values (\"imputations\") missing data computed. See details information. level type = \"lv\", used specify whether one desires level 1 latent variables level 2 latent variables.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"predict() function calls blavPredict() function default options. , provide information type option. options work target=\"stan\", \"number samples\" defined number posterior samples across chains. type=\"lv\": posterior distribution latent variables conditioned observed variables. Returns list \"number samples\" entries, entry matrix rows  observations columns latent variables. type=\"yhat\": posterior expected value observed variables conditioned sampled latent variables. Returns list \"number samples\" entries, entry matrix rows observations columns observed variables. type=\"ypred\": posterior predictive distribution observed variables conditioned sampled latent variables (including residual variances). Returns list \"number samples\" entries, entry data frame rows observations columns observed variables. type=\"ymis\": posterior predictive distribution missing values conditioned observed variables. Returns matrix \"number samples\" rows \"number missing variables\" columns.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/blavPredict.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Predict the values of latent variables, observed variables, and missing variables. — blavPredict","text":"","code":"if (FALSE) { data(HolzingerSwineford1939)  ## fit model HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data = HolzingerSwineford1939, save.lvs = TRUE) lapply(blavPredict(fit)[1:2], head) # first 6 rows of first 10 posterior samples head(blavPredict(fit, type = \"yhat\")[[1]]) # top of first posterior sample  ## multigroup models return a list of factor scores (one per group) mgfit <- bcfa(HS.model, data = HolzingerSwineford1939, group = \"school\",               group.equal = c(\"loadings\",\"intercepts\"), save.lvs = TRUE)  lapply(blavPredict(fit)[1:2], head) head(blavPredict(fit, type = \"ypred\")[[1]]) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blav_internal.html","id":null,"dir":"Reference","previous_headings":"","what":"blavaan internal functions — blav_internal","title":"blavaan internal functions — blav_internal","text":"Internal functions related Bayesian model estimation.   called user.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":null,"dir":"Reference","previous_headings":"","what":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"blavaan class contains lavaan   class, representing (fitted) Bayesian latent variable   model. contains description model specified user,   summary data, internal matrix representation, model   fitted, fitting results.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"objects-from-the-class","dir":"Reference","previous_headings":"","what":"Objects from the Class","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"Objects can created via   bcfa, bsem, bgrowth   blavaan functions.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"slots","dir":"Reference","previous_headings":"","what":"Slots","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"version: lavaan package version used create objects call: function call returned match.call(). timing: elapsed time (user+system) various parts       program list, including total time. Options: Named list options provided       user, filled-automatically. ParTable: Named list describing model parameters. Can coerced data.frame. documentation, called `parameter table'. pta: Named list containing parameter table attributes. Data: Object internal class \"Data\": information data. SampleStats: Object internal class \"SampleStats\": sample       statistics Model: Object internal class \"Model\":       internal (matrix) representation model Cache: List using objects try compute , reuse many times. Fit: Object internal class \"Fit\":       results fitting model. longer used. boot: List. Unused Bayesian models. optim: List. Information optimization. loglik: List. Information loglikelihood model (maximum likelihood used). implied: List. Model implied statistics. vcov: List. Information variance matrix (vcov) model parameters. test: List. Different test statistics. h1: List. Information unrestricted h1 model (available). baseline: List. Information baseline model (often independence model) (available). external: List. Includes Stan JAGS objects used MCMC.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"methods","dir":"Reference","previous_headings":"","what":"Methods","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"coef signature(object = \"blavaan\", type = \"free\"): Returns       estimates parameters model named numeric vector.       type=\"free\", free parameters returned.       type=\"user\", parameters listed parameter table       returned, including constrained fixed parameters. vcov signature(object = \"lavaan\"): returns       covariance matrix estimated parameters. show signature(object = \"blavaan\"): Print short summary       model fit summary signature(object = \"blavaan\", header = TRUE,      fit.measures = FALSE, estimates = TRUE, ci = TRUE,       standardized = FALSE, rsquare = FALSE, std.nox = FALSE,      psrf = TRUE, neff = FALSE, postmedian = FALSE, postmode = FALSE,      priors = TRUE, bf = FALSE, nd = 3L):       Print nice summary model estimates.       header = TRUE, header section (including fit measures)       printed.       fit.measures = TRUE, additional fit measures added       header section.       estimates = TRUE, print parameter estimates section.       ci = TRUE, add confidence intervals parameter estimates       section.       standardized = TRUE,       standardized solution also printed.  Note SEs       tests still based unstandardized estimates. Use       standardizedSolution obtain SEs test       statistics standardized estimates.       rsquare=TRUE, R-Square values dependent variables       model printed.       std.nox = TRUE, std.column contains       std.nox column parameterEstimates() output.       psrf = TRUE, potential scale reduction factors (Rhats)       printed.       neff = TRUE, effective sample sizes printed.       postmedian postmode TRUE, posterior       medians modes printed instead posterior means.       priors = TRUE, parameter prior distributions       printed.       bf = TRUE, Savage-Dickey approximations Bayes       factor printed certain parameters.       Nothing returned (use       lavInspect another extractor function       extract information fitted model).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan-class.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Class For Representing A (Fitted) Bayesian Latent Variable Model — blavaan-class","text":"","code":"if (FALSE) { HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939)  summary(fit, standardized=TRUE, fit.measures=TRUE, rsquare=TRUE) coef(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit a Bayesian Latent Variable Model — blavaan","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"Fit Bayesian latent variable model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"","code":"blavaan(..., cp = \"srs\",     dp = NULL, n.chains = 3, burnin, sample,     adapt, mcmcfile = FALSE, mcmcextra = list(), inits = \"simple\",     convergence = \"manual\", target = \"stan\", save.lvs = FALSE,     wiggle = NULL, wiggle.sd = 0.1, prisamp = FALSE, jags.ic = FALSE,     seed = NULL, bcontrol = list())"},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"... Default lavaan arguments.  See lavaan. cp Handling prior distributions covariance parameters:   possible values \"srs\" (default) \"fa\".  Option   \"fa\" available target=\"jags\". dp Default prior distributions different types     parameters, typically result call dpriors().     See dpriors() help file information. n.chains Number desired MCMC chains. burnin Number burnin/warmup iterations (including adaptive   iterations, target=\"jags\"). Defaults 4000 target=\"jags\"   500 Stan targets. sample total number samples take burnin. Defaults 10000 target=\"jags\" 1000 Stan targets. adapt target=\"jags\", number adaptive iterations use start   sampling. Defaults 1000. mcmcfile TRUE, JAGS/Stan model data written   files (lavExport directory). Can also supply character   string, serves name directory files written. mcmcextra list potential names syntax (unavailable   target=\"stan\"),   monitor, data, llnsamp. syntax object text string containing extra   code insert JAGS/Stan model syntax. data object   list extra data send JAGS/Stan model.    moment_match_k_threshold specified within data looic    model calculated using moment matching. monitor object   character vector containing extra JAGS/Stan parameters   monitor. llnsamp object relevant models ordinal   variables, specifies number samples drawn approximate   model log-likelihood (larger numbers imply higher accuracy   longer time). log-likelihood specifically used compute   information criteria. inits character string, options currently     \"simple\" (default), \"Mplus\", \"prior\", \"jags\".  first two     cases, parameter values set though estimated via     ML (see lavaan).  starting parameter value     chain perturbed original values     addition random uniform noise.  \"prior\" used, starting     parameter values obtained based prior distributions     (also trying ensure starting values crash     model estimation).  \"jags\", starting values     specified JAGS choose values (probably     crash Stan targets). can also supply     list starting values chain, list format can     obtained , e.g., blavInspect(fit, \"inits\"). Finally,     can specify starting values similar way lavaan,     using lavaan start argument (see lavaan     documentation options ). case, also set     inits=\"simple\", aware starting values     used chain. convergence Useful target=\"jags\". \"auto\", parameters   sampled convergence achieved (via autorun.jags()).   case, arguments burnin sample passed   autorun.jags() startburnin startsample,   respectively. Otherwise, parameters   sampled specified user (run.jags   defaults). target Desired MCMC sampling, \"stan\" (pre-compiled   marginal approach)   default. Also available \"vb\", calls rstan function   vb(). options include \"jags\", \"stancond\",   \"stanclassic\", sample latent variables provide   greater functionality (syntax written \"fly\").   slower less efficient. save.lvs sampled latent variables (factor scores)   saved? Logical; defaults FALSE wiggle Labels equality-constrained parameters   \"approximately\" equal. Can also \"intercepts\", \"loadings\",   \"regressions\", \"means\". wiggle.sd prior sd (normal distribution) used approximate equality   constraints. Can one value, (target=\"stan\") numeric vector   values length wiggle. prisamp samples drawn prior, instead   posterior (target=\"stan\" )? Logical; defaults FALSE jags.ic DIC computed JAGS way, addition BUGS way? Logical; defaults FALSE seed vector length n.chains (target   \"jags\") integer (target \"stan\") containing random   seeds MCMC run. NULL, seeds chosen randomly. bcontrol list containing additional parameters passed     run.jags (autorun.jags) stan.  See manpage functions     overview additional parameters can set.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"object inherits class lavaan, several methods   available, including summary method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/blavaan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit a Bayesian Latent Variable Model — blavaan","text":"","code":"if (FALSE) { # The Holzinger and Swineford (1939) example HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- blavaan(HS.model, data=HolzingerSwineford1939,                auto.var=TRUE, auto.fix.first=TRUE,                auto.cov.lv.x=TRUE) summary(fit) coef(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit Structural Equation Models — bsem","title":"Fit Structural Equation Models — bsem","text":"Fit Structural Equation Model (SEM).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit Structural Equation Models — bsem","text":"","code":"bsem(..., cp = \"srs\",      dp = NULL, n.chains = 3, burnin, sample,      adapt, mcmcfile = FALSE, mcmcextra = list(), inits = \"simple\",      convergence = \"manual\", target = \"stan\", save.lvs = FALSE,      wiggle = NULL, wiggle.sd = 0.1, prisamp = FALSE, jags.ic = FALSE,      seed = NULL, bcontrol = list())"},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit Structural Equation Models — bsem","text":"... Default lavaan arguments.  See lavaan. cp Handling prior distributions covariance parameters:   possible values \"srs\" (default) \"fa\". Option \"fa\" available target=\"jags\". dp Default prior distributions different types     parameters, typically result call dpriors().     See dpriors() help file information. n.chains Number desired MCMC chains. burnin Number burnin/warmup iterations (including adaptive   iterations, target=\"jags\"). Defaults 4000 target=\"jags\"   500 Stan targets. sample total number samples take burnin. Defaults 10000 target=\"jags\" 1000 Stan targets. adapt target=\"jags\", number adaptive iterations use start   sampling. Defaults 1000. mcmcfile TRUE, JAGS/Stan model written file   (lavExport directory). Can also supply character   string, serves name directory files written. mcmcextra list potential names syntax (unavailable   target=\"stan\"),   monitor, data, llnsamp. syntax object text string containing extra   code insert JAGS/Stan model syntax. data object   list extra data send JAGS/Stan model.    moment_match_k_threshold specified within data looic    model calculated using moment matching. monitor object   character vector containing extra JAGS/Stan parameters   monitor. llnsamp object relevant models ordinal   variables, specifies number samples drawn approximate   model log-likelihood (larger numbers imply higher accuracy   longer time). log-likelihood specifically used compute   information criteria. inits character string, options currently     \"simple\" (default), \"Mplus\", \"prior\", \"jags\".  first two     cases, parameter values set though estimated via     ML (see lavaan).  starting parameter value     chain perturbed original values     addition random uniform noise.  \"prior\" used, starting     parameter values obtained based prior distributions     (also trying ensure starting values crash     model estimation).  \"jags\", starting values     specified JAGS choose values (probably     crash Stan targets). can also supply     list starting values chain, list format can     obtained , e.g., blavInspect(fit, \"inits\"). Finally,     can specify starting values similar way lavaan,     using lavaan start argument (see lavaan     documentation options ). case, also set     inits=\"simple\", aware starting values     used chain. convergence Useful target=\"jags\". \"auto\", parameters   sampled convergence achieved (via autorun.jags()).   case, arguments burnin sample passed   autorun.jags() startburnin startsample,   respectively. Otherwise, parameters   sampled specified user (run.jags   defaults). target Desired MCMC sampling, \"stan\" (pre-compiled   marginal approach)   default. Also available \"vb\", calls rstan function   vb(). options include \"jags\", \"stancond\",   \"stanclassic\", sample latent variables provide   greater functionality (syntax written \"fly\").   slower less efficient. save.lvs sampled latent variables (factor scores) saved? Logical; defaults FALSE wiggle Labels equality-constrained parameters   \"approximately\" equal. Can also \"intercepts\", \"loadings\",   \"regressions\", \"means\". wiggle.sd prior sd (normal distribution) used approximate equality   constraints. Can one value, (target=\"stan\") numeric vector   values length wiggle. prisamp samples drawn prior, instead   posterior (target=\"stan\" )? Logical; defaults FALSE jags.ic DIC computed JAGS way, addition BUGS way? Logical; defaults FALSE seed vector length n.chains (target   \"jags\") integer (target \"stan\") containing random   seeds MCMC run. NULL, seeds chosen randomly. bcontrol list containing additional parameters passed     run.jags (autorun.jags) stan.  See manpage functions     overview additional parameters can set.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Fit Structural Equation Models — bsem","text":"bsem function wrapper general     blavaan function, using following default     lavaan arguments:     int.ov.free = TRUE, int.lv.free = FALSE,     auto.fix.first = TRUE (unless std.lv = TRUE),     auto.fix.single = TRUE, auto.var = TRUE,     auto.cov.lv.x = TRUE,     auto.th = TRUE, auto.delta = TRUE,     auto.cov.y = TRUE.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Fit Structural Equation Models — bsem","text":"object class lavaan, several methods   available, including summary method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Fit Structural Equation Models — bsem","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/. Yves Rosseel (2012). lavaan: R Package Structural Equation Modeling. Journal Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/bsem.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Fit Structural Equation Models — bsem","text":"","code":"if (FALSE) { ## The industrialization and Political Democracy Example ## Bollen (1989), page 332 model <- '   # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ y1 + a*y2 + b*y3 + c*y4      dem65 =~ y5 + a*y6 + b*y7 + c*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  ## unique priors for mv intercepts; parallel chains fit <- bsem(model, data=PoliticalDemocracy,             dp=dpriors(nu=\"normal(5,10)\")) summary(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":null,"dir":"Reference","previous_headings":"","what":"Specify Default Prior Distributions — dpriors","title":"Specify Default Prior Distributions — dpriors","text":"Specify \"default\" prior distributions classes model parameters.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Specify Default Prior Distributions — dpriors","text":"","code":"dpriors(..., target = \"stan\")"},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Specify Default Prior Distributions — dpriors","text":"... Parameter names paired desired priors (see example     ). target priors jags, stan (default), stanclassic?","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Specify Default Prior Distributions — dpriors","text":"prior distributions always use JAGS/Stan syntax parameterizations.   example, normal distribution JAGS parameterized via   precision, whereas normal distribution Stan parameterized   via standard deviation. User-specified prior distributions specific parameters   (using prior() operator within model syntax) always   override prior distributions set using dpriors(). parameter names : nu: Observed variable intercept parameters. alpha: Latent variable intercept parameters. lambda: Loading parameters. beta: Regression parameters. itheta: Observed variable precision parameters. ipsi: Latent variable precision parameters. rho: Correlation parameters (associated covariance parameters). ibpsi: Inverse covariance matrix     blocks latent variables (used target=\"jags\"). tau: Threshold parameters (ordinal data ). delta: Delta parameters (ordinal data ).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Specify Default Prior Distributions — dpriors","text":"character vector containing prior distribution type parameter.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Specify Default Prior Distributions — dpriors","text":"Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling Stan. Journal Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/. Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/.","code":""},{"path":[]},{"path":"http://ecmerkle.github.io/blavaan/reference/dpriors.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Specify Default Prior Distributions — dpriors","text":"","code":"dpriors(nu = \"normal(0,10)\", lambda = \"normal(0,1)\", rho = \"beta(3,3)\") #>                nu             alpha            lambda              beta  #>    \"normal(0,10)\"    \"normal(0,10)\"     \"normal(0,1)\"    \"normal(0,10)\"  #>             theta               psi               rho             ibpsi  #> \"gamma(1,.5)[sd]\" \"gamma(1,.5)[sd]\"       \"beta(3,3)\" \"wishart(3,iden)\"  #>               tau  #>   \"normal(0,1.5)\""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":null,"dir":"Reference","previous_headings":"","what":"blavaan Diagnostic Plots — plot.blavaan","title":"blavaan Diagnostic Plots — plot.blavaan","text":"Convenience functions create plots blavaan objects, via bayesplot package.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"blavaan Diagnostic Plots — plot.blavaan","text":"","code":"# S3 method for blavaan plot(x, pars = NULL, plot.type = \"trace\", showplot = TRUE, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"blavaan Diagnostic Plots — plot.blavaan","text":"x object class blavaan. pars Parameter numbers plot, numbers correspond order parameters reported coef() (also shown 'free' column parTable). numbers provided, free parameters plotted. plot.type type plot desired. name MCMC function, without mcmc_ prefix. showplot plot sent graphic device? Defaults TRUE. ... arguments sent bayesplot function.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"blavaan Diagnostic Plots — plot.blavaan","text":"previous versions blavaan, plotting functionality   handled separately JAGS Stan (using plot functionality   packages runjags rstan, respectively). uniformity,   plotting functionality now handled bayesplot. users desire   additional functionality immediately available, can extract matrix MCMC draws via .matrix(blavInspect(x, 'mcmc')).","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"blavaan Diagnostic Plots — plot.blavaan","text":"invisible ggplot object , desired, can customized.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/plot.blavaan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"blavaan Diagnostic Plots — plot.blavaan","text":"","code":"if (FALSE) { HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 '  fit <- bcfa(HS.model, data=HolzingerSwineford1939)  # trace plots of free loadings plot(fit, pars = 1:6) }"},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":null,"dir":"Reference","previous_headings":"","what":"Posterior Predictive Model Checks — ppmc","title":"Posterior Predictive Model Checks — ppmc","text":"function allows users conduct posterior predictive model check assess global local fit latent variable model using discrepancy function can applied lavaan model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Posterior Predictive Model Checks — ppmc","text":"","code":"ppmc(object, thin = 1, fit.measures = c(\"srmr\",\"chisq\"), discFUN = NULL,      conditional = FALSE)  # S4 method for blavPPMC summary(object, ...)  # S3 method for ppmc summary(object, discFUN, dist = c(\"obs\",\"sim\"),         central.tendency = c(\"mean\",\"median\",\"mode\"),         hpd = TRUE, prob = .95, to.data.frame = FALSE, diag = TRUE,         sort.by = NULL, decreasing = FALSE)  # S3 method for blavPPMC plot(x, ..., discFUN, element, central.tendency = \"\",      hpd = TRUE, prob = .95, nd = 3)  # S3 method for blavPPMC hist(x, ..., discFUN, element, hpd = TRUE, prob = .95,      printLegend = TRUE, legendArgs = list(x = \"topleft\"),      densityArgs = list(), nd = 3)  # S3 method for blavPPMC pairs(x, discFUN, horInd = 1:DIM, verInd = 1:DIM,       printLegend = FALSE, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Posterior Predictive Model Checks — ppmc","text":"object,x object class blavaan. thin Optional integer indicating much thin chain.     Default 1L, indicating thin chains object. fit.measures character vector indicating names global     discrepancy measures returned fitMeasures. Ignored     unless discFUN NULL, users may include     fitMeasures list discrepancy functions     discFUN. ordinal models, \"logl\" \"chisq\"     computations done via lavaan. discFUN function, list functions, can     called object class lavaan. function     must return object whose mode numeric, may     vector, matrix, multidimensional array.     summary plot methods, discFUN     character indicating discrepancy function     summarize. conditional logical indicating whether , artificial data     generation, condition estimated latent   variables. Requires model estimated save.lvs = TRUE. element numeric character indicating index (    dimension discFUN output, multiple) plot. horInd,verInd Similar element, numeric     character vector indicating indices matrix plot     scatterplot matrix. horInd==verInd, histograms     plotted upper triangle. dist character indicating whether summarize distribution     discFUN either observed simulated data. central.tendency character indicating statistics     used characterize location posterior (predictive)     distribution. default, 3 statistics returned     summary method, none plot method. posterior     mean labeled EAP expected posteriori estimate,     mode labeled MAP modal posteriori estimate. hpd logical indicating whether calculate highest     posterior density (HPD) credible interval discFUN. prob \"confidence\" level credible interval(s). nd number digits print scatterplot. .data.frame logical indicating whether summary     symmetric 2-dimensional matrix returned discFUN     unique elements stored rows data.frame can sorted     convenience identifying large discrepancies. discFUN     returns asymmetric 2-dimensional matrix, list matrices     returned summary can also converted data.frame. diag Passed lower.tri .data.frame=TRUE. sort.character. summary returns data.frame,     can sorted column name using order. Note     discFUN returns asymmetric 2-dimensional matrix,     data.frame returned list sorted     independently, rows unlikely consistent across     summary statistics. decreasing Passed order     !.null(sort.). ... Additional graphical parameters     passed plot.default. printLegend logical. TRUE (default), legend     printed histogram legendArgs list arguments passed     legend function.  default argument list     placing legend top-left figure. densityArgs list arguments passed     density function, used obtain densities     hist method.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Posterior Predictive Model Checks — ppmc","text":"S4 object class blavPPMC consisting 5 list slots: @discFUN user-supplied discFUN, call     fitMeasures returns fit.measures. @dims dimensions object returned     discFUN. @PPP posterior predictive p value     discFUN element. @obsDist posterior distribution realize values     discFUN applied observed data. @simDist posterior predictive distribution values     discFUN applied data simulated posterior samples. summary() method returns numeric vector discFUN returns scalar, data.frame one discrepancy function per row     discFUN returns numeric vector, list     one summary statistic per element discFUN returns matrix multidimensional array. plot pairs methods invisibly return NULL,   printing plot (scatterplot matrix) current device. hist method invisibly returns list arguments can   passed function list element named.  Users   can edit arguments list customize histograms.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Posterior Predictive Model Checks — ppmc","text":"Terrence D. Jorgensen (University Amsterdam; TJorgensen314@gmail.com)","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Posterior Predictive Model Checks — ppmc","text":"Levy, R. (2011). Bayesian data--model fit assessment structural equation   modeling. Structural Equation Modeling, 18(4), 663--685.   doi:10.1080/10705511.2011.607723","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/ppmc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Posterior Predictive Model Checks — ppmc","text":"","code":"if (FALSE) { HS.model <- ' visual  =~ x1 + x2 + x3               textual =~ x4 + x5 + x6               speed   =~ x7 + x8 + x9 ' ## fit single-group model fit <- bcfa(HS.model, data = HolzingerSwineford1939,              n.chains = 2, burnin = 1000, sample = 500) ## fit multigroup model fitg <- bcfa(HS.model, data = HolzingerSwineford1939,              n.chains = 2, burnin = 1000, sample = 500, group = \"school\")   ## Use fit.measures as a shortcut for global fitMeasures only ## - Note that indices calculated from the \"df\" are only appropriate under ##   noninformative priors, such that pD approximates the number of estimated ##   parameters counted under ML estimation; incremental fit indices ##   introduce further complications)  AFIs <- ppmc(fit, thin = 10, fit.measures = c(\"srmr\",\"chisq\",\"rmsea\",\"cfi\")) summary(AFIs)                 # summarize the whole vector in a data.frame hist(AFIs, element = \"rmsea\") # only plot one discrepancy function at a time plot(AFIs, element = \"srmr\")   ## define a list of custom discrepancy functions ## - (global) fit measures ## - (local) standardized residuals  discFUN <- list(global = function(fit) {                   fitMeasures(fit, fit.measures = c(\"cfi\",\"rmsea\",\"srmr\",\"chisq\"))                 },                 std.cov.resid = function(fit) lavResiduals(fit, zstat = FALSE,                                                            summary = FALSE)$cov,                 std.mean.resid = function(fit) lavResiduals(fit, zstat = FALSE,                                                             summary = FALSE)$mean) out1g <- ppmc(fit, discFUN = discFUN)  ## summarize first discrepancy by default (fit indices) summary(out1g) ## some model-implied correlations look systematically over/underestimated summary(out1g, discFUN = \"std.cov.resid\", central.tendency = \"EAP\") hist(out1g, discFUN = \"std.cov.resid\", element = c(1, 7)) plot(out1g, discFUN = \"std.cov.resid\", element = c(\"x1\",\"x7\")) ## For ease of investigation, optionally export summary as a data.frame, ## sorted by size of average residual summary(out1g, discFUN = \"std.cov.resid\", central.tendency = \"EAP\",         to.data.frame = TRUE, sort.by = \"EAP\") ## or sorted by size of PPP summary(out1g, discFUN = \"std.cov.resid\", central.tendency = \"EAP\",         to.data.frame = TRUE, sort.by = \"PPP_sim_LessThan_obs\")  ## define a list of custom discrepancy functions for multiple groups ## (return each group's numeric output using a different function)  disc2g <- list(global = function(fit) {                  fitMeasures(fit, fit.measures = c(\"cfi\",\"rmsea\",\"mfi\",\"srmr\",\"chisq\"))                },                cor.resid1 = function(fit) lavResiduals(fit, zstat = FALSE,                                                        type = \"cor.bollen\",                                                        summary = FALSE)[[1]]$cov,                cor.resid2 = function(fit) lavResiduals(fit, zstat = FALSE,                                                        type = \"cor.bollen\",                                                        summary = FALSE)[[2]]$cov) out2g <- ppmc(fitg, discFUN = disc2g, thin = 2) ## some residuals look like a bigger problem in one group than another pairs(out2g, discFUN = \"cor.resid1\", horInd = 1:3, verInd = 7:9) # group 1 pairs(out2g, discFUN = \"cor.resid2\", horInd = 1:3, verInd = 7:9) # group 2  ## print all to file: must be a LARGE picture. First group 1 ... png(\"cor.resid1.png\", width = 1600, height = 1200) pairs(out2g, discFUN = \"cor.resid1\") dev.off() ## ... then group 2 png(\"cor.resid2.png\", width = 1600, height = 1200) pairs(out2g, discFUN = \"cor.resid2\") dev.off() }"},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":null,"dir":"Reference","previous_headings":"","what":"Standardized Posterior — standardizedPosterior","title":"Standardized Posterior — standardizedPosterior","text":"Standardized posterior distribution latent variable model.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Standardized Posterior — standardizedPosterior","text":"","code":"standardizedPosterior(object, ...)"},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Standardized Posterior — standardizedPosterior","text":"object object class blavaan. ... Additional arguments passed lavaan's   standardizedSolution()","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Standardized Posterior — standardizedPosterior","text":"allowed standardizedSolution() arguments type, cov.std, remove.eq, remove.ineq, remove.def. arguments immediately suited posterior distributions.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Standardized Posterior — standardizedPosterior","text":"matrix containing standardized posterior draws, rows draws   columns parameters.","code":""},{"path":"http://ecmerkle.github.io/blavaan/reference/standardizedPosterior.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Standardized Posterior — standardizedPosterior","text":"","code":"if (FALSE) { model <- '    # latent variable definitions      ind60 =~ x1 + x2 + x3      dem60 =~ y1 + a*y2 + b*y3 + c*y4      dem65 =~ y5 + a*y6 + b*y7 + c*y8    # regressions     dem60 ~ ind60     dem65 ~ ind60 + dem60    # residual correlations     y1 ~~ y5     y2 ~~ y4 + y6     y3 ~~ y7     y4 ~~ y8     y6 ~~ y8 '  fit <- bsem(model, data=PoliticalDemocracy,             dp=dpriors(nu=\"dnorm(5,1e-2)\"),             bcontrol=list(method=\"rjparallel\"))  standardizedPosterior(fit) }"},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-05-2","dir":"Changelog","previous_headings":"","what":"Version 0.5-2","title":"Version 0.5-2","text":"CRAN release: 2023-09-25","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-5-2","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.5-2","text":"maintenance release, primarily adding new array declaration syntax Stan models (syntax became available new version rstan).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-5-2","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.5-2","text":"blavCompare() work models meanstructure = FALSE (reported Pedro Ribeiro).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-05-1","dir":"Changelog","previous_headings":"","what":"Version 0.5-1","title":"Version 0.5-1","text":"CRAN release: 2023-08-29","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-5-1","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.5-1","text":"Two-level models now supported (complete, continuous data) via cluster argument.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-5-1","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.5-1","text":"two-level model specification, levels labeled “within” “”. restrictive lavaan specification. target=“jags”, latent variable extraction via blavInspect(, “lvs”) fails (reported Joseph Saraceno).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-8","dir":"Changelog","previous_headings":"","what":"Version 0.4-8","title":"Version 0.4-8","text":"CRAN release: 2023-06-12","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-8","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-8","text":"maintenance release bug fixes changes compiler settings","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-8","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-8","text":"certain models residual correlations /correlated factors, initial values target=‘stan’ lead non-positive definite matrices (reported Yuanyuan Hu). models latent variable regressed observed variable (lv ~ ov), latent variable samples account mean observed variable (centered around 0 constant).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-7","dir":"Changelog","previous_headings":"","what":"Version 0.4-7","title":"Version 0.4-7","text":"CRAN release: 2023-03-01","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-7","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-7","text":"primarily update address C++14 vs C++17 compilation issue identified CRAN bugs 0.4-6 also fixed","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-7","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-7","text":"Sampling priors (prisamp = TRUE) fails models meanstructure = FALSE; posterior still estimated (reported Armel Brizuela Rodríguez). target = “jags”, models single-indicator latent variable, latent variable regressed variables, return incorrect parameter estimates (reported Brad Cosentino).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-6","dir":"Changelog","previous_headings":"","what":"Version 0.4-6","title":"Version 0.4-6","text":"CRAN release: 2023-02-11","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-6","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-6","text":"target = “stan”, meanstructure=FALSE allowed, along use sample.cov sample.nobs instead raw data Users warned priors covariance matrices neither diagonal unrestricted models observed variable intercepts appear latent intercept vector (alpha), default priors come observed intercept vector nu (user expect) inits = “simple” now default (instead “prior”), address convergence problems stan targets, “:=” can now used identity function target = “stan”, fix missing data issue 0.4-3 (complete data one group ) Column names added blavPredict(, type=“lv”)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-6","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-6","text":"blavFitIndices() save.lvs = TRUE work correctly models without meanstructure. Workaround use meanstructure = TRUE model estimation command (reported Charles Hofacker). lavaan summary() method sometimes called instead blavaan summary() method (reported multiple users, Shu Fai Cheung providing helpful examples).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-3","dir":"Changelog","previous_headings":"","what":"Version 0.4-3","title":"Version 0.4-3","text":"CRAN release: 2022-05-11","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-3","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-3","text":"target = “stan”, models run faster earlier versions (use sufficient statistics) Posterior summaries faster ordinal models (using mnormt::sadmvn() default) Variational Bayes option added: target=“vb”, uses rstan::vb() cmdstanr functionality added: target=“cmdstanr”, uses model target=“stan” Fix blavInspect(., “lvs”/“lvmeans”) multiple groups + missing data Fixes ppmc() ordinal models; blavFitIndices() turned ordinal models (research needed) loo() moment matching available passing mcmcextra = list(data = list(moment_match_k_threshold))","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-3","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-3","text":"target = “stan” fails complete data one group missing data another group (reported Ronja Runge). blavPredict(, type=“ymis”) still available models ordinal variables","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-04-1","dir":"Changelog","previous_headings":"","what":"Version 0.4-1","title":"Version 0.4-1","text":"CRAN release: 2022-01-27","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-4-1","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.4-1","text":"Functionality ordinal observed variables now available. models missing data, posterior summaries sped (log-likelihood computations now done Stan).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-4-1","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.4-1","text":"blavPredict(, type=“ymis”) working models ordinal variables blavInspect(, ‘lvs’) (, ‘lvmeans’) can fail models combination multiple groups, missing values, excluded cases blavFitIndices() ppmc() working models ordinal variables, may indicate excessively bad fit blavFitIndices(, rescale=“mcmc”) fails","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-18","dir":"Changelog","previous_headings":"","what":"Version 0.3-18","title":"Version 0.3-18","text":"CRAN release: 2021-11-27","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-18","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-18","text":"version adds reference new JSS paper, including DOI, corrects inconsistent version dependency. changes compared 0.3-17.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-17","dir":"Changelog","previous_headings":"","what":"Version 0.3-17","title":"Version 0.3-17","text":"CRAN release: 2021-07-19","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-17","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-17","text":"maintenance release correct major bugs previous version.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-16","dir":"Changelog","previous_headings":"","what":"Version 0.3-16","title":"Version 0.3-16","text":"CRAN release: 2021-07-11","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-16","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-16","text":"blavPredict() function added predicting latent variables missing data. posterior summaries sped . (fitMeasures available test=“none”) bug fixes previous version.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-16","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-16","text":"certain models missing data, ppp-values incorrect (sometimes equaling 1.0). target=“stan”, multiple group models fail cases missing observed variables (reported DeAnne Hunter).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-15","dir":"Changelog","previous_headings":"","what":"Version 0.3-15","title":"Version 0.3-15","text":"CRAN release: 2021-02-19","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-15","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-15","text":"Added S3 summary() method ppmc Posterior intervals summary() bug fixed","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-15","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-15","text":"summary() method ppmc() fitIndices() always work correctly. Jacobian incorrect target=“stan”, (non-default) priors placed precisions variances instead standard deviations. impact estimates posterior variability (reported Roy Levy).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-14","dir":"Changelog","previous_headings":"","what":"Version 0.3-14","title":"Version 0.3-14","text":"CRAN release: 2021-01-20 (version 0.3-13 violated CRAN policy)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-14","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-14","text":"maintenance release response change package Matrix.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-14","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-14","text":"Posterior intervals NA summary(). Workarounds use parameterEstimates() (intervals assuming posterior normality) compute using posterior samples (`blavInspect(fit, “mcmc”)’)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-12","dir":"Changelog","previous_headings":"","what":"Version 0.3-12","title":"Version 0.3-12","text":"CRAN release: 2020-11-12 (version 0.3-11 failed Windows CRAN checks)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-12","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-12","text":"vector values wiggle.sd allowed different priors approximate equality constraints logical argument “prisamp” added, sampling model’s prior target=“stan”, lkj prior used unrestricted lv correlation matrices default priors conditional approaches (targets jags stanclassic) revert placed precisions (opposed SDs), improvement sampling efficiency","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-10","dir":"Changelog","previous_headings":"","what":"Version 0.3-10","title":"Version 0.3-10","text":"CRAN release: 2020-08-03","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-10","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-10","text":"save.lvs=TRUE works missing data target=“stan” new arguments “wiggle” “wiggle.sd” approximate equality constraints target=“stan”","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-10","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-10","text":"plot labels target=“stan” sometimes incorrect (displaying parameter different panel label). complex equality constraints sometimes ignored (target=“jags” “stanclassic”) equality constraints std.lv=TRUE sometimes fail (target=“stan”) placing priors variances precisions yields incorrect results (target=“stan”; reported Roy Levy)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-9","dir":"Changelog","previous_headings":"","what":"Version 0.3-9","title":"Version 0.3-9","text":"CRAN release: 2020-03-09","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-9","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-9","text":"improvements save.lvs=TRUE target=“stan”. target=“stancond” added, experimental, noncentered Stan approach. bug fixes prior settings std.lv target=“stan”, defined parameters.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-9","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-9","text":"target=“stan”, problems sampling lvs multiple groups missing data. Errors blavCompare() blavFitIndices() due version updates packages. target=“stan”, models std.lv=TRUE converge.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-8","dir":"Changelog","previous_headings":"","what":"Version 0.3-8","title":"Version 0.3-8","text":"CRAN release: 2019-11-19","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-8","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-8","text":"post-estimation, posterior predictive computations sped considerably. 0.3-7 bugs fixed.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-8","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-8","text":"target=“stan” std.lv=TRUE, estimation fails certain (growth) models (reported Mauricio Garnier-Villareal). defined variables fail target=“jags” “stanclassic” (reported Mariëlle Zondervan-Zwijnenburg). User-specified priors sometimes placed wrong parameter, related 0.3-7 bug (reported Mauricio Garnier-Villareal). dpriors() issue 0.3-3 remains.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-7","dir":"Changelog","previous_headings":"","what":"Version 0.3-7","title":"Version 0.3-7","text":"CRAN release: 2019-09-27","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-7","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-7","text":"target=“stan”, gamma priors can now placed user’s choice variances, standard deviations, precisions. plot() now works uniformly across Stan JAGS, relying bayesplot. post-MCMC parallelization now handled via future.apply package (requires extra “plan” command user, works windows). 0.3-6 bugs fixed.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-7","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-7","text":"blavInspect(, ‘lvmeans’) returns rows wrong order target=“stan” (reported Mehdi Momen). User-specified priors sometimes placed wrong parameter, target=“stan” (reported Enrico Toffalini). dpriors() issue 0.3-3 remains.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-6","dir":"Changelog","previous_headings":"","what":"Version 0.3-6","title":"Version 0.3-6","text":"CRAN release: 2019-08-08","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-6","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-6","text":"fixes stan plot bug 0.3-5.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-6","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-6","text":"user-specified priors correlation parameters silently ignored target=“stan” (reported James Uanhoro). save.lvs=TRUE work target=“stan” (reported Mauricio Garnier-Villareal). dpriors() issue 0.3-3 remains.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-5","dir":"Changelog","previous_headings":"","what":"Version 0.3-5","title":"Version 0.3-5","text":"CRAN release: 2019-08-03","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-5","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-5","text":"target=“stan” now default, using pre-compiled Stan model instead “fly” code. ppmc() function added Terrence Jorgensen, facilitating posterior predictive checks. default priors changed gamma precisions gamma standard deviations.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-5","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-5","text":"Stan plot method silently fails (reported Matt Yalch). dpriors() issue 0.3-3 remains.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-4","dir":"Changelog","previous_headings":"","what":"Version 0.3-4","title":"Version 0.3-4","text":"CRAN release: 2019-01-11","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-4","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-4","text":"Add function standardizedPosterior() standardizing posterior draws. Turn posterior modes target=“jags”, due conflict current versions runjags modeest. Rearrange posterior predictive internals.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-4","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-4","text":"dpriors() issue 0.3-3 remains. target=“jags”, lv means obtained blavInspect() (via argument ‘lvmeans’) incorrect. (reported Mauricio Garnier-Villareal) Use plot() target=“stan” causes problems future blavInspect() calls.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-3","dir":"Changelog","previous_headings":"","what":"Version 0.3-3","title":"Version 0.3-3","text":"CRAN release: 2018-10-31","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-3","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-3","text":"convergence=“auto”, max time previously 5 min (undocumented). now Inf. Axis labels (parameter names) now sensible convergence plots. Relative effective sample size now used compute loo/waic SEs, SEs now returned via fitMeasures(). Added unit testing via package testthat. Fixed bugs 0.3-2 (exception identity assignments using ‘:=’)","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-3","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-3","text":"Use ‘dpriors()’: observed variable precisions assigned latent precision (ipsi) prior; latent means assigned observed mean (nu) prior.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-2","dir":"Changelog","previous_headings":"","what":"Version 0.3-2","title":"Version 0.3-2","text":"CRAN release: 2018-06-10","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-2","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-2","text":"Conditional (latent variables) information criteria available save.lvs = TRUE. Experimental function ‘blavFitIndices()’ added Bayesian versions SEM metrics, contributed Terrence Jorgensen. blavaan “intelligently” chooses target, either runjags rstan () installed. Fixed bugs 0.3-1, especially related missing data Stan.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-2","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-2","text":"Errors Stan models std.lv=TRUE, observed variable regressed latent variable (reported Bo Zhang). Error identity assignments using ‘:=’ (reported Marco Tullio Liuzza). Explicitly adding argument ‘.fit=TRUE’ fails (reported Esteban Montenegro).","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"version-03-1","dir":"Changelog","previous_headings":"","what":"Version 0.3-1","title":"Version 0.3-1","text":"CRAN release: 2018-01-12","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"new-features-0-3-1","dir":"Changelog","previous_headings":"","what":"New features","title":"Version 0.3-1","text":"Stan export now supported; use target=“stan”. Improved handling complex models, including growth/change models. Sampling factor scores (lvs) available via ‘save.lvs=TRUE’. Samples/means can obtained supplying arguments ‘lvs’ ‘lvmeans’ ‘blavInspect()’. Fixed bugs 0.2-4.","code":""},{"path":"http://ecmerkle.github.io/blavaan/news/index.html","id":"bugsglitches-discovered-after-the-release-0-3-1","dir":"Changelog","previous_headings":"","what":"Bugs/glitches discovered after the release:","title":"Version 0.3-1","text":"Errors Stan models missing data, exogenous (“x”) variables. Errors multi-group Stan models std.lv=TRUE.","code":""}]