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Useful +when looking at the marginal effect of an interaction. Note that grouping by a covariate +with many values will result in slow performance. + pred_outcome Numeric value for level of outcome to predict for ordinal responses. diff --git a/_quarto/man/id_plot_cov.qmd b/_quarto/man/id_plot_cov.qmd index ac49f45..3666058 100644 --- a/_quarto/man/id_plot_cov.qmd +++ b/_quarto/man/id_plot_cov.qmd @@ -4,11 +4,10 @@ ### Description -This function will calculate marginal effects, or the first derivative +This function will calculate and plot the ideal point marginal effects, or the first derivative of the IRT/ideal point model with respect to the hierarchical covariate, -separately for the two poles of the latent variable. These two marginal -effects permit the interpretation of the effect of the covariate on -with respect to either end of the latent variable. +for each item in the model. The function id_me is used +to first calculate the ideal point marginal effects. @@ -19,12 +18,13 @@ with respect to either end of the latent variable. calc_param = NULL, label_high = "High", label_low = "Low", - cov_type = "person_cov", + group_effects = NULL, plot_model_id = NULL, pred_outcome = NULL, - high_quantile = 0.95, - low_quantile = 0.05, - new_cov_names = NULL, + lb = 0.05, + upb = 0.95, + facet_ncol = 2, + cov_type = "person_cov", ... ) @@ -56,12 +56,6 @@ latent scale What label to use on the plot for the low end of the latent scale -cov_type - -Either 'person_cov' for person or group-level hierarchical parameters, -'discrim_reg_cov' for bill/item discrimination parameters from regular (non-inflated) model, and -'discrim_infl_cov' for bill/item discrimination parameters from inflated model. - plot_model_id The integer of the model ID to plot. If NULL and there @@ -75,50 +69,39 @@ or binary models with missing data, which outcome to predict. This should be the value that matches what the outcome was coded as in the data passed to id_make. -high_quantile +lb -The upper limit of the posterior density to use for +The lower limit of the posterior density to use for calculating credible intervals -low_quantile +upb -The lower limit of the posterior density to use for +The upper limit of the posterior density to use for calculating credible intervals -new_cov_names +facet_ncol -A character vector of length equal to the number -of covariates (plus 1 for the intercept) to change the default labels. -To see the default labels, use the plot function with this option blank. -The character vector should be of th form used by +If facetting by multiple models or grouped factors, sets the +number of columns in the multiple plots -... +cov_type -Additional argument passed on to id_me +Either 'person_cov' for person or group-level hierarchical parameters, +'discrim_reg_cov' for bill/item discrimination parameters from regular (non-inflated) model, and +'discrim_infl_cov' for bill/item discrimination parameters from inflated model. -filter_cov +... -A character vector of coefficients from covariate plots to exclude from -plotting (should be the names of coefficients as they appear in the plots) +Additional argument passed on to id_me ### Details -Because the marginal effects are always with respect to a given -outcome/response, the outcome to be predicted must be specified -in pred_outcome. If it is not specified, the function -will prompt you to select one of the outcome's values in the data. - The ends of the latent variable can be specified via the label_low and label_high options, which will use those -labels in the ensuing plot. - -To exclude parameters from the plot, use the filter_cov option. -Note that the parameters must be specified using the underlying model -syntax (however they are labeled in the plot). You can also change -the names of parameters using the new_cov_names option. +labels for item discrimination. Note that the function produces a ggplot2 object, which can be further modified with ggplot2 functions. diff --git a/_quarto/vignettes/Package_Introduction.qmd b/_quarto/vignettes/Package_Introduction.qmd index 64f9380..5d5e3cd 100755 --- a/_quarto/vignettes/Package_Introduction.qmd +++ b/_quarto/vignettes/Package_Introduction.qmd @@ -3,7 +3,6 @@ title: "Introduction to Idealstan" author: "Robert Kubinec" date: last-modified format: html -cache: true vignette: > %\VignetteIndexEntry{Time-Varying Ideal Points} %\VignetteEngine{R.rsp::asis} @@ -37,7 +36,7 @@ The approach to handling missing data in this package is to model cases where mi The package includes the following models: | Model ID | Model Type | Response Type | Missing Data Adjustment | -|-----------------|-----------------------|-----------------|-----------------| +|-----------------|---------------------|-----------------|-----------------| | 1 | IRT 2-PL | Binary | No | | 2 | IRT 2-PL | Binary | Yes | | 3 | IRT rating scale | Ordinal | No | @@ -88,6 +87,7 @@ To begin with, we can simulate data from an ordinal ideal-point model in which t The function `id_sim_gen()` allows you to simulate data from any of the sixteen models currently implemented in `idealstan` (see previous list). To include missing data, specify the `inflate` option as `TRUE`. For example, here we sample data from an ordinal graded response model: ```{r sim_data} +#| cache: false ord_ideal_sim <- id_sim_gen(model='ordinal_grm',inflate = T) @@ -157,6 +157,8 @@ To demonstrate how the package functions empirically, I include in the package a We can first take a look at the raw data: ```{r check_data} +#| cache: false + data('senate114') @@ -243,6 +245,9 @@ The wide high-posterior density (HPD) interval of the absence midpoint ruglines We can obtain summary estimates of all the ideal points and item/bill discrimination/difficulty parameters using the summary function that provides the median value of the parameters in addition to a specified posterior density interval (i.e., 5%-95%). For example, we can extract summaries for the ideal points: ```{r ideal_pts_sum} +#| cache: false + + ideal_pts_sum <- summary(sen_est,pars='ideal_pts') tt(head(ideal_pts_sum)) ``` @@ -266,8 +271,9 @@ stan_trace(sen_est,par='L_full[1]') Finally we can also extract all of the posterior iterations to do additional calculations that average over posterior uncertainty by changing the `aggregate` option in `summary`. In the following code, I access the individual posterior iterations for the item/bill parameters, including difficulty (average probability of voting yes), discrimination (how strongly the item/bill loads on either end of the ideal point scale) and the midpoints (position where someone with that ideal point would be indifferent to voting yes/no). ```{r ideal_pts_ind} +#| cache: false item_all <- summary(sen_est,pars='items', aggregate=F) -knitr::kable(head(item_all)) +tt(head(item_all)) ``` ## Hierarchical Covariates @@ -358,6 +364,8 @@ Because these covariates are on the ideal point scale, the meaning of the scale We can also extract the covariate summary values using the `summary` function: ```{r cov_values} +#| cache: false + cov_sum <- summary(sen_est_cov,pars='person_cov') tt(cov_sum) ``` diff --git a/docs/freeze.rds b/docs/freeze.rds index 3dbc772b0cb181c2d7c20f9a88d626df15768742..ef9046f717f3cfb2573694750410114169dacaec 100644 GIT binary patch delta 817 zcmV-11J3;F3G4~5B>`cY$)l{=$koJ>T1&>5-VL5#JiEERoF#{9_mA}woN^K83Rg9* zvCjJS?1FKuzQaLi*fRwS9PHmlcO@BwUm4Bxpt1hGSlRH<1%AF)OJT9YBQ#WXe4uoW4oXF z+eAaIHlXhm8saFG#?8A(RAQUrv1^`ThK%Y!L$*%B(qOi%XzHYMilLHHf5g^lu(m~7 zG)U2&mO`9#3D`ijWCQcY&edV0R50>A_e`}-yq;mWfW~4+aHzc}kEGNo$L`qJNk0m3 zS;bW;3CeXLNf`oJY#uxBwW?SdRglIdjCb^nVOB{MLUD7GuWW%&T_P?-VjXI9IojYG z_JmNG_GwVJ-)bCt*ML8Ke^qqOw&p9wZPpo@u#LtLyh^Q!O%}Ri#9`IY%~W43m~c|{ z#XFZe`iGf>(>h+f*KyJX&qo`GSSm!!#$$&#YQ=agBj<(z9~i^%!6pCxM%FqGcZTB+ zjR!BD|Mc^(&!4?oAJ)gmYuWtRbR~buR-e5%96$N*c)NV9i+U={f6WX%-b2f_&~dk1 z%kJpXHwWbJ-B#-EWZ6_!<4!gwYu%lmwVCbQJ|hHs(us5f%q2~Bo#QdcsL??T@`@EZE) z3Ob+vus>hP#ipJv#?$5I&D+cG*XilI_}6^4)s@Pqi&q!>JCQrvTrXqP4aU$~e{B-? vp%(l3(*K*pnR(4B`YyDK{>Xjmfd5Xw^lFl)W~wWXfD$&XPm5`^S0-PI1Y(!c~oH zth0VSyI>rv@3Bl3;U7DIpHSuccztk`riQa_>FY&M{bKntX3uW(;16Ga6`ixK`HFFyb%rKvqcH@pQp2uD7P@1^Vb##hTptG(ObuLI zVsXYnA5Y#G1OFT2CSCA+w1J4FLd0x5c8H@^jPKnzHw^f|7={ln`S&-n)^WHq9Dis$ zc=7zFpMQP+?A7|PK0aQ{=EtTh`AfF??8V{u$$!V&7n?)0q9%ulW|XW-!_u$DiM0zbVxJzt&e7P49`PM71+ zrO%JydbU2l@|4F{(bw-mmfJofUmPPVeYqSL?ak&^{IzUn{L>rwjD35IouAiRWO{s! z`kn;aQ`wEzdUwEo#^w45`sxU}CGW!{+I;%m;q+`oHCt`BM0j$YJ42scLR&2t%N1IE zzP#B=l)dkjZsn!kw9OuUshgYW_P|!h&_`F$ z`TU3d`ARM}^>i_wE;n!9UVgt$Pv6DA=CiG?R7PFAy4a68+}Y-O8KZ76hSvIPleiDH t*w2^#-z3h=YgQRA)@#|mx#j+shk?B<$ww1ue>M#N{0n8j9Usage id_me( object, covariate = NULL, + group_effects = NULL, pred_outcome = NULL, eps = 1e-04, draws = 100, @@ -425,6 +426,14 @@

Arguments

+group_effects + + +character value of a covariate included in the formula passed to ‘id_make’ for which marginal effect summaries should be grouped by. Useful when looking at the marginal effect of an interaction. Note that grouping by a covariate with many values will result in slow performance. + + + + pred_outcome diff --git a/docs/man/id_plot_cov.html b/docs/man/id_plot_cov.html index 68e3a1b..250abda 100644 --- a/docs/man/id_plot_cov.html +++ b/docs/man/id_plot_cov.html @@ -387,7 +387,7 @@

Marginal Effects Plot for Hierarchical Covariates

Description

-

This function will calculate marginal effects, or the first derivative of the IRT/ideal point model with respect to the hierarchical covariate, separately for the two poles of the latent variable. These two marginal effects permit the interpretation of the effect of the covariate on with respect to either end of the latent variable.

+

This function will calculate and plot the ideal point marginal effects, or the first derivative of the IRT/ideal point model with respect to the hierarchical covariate, for each item in the model. The function id_me is used to first calculate the ideal point marginal effects.

Usage

@@ -396,12 +396,13 @@

Usage

calc_param = NULL, label_high = "High", label_low = "Low", - cov_type = "person_cov", + group_effects = NULL, plot_model_id = NULL, pred_outcome = NULL, - high_quantile = 0.95, - low_quantile = 0.05, - new_cov_names = NULL, + lb = 0.05, + upb = 0.95, + facet_ncol = 2, + cov_type = "person_cov", ... ) @@ -443,14 +444,6 @@

Arguments

-cov_type - - -Either ‘person_cov’ for person or group-level hierarchical parameters, ‘discrim_reg_cov’ for bill/item discrimination parameters from regular (non-inflated) model, and ‘discrim_infl_cov’ for bill/item discrimination parameters from inflated model. - - - - plot_model_id @@ -467,51 +460,49 @@

Arguments

-high_quantile +lb -The upper limit of the posterior density to use for calculating credible intervals +The lower limit of the posterior density to use for calculating credible intervals -low_quantile +upb -The lower limit of the posterior density to use for calculating credible intervals +The upper limit of the posterior density to use for calculating credible intervals -new_cov_names +facet_ncol -A character vector of length equal to the number of covariates (plus 1 for the intercept) to change the default labels. To see the default labels, use the plot function with this option blank. The character vector should be of th form used by +If facetting by multiple models or grouped factors, sets the number of columns in the multiple plots -… +cov_type -Additional argument passed on to id_me +Either ‘person_cov’ for person or group-level hierarchical parameters, ‘discrim_reg_cov’ for bill/item discrimination parameters from regular (non-inflated) model, and ‘discrim_infl_cov’ for bill/item discrimination parameters from inflated model. -filter_cov +… -A character vector of coefficients from covariate plots to exclude from plotting (should be the names of coefficients as they appear in the plots) +Additional argument passed on to id_me

Details

-

Because the marginal effects are always with respect to a given outcome/response, the outcome to be predicted must be specified in pred_outcome. If it is not specified, the function will prompt you to select one of the outcome’s values in the data.

-

The ends of the latent variable can be specified via the label_low and label_high options, which will use those labels in the ensuing plot.

-

To exclude parameters from the plot, use the filter_cov option. Note that the parameters must be specified using the underlying model syntax (however they are labeled in the plot). You can also change the names of parameters using the new_cov_names option.

+

The ends of the latent variable can be specified via the label_low and label_high options, which will use those labels for item discrimination.

Note that the function produces a ggplot2 object, which can be further modified with ggplot2 functions.

diff --git a/docs/search.json b/docs/search.json index b387007..f7dd0fd 100644 --- a/docs/search.json +++ b/docs/search.json @@ -46,7 +46,7 @@ "href": "vignettes/Package_Introduction.html#simulation-of-ordinal-irt-with-missing-data", "title": "Introduction to Idealstan", "section": "Simulation of Ordinal IRT with Missing Data", - "text": "Simulation of Ordinal IRT with Missing Data\nTo begin with, we can simulate data from an ordinal ideal-point model in which there are three possible responses corresponding to a legislator voting: yes, abstain and no. An additional category is also simulated that indicates whether a legislator shows up to vote or is absent, which traditional IRT models would record as missing data and would drop from the estimation. This package can instead utilize missing data via a hurdle model in which the censoring of the vote/score data is estimated as a function of individual item/bill intercepts and discrimination parameters for the decision to be absent or present. In other words, if the missing data is a reflection of the person’s ideal point, such as more conservative legislators refusing to show up to vote, than the model will make use of this missing data to infer additional information about the legislators’ ideal points.\nThe function id_sim_gen() allows you to simulate data from any of the sixteen models currently implemented in idealstan (see previous list). To include missing data, specify the inflate option as TRUE. For example, here we sample data from an ordinal graded response model:\n\nord_ideal_sim <- id_sim_gen(model='ordinal_grm',inflate = T)\n\nWarning: `data_frame()` was deprecated in tibble 1.1.0.\nℹ Please use `tibble()` instead.\nℹ The deprecated feature was likely used in the idealstan package.\n Please report the issue at <https://github.com/saudiwin/idealstan/issues>.\n\ntt(head(ord_ideal_sim@score_matrix))\n\n\n\n \n\n \n \n \n \n \n \n item_id\n person_id\n model_id\n group_id\n time_id\n outcome_disc\n ordered_id\n personcov0\n itemcov0\n itemcovmiss0\n discrete\n \n \n \n \n \n 1\n 1\n missing\n G\n 1\n Missing\n 3\n 0\n 0\n 0\n 0\n \n \n 2\n 1\n missing\n G\n 1\n Missing\n 3\n 0\n 0\n 0\n 0\n \n \n 3\n 1\n missing\n G\n 1\n Missing\n 3\n 0\n 0\n 0\n 0\n \n \n 4\n 1\n missing\n G\n 1\n Missing\n 3\n 0\n 0\n 0\n 0\n \n \n 5\n 1\n missing\n G\n 1\n 3 \n 3\n 0\n 0\n 0\n 0\n \n \n 6\n 1\n missing\n G\n 1\n Missing\n 3\n 0\n 0\n 0\n 0\n \n \n \n \n\n\n\nThe vote/score matrix in the idealdata object ord_ideal_sim has legislators/persons in the rows and bills/items in the columns. The outcome_disc column has the simulated 3-category ordered outcome.\nThe function id_estimate will take this processed data and run an IRT ideal point model with the model ID . To specify the model type, either include the model ID from Table 1 as the model_id argument in the id_estimate function or, in the case of multiple models/item types, pass a column model_id to the id_make function that specifies the model ID for each row in the data. This latter option is useful when you have items of mixed types, such as binary, ordinal and/or continuous items. The function id_make also includes the ability to incorporate hierarchical (person or item-level) covariates, as discussed below.\nTo speed up processing, all of the models shown in Table 1 make use of multiple core parallel computation. To use this option, the specified number of available cores in the ncores option must exceed the number of MCMC chains nchains. cmdstanr will automatically assign cores by dividing the number of chains by the number of cores. In all of the examples in this vignette, I use a machine with 8 cores and estimate 2 chains, so there are 4 cores per chain. By default, id_estimate parallelizes over persons, although that can be changed to items with the map_over_id option (only works with static models).\nThe package has options for identification that are similar to other IRT packages in which the IDs of legislators/persons to constrain are specified to the id_estimate function. For example, we can use the true values of the simulated legislators to constrain one legislator/person with the highest simulated ideal point and one legislator/person with the lowest ideal point. Each constrained parameter must be fixed to a specific value, preferably at either end of the ideal point spectrum, to identify the model. In particular, two pieces of information are necessary: a value for the high ideal point, and the difference between the high and low points. In this example I pre-specify which parameters to constrain based on the simulated data as restrict_ind_high and restrict_ind_low, and use the actual values to pin the parameters to specific values with fix_high and fix_low.\n\ntrue_legis <- ord_ideal_sim@simul_data$true_person\nhigh_leg <- sort(true_legis,decreasing = TRUE,index.return=TRUE)\nlow_leg <- sort(true_legis,index.return=TRUE)\n\nord_ideal_est <- id_estimate(idealdata=ord_ideal_sim,\n model_type=6,\n fixtype='prefix',\n restrict_ind_high = as.character(high_leg$ix[1]),\n restrict_ind_low=as.character(low_leg$ix[1]),\n fix_high = sort(true_legis,decreasing = TRUE)[1],\n fix_low = sort(true_legis,decreasing = FALSE)[1],\n id_refresh=500,\n ncores=8,\n nchains=2)\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"Running pathfinder to find starting values\"\nPath [1] :Initial log joint density = -1572.319503 \nPath [1] : Iter log prob ||dx|| ||grad|| alpha alpha0 # evals ELBO Best ELBO Notes \n 93 -7.521e+02 2.715e-03 4.924e-03 4.981e-01 1.000e+00 2326 -9.485e+02 -9.485e+02 \nPath [1] :Best Iter: [88] ELBO (-931.144330) evaluations: (2326) \nFinished in 0.8 seconds.\n[1] \"Estimating model with full Stan MCMC sampler.\"\n\n\nInit values were only set for a subset of parameters. \nMissing init values for the following parameters:\n - chain 1: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw\n - chain 2: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw\n\nTo disable this message use options(cmdstanr_warn_inits = FALSE).\n\n\nRunning MCMC with 2 parallel chains, with 4 thread(s) per chain...\n\nChain 1 Iteration: 1 / 2000 [ 0%] (Warmup) \n\n\nChain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -115.417, but should be greater than the previous element, -115.417 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 1 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 1 \n\n\nChain 2 Iteration: 1 / 2000 [ 0%] (Warmup) \n\n\nChain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -72.5968, but should be greater than the previous element, -72.5968 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 2 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 2 \n\n\nChain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is 1.48349, but should be greater than the previous element, 1.48349 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 1 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 1 \n\n\nChain 2 Iteration: 500 / 2000 [ 25%] (Warmup) \nChain 1 Iteration: 500 / 2000 [ 25%] (Warmup) \nChain 2 Iteration: 1000 / 2000 [ 50%] (Warmup) \nChain 2 Iteration: 1001 / 2000 [ 50%] (Sampling) \nChain 1 Iteration: 1000 / 2000 [ 50%] (Warmup) \nChain 1 Iteration: 1001 / 2000 [ 50%] (Sampling) \nChain 1 Iteration: 1500 / 2000 [ 75%] (Sampling) \nChain 2 Iteration: 1500 / 2000 [ 75%] (Sampling) \nChain 1 Iteration: 2000 / 2000 [100%] (Sampling) \nChain 1 finished in 46.7 seconds.\nChain 2 Iteration: 2000 / 2000 [100%] (Sampling) \nChain 2 finished in 49.3 seconds.\n\nBoth chains finished successfully.\nMean chain execution time: 48.0 seconds.\nTotal execution time: 49.6 seconds.\n\n\nWe can then check and see how well the Stan estimation engine was able to capture the “true” values used in the simulation by plotting the true ideal points relative to the estimated ones:\n\nid_plot_legis(ord_ideal_est,show_true = TRUE)\n\nWarning: Dropping 'draws_df' class as required metadata was removed.\n\n\nJoining with `by = join_by(id_num)`\nJoining with `by = join_by(id_num)`\n\n\n\n\n\n\n\n\n\nGiven the small amount of data used to estimate the model, the imprecision with which the ideal points were recovered is not surprising. However, the uncertainty intervals generally include the true values, indicating a model that is functioning correctly at recovering estimates even with substantial measurement error.\nTo automatically identify the model (that is, identify people to fix high or low), simply change the fixtype option to 'vb_full'. By default, the model will select the highest and lowest ideal points to constrain by running an approximation to the full posterior using cmdstanr’s pathfinder() function. While this method works, the exact rotation is not known a priori, and so it may produce a different result with multiple runs. Note that there will be two pathfinder runs as the first run identifies the parameters to constrain and the second is used to create starting values for the Hamiltonian Monte Carlo estimation.\nFor example, using our simulated data and identifying the model automatically with 'vb_full':\n\nord_ideal_est <- id_estimate(idealdata=ord_ideal_sim,\n model_type=6,\n id_refresh=2000,fixtype=\"vb_full\",\n ncores=8,\n nchains=2)\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"(First Step): Estimating model with Pathfinder (variational inference) to identify modes to constrain.\"\nPath [1] :Initial log joint density = -2121.033157 \nPath [1] : Iter log prob ||dx|| ||grad|| alpha alpha0 # evals ELBO Best ELBO Notes \n 99 -7.605e+02 6.214e-03 2.023e-02 1.000e+00 1.000e+00 2476 -9.697e+02 -9.697e+02 \nPath [1] : Iter log prob ||dx|| ||grad|| alpha alpha0 # evals ELBO Best ELBO Notes \n 109 -7.605e+02 7.750e-04 3.252e-03 7.237e-01 7.237e-01 2726 -9.639e+02 -9.639e+02 \nPath [1] :Best Iter: [100] ELBO (-957.463122) evaluations: (2726) \nFinished in 0.9 seconds.\n\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"Running pathfinder to find starting values\"\nPath [1] :Initial log joint density = -1561.800868 \nPath [1] : Iter log prob ||dx|| ||grad|| alpha alpha0 # evals ELBO Best ELBO Notes \n 103 -7.411e+02 9.196e-04 5.285e-03 1.000e+00 1.000e+00 2576 -9.406e+02 -9.406e+02 \nPath [1] :Best Iter: [94] ELBO (-936.862674) evaluations: (2576) \nFinished in 0.9 seconds.\n[1] \"Estimating model with full Stan MCMC sampler.\"\n\n\nInit values were only set for a subset of parameters. \nMissing init values for the following parameters:\n - chain 1: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw\n - chain 2: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw\n\nTo disable this message use options(cmdstanr_warn_inits = FALSE).\n\n\nRunning MCMC with 2 parallel chains, with 4 thread(s) per chain...\n\nChain 1 Iteration: 1 / 2000 [ 0%] (Warmup) \n\n\nChain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -20.578, but should be greater than the previous element, -20.578 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 1 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 1 \n\n\nChain 2 Iteration: 1 / 2000 [ 0%] (Warmup) \n\n\nChain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -5.64329, but should be greater than the previous element, -5.64329 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 1 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 1 \n\n\nChain 2 Iteration: 1001 / 2000 [ 50%] (Sampling) \nChain 1 Iteration: 1001 / 2000 [ 50%] (Sampling) \nChain 1 Iteration: 2000 / 2000 [100%] (Sampling) \nChain 1 finished in 42.7 seconds.\nChain 2 Iteration: 2000 / 2000 [100%] (Sampling) \nChain 2 finished in 44.8 seconds.\n\nBoth chains finished successfully.\nMean chain execution time: 43.7 seconds.\nTotal execution time: 44.9 seconds.\n\n\nWe can see from the plot of the Rhats, which is an MCMC convergence diagnostic, that all the Rhats are below 1.1, which is a good (though not perfect) sign that the model is fully identified:\n\nid_plot_rhats(ord_ideal_est)\n\n`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n\n\n\n\n\n\n\n\nid_plot_legis(ord_ideal_est,show_true = T)\n\nWarning: Dropping 'draws_df' class as required metadata was removed.\n\n\nJoining with `by = join_by(id_num)`\nJoining with `by = join_by(id_num)`\n\n\n\n\n\n\n\n\n\nIn general, it is always a good idea to check the Rhats before proceeding with further analysis. Identification of time-varying ideal point models can be more complicated and is discussed in the accompanying vignette. As can be seen above, while the Pathfinder algorithm will usually identify a unique rotation of the ideal points without using any other prior information, it may not be the rotation that is theoretically interesting. For that reason, I recommend specifying persons or items to pin to specific values for applied use of the package as I show in the next section.", + "text": "Simulation of Ordinal IRT with Missing Data\nTo begin with, we can simulate data from an ordinal ideal-point model in which there are three possible responses corresponding to a legislator voting: yes, abstain and no. An additional category is also simulated that indicates whether a legislator shows up to vote or is absent, which traditional IRT models would record as missing data and would drop from the estimation. This package can instead utilize missing data via a hurdle model in which the censoring of the vote/score data is estimated as a function of individual item/bill intercepts and discrimination parameters for the decision to be absent or present. In other words, if the missing data is a reflection of the person’s ideal point, such as more conservative legislators refusing to show up to vote, than the model will make use of this missing data to infer additional information about the legislators’ ideal points.\nThe function id_sim_gen() allows you to simulate data from any of the sixteen models currently implemented in idealstan (see previous list). To include missing data, specify the inflate option as TRUE. For example, here we sample data from an ordinal graded response model:\n\nord_ideal_sim <- id_sim_gen(model='ordinal_grm',inflate = T)\n\ntt(head(ord_ideal_sim@score_matrix))\n\n\n\n \n\n \n \n \n \n \n \n item_id\n person_id\n model_id\n group_id\n time_id\n outcome_disc\n ordered_id\n personcov0\n itemcov0\n itemcovmiss0\n discrete\n \n \n \n \n \n 1\n 1\n missing\n G\n 1\n Missing\n 3\n 0\n 0\n 0\n 0\n \n \n 2\n 1\n missing\n G\n 1\n Missing\n 3\n 0\n 0\n 0\n 0\n \n \n 3\n 1\n missing\n G\n 1\n 1 \n 3\n 0\n 0\n 0\n 0\n \n \n 4\n 1\n missing\n G\n 1\n 2 \n 3\n 0\n 0\n 0\n 0\n \n \n 5\n 1\n missing\n G\n 1\n 1 \n 3\n 0\n 0\n 0\n 0\n \n \n 6\n 1\n missing\n G\n 1\n 3 \n 3\n 0\n 0\n 0\n 0\n \n \n \n \n\n\n\nThe vote/score matrix in the idealdata object ord_ideal_sim has legislators/persons in the rows and bills/items in the columns. The outcome_disc column has the simulated 3-category ordered outcome.\nThe function id_estimate will take this processed data and run an IRT ideal point model with the model ID . To specify the model type, either include the model ID from Table 1 as the model_id argument in the id_estimate function or, in the case of multiple models/item types, pass a column model_id to the id_make function that specifies the model ID for each row in the data. This latter option is useful when you have items of mixed types, such as binary, ordinal and/or continuous items. The function id_make also includes the ability to incorporate hierarchical (person or item-level) covariates, as discussed below.\nTo speed up processing, all of the models shown in Table 1 make use of multiple core parallel computation. To use this option, the specified number of available cores in the ncores option must exceed the number of MCMC chains nchains. cmdstanr will automatically assign cores by dividing the number of chains by the number of cores. In all of the examples in this vignette, I use a machine with 8 cores and estimate 2 chains, so there are 4 cores per chain. By default, id_estimate parallelizes over persons, although that can be changed to items with the map_over_id option (only works with static models).\nThe package has options for identification that are similar to other IRT packages in which the IDs of legislators/persons to constrain are specified to the id_estimate function. For example, we can use the true values of the simulated legislators to constrain one legislator/person with the highest simulated ideal point and one legislator/person with the lowest ideal point. Each constrained parameter must be fixed to a specific value, preferably at either end of the ideal point spectrum, to identify the model. In particular, two pieces of information are necessary: a value for the high ideal point, and the difference between the high and low points. In this example I pre-specify which parameters to constrain based on the simulated data as restrict_ind_high and restrict_ind_low, and use the actual values to pin the parameters to specific values with fix_high and fix_low.\n\ntrue_legis <- ord_ideal_sim@simul_data$true_person\nhigh_leg <- sort(true_legis,decreasing = TRUE,index.return=TRUE)\nlow_leg <- sort(true_legis,index.return=TRUE)\n\nord_ideal_est <- id_estimate(idealdata=ord_ideal_sim,\n model_type=6,\n fixtype='prefix',\n restrict_ind_high = as.character(high_leg$ix[1]),\n restrict_ind_low=as.character(low_leg$ix[1]),\n fix_high = sort(true_legis,decreasing = TRUE)[1],\n fix_low = sort(true_legis,decreasing = FALSE)[1],\n id_refresh=500,\n ncores=8,\n nchains=2)\n\n[1] \"Running pathfinder to find starting values\"\nPath [1] :Initial log joint density = -1577.176212 \nPath [1] : Iter log prob ||dx|| ||grad|| alpha alpha0 # evals ELBO Best ELBO Notes \n 87 -8.501e+02 4.265e-04 3.971e-03 7.494e-01 7.494e-01 2176 -1.065e+03 -1.065e+03 \nPath [1] :Best Iter: [85] ELBO (-1059.338643) evaluations: (2176) \nFinished in 0.5 seconds.\n[1] \"Estimating model with full Stan MCMC sampler.\"\nRunning MCMC with 2 parallel chains, with 4 thread(s) per chain...\n\nChain 1 Iteration: 1 / 2000 [ 0%] (Warmup) \n\n\nChain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -11.3421, but should be greater than the previous element, -11.3421 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 1 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 1 \n\n\nChain 2 Iteration: 1 / 2000 [ 0%] (Warmup) \n\n\nChain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -163.557, but should be greater than the previous element, -163.557 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 2 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 2 \n\n\nChain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -14.201, but should be greater than the previous element, -14.201 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 2 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 2 \n\n\nChain 2 Iteration: 500 / 2000 [ 25%] (Warmup) \nChain 1 Iteration: 500 / 2000 [ 25%] (Warmup) \nChain 1 Iteration: 1000 / 2000 [ 50%] (Warmup) \nChain 1 Iteration: 1001 / 2000 [ 50%] (Sampling) \nChain 2 Iteration: 1000 / 2000 [ 50%] (Warmup) \nChain 2 Iteration: 1001 / 2000 [ 50%] (Sampling) \nChain 1 Iteration: 1500 / 2000 [ 75%] (Sampling) \nChain 2 Iteration: 1500 / 2000 [ 75%] (Sampling) \nChain 1 Iteration: 2000 / 2000 [100%] (Sampling) \nChain 2 Iteration: 2000 / 2000 [100%] (Sampling) \nChain 1 finished in 21.8 seconds.\nChain 2 finished in 21.7 seconds.\n\nBoth chains finished successfully.\nMean chain execution time: 21.8 seconds.\nTotal execution time: 21.9 seconds.\n\n\nWe can then check and see how well the Stan estimation engine was able to capture the “true” values used in the simulation by plotting the true ideal points relative to the estimated ones:\n\nid_plot_legis(ord_ideal_est,show_true = TRUE)\n\nJoining with `by = join_by(id_num)`\nJoining with `by = join_by(id_num)`\n\n\n\n\n\n\n\n\n\nGiven the small amount of data used to estimate the model, the imprecision with which the ideal points were recovered is not surprising. However, the uncertainty intervals generally include the true values, indicating a model that is functioning correctly at recovering estimates even with substantial measurement error.\nTo automatically identify the model (that is, identify people to fix high or low), simply change the fixtype option to 'vb_full'. By default, the model will select the highest and lowest ideal points to constrain by running an approximation to the full posterior using cmdstanr’s pathfinder() function. While this method works, the exact rotation is not known a priori, and so it may produce a different result with multiple runs. Note that there will be two pathfinder runs as the first run identifies the parameters to constrain and the second is used to create starting values for the Hamiltonian Monte Carlo estimation.\nFor example, using our simulated data and identifying the model automatically with 'vb_full':\n\nord_ideal_est <- id_estimate(idealdata=ord_ideal_sim,\n model_type=6,\n id_refresh=2000,fixtype=\"vb_full\",\n ncores=8,\n nchains=2)\n\n[1] \"(First Step): Estimating model with Pathfinder (variational inference) to identify modes to constrain.\"\nPath [1] :Initial log joint density = -1927.222174 \nPath [1] : Iter log prob ||dx|| ||grad|| alpha alpha0 # evals ELBO Best ELBO Notes \n 98 -8.586e+02 1.010e-03 4.650e-03 1.000e+00 1.000e+00 2451 -1.074e+03 -1.074e+03 \nPath [1] :Best Iter: [95] ELBO (-1068.256459) evaluations: (2451) \nFinished in 0.5 seconds.\n\n\n[1] \"Running pathfinder to find starting values\"\nPath [1] :Initial log joint density = -1533.547548 \nPath [1] : Iter log prob ||dx|| ||grad|| alpha alpha0 # evals ELBO Best ELBO Notes \n 107 -8.459e+02 6.874e-04 2.590e-03 1.000e+00 1.000e+00 2676 -1.071e+03 -1.071e+03 \nPath [1] :Best Iter: [101] ELBO (-1052.747760) evaluations: (2676) \nFinished in 0.5 seconds.\n[1] \"Estimating model with full Stan MCMC sampler.\"\nRunning MCMC with 2 parallel chains, with 4 thread(s) per chain...\n\nChain 1 Iteration: 1 / 2000 [ 0%] (Warmup) \nChain 2 Iteration: 1 / 2000 [ 0%] (Warmup) \n\n\nChain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -261.141, but should be greater than the previous element, -261.141 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 2 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 2 \n\n\nChain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n\n\nChain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -11.4019, but should be greater than the previous element, -11.4019 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from\n\n\nChain 2 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from\n\n\nChain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)\n\n\nChain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n\n\nChain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n\n\nChain 2 \n\n\nChain 2 Iteration: 1001 / 2000 [ 50%] (Sampling) \nChain 1 Iteration: 1001 / 2000 [ 50%] (Sampling) \nChain 2 Iteration: 2000 / 2000 [100%] (Sampling) \nChain 2 finished in 25.7 seconds.\nChain 1 Iteration: 2000 / 2000 [100%] (Sampling) \nChain 1 finished in 26.6 seconds.\n\nBoth chains finished successfully.\nMean chain execution time: 26.1 seconds.\nTotal execution time: 26.7 seconds.\n\n\nWe can see from the plot of the Rhats, which is an MCMC convergence diagnostic, that all the Rhats are below 1.1, which is a good (though not perfect) sign that the model is fully identified:\n\nid_plot_rhats(ord_ideal_est)\n\n`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n\n\n\n\n\n\n\n\nid_plot_legis(ord_ideal_est,show_true = T)\n\nJoining with `by = join_by(id_num)`\nJoining with `by = join_by(id_num)`\n\n\n\n\n\n\n\n\n\nIn general, it is always a good idea to check the Rhats before proceeding with further analysis. Identification of time-varying ideal point models can be more complicated and is discussed in the accompanying vignette. As can be seen above, while the Pathfinder algorithm will usually identify a unique rotation of the ideal points without using any other prior information, it may not be the rotation that is theoretically interesting. For that reason, I recommend specifying persons or items to pin to specific values for applied use of the package as I show in the next section.", "crumbs": [ "Articles", "Introduction to Idealstan" @@ -57,7 +57,7 @@ "href": "vignettes/Package_Introduction.html#parameter-values", "title": "Introduction to Idealstan", "section": "Parameter Values", - "text": "Parameter Values\nWe can obtain summary estimates of all the ideal points and item/bill discrimination/difficulty parameters using the summary function that provides the median value of the parameters in addition to a specified posterior density interval (i.e., 5%-95%). For example, we can extract summaries for the ideal points:\n\nideal_pts_sum <- summary(sen_est,pars='ideal_pts')\n\nWarning: Dropping 'draws_df' class as required metadata was removed.\n\n\nJoining with `by = join_by(id_num)`\n\n\nWarning: Unknown or uninitialised column: `time_id`.\n\ntt(head(ideal_pts_sum))\n\n\n\n \n\n \n \n \n \n \n \n Person\n Group\n Time_Point\n Low Posterior Interval\n Posterior Median\n High Posterior Interval\n Parameter Name\n \n \n \n \n \n WYDEN, Ronald Lee \n D\n 1\n -9.158463\n -7.509925\n -6.155738\n L_full[100]\n \n \n BOXER, Barbara \n D\n 1\n -10.985220\n -8.691115\n -7.031368\n L_full[10] \n \n \n BROWN, Sherrod \n D\n 1\n -11.973265\n -9.486375\n -7.520037\n L_full[11] \n \n \n BURR, Richard M. \n R\n 1\n 4.917415\n 5.856475\n 6.882041\n L_full[12] \n \n \n CANTWELL, Maria E. \n D\n 1\n -11.067110\n -8.880885\n -7.215407\n L_full[13] \n \n \n CAPITO, Shelley Moore\n R\n 1\n 4.408447\n 5.175785\n 6.017246\n L_full[14] \n \n \n \n \n\n\n\nParameter Name is the name of the parameter in the underlying Stan code, which can be useful f you want to peruse the fitted Stan model (and can be accessed as given in the code below). The name of the parameters for ideal points in the Stan model is L_full (as seen in the summary from above).\n\nstan_obj <- sen_est@stan_samples\n# show the \nstan_obj$draws(c(\"L_full[1]\",\n 'L_full[2]',\n 'L_full[3]'))\n\n# A draws_array: 1000 iterations, 2 chains, and 3 variables\n, , variable = L_full[1]\n\n chain\niteration 1 2\n 1 3.8 3.6\n 2 3.3 4.3\n 3 4.4 3.3\n 4 4.2 4.5\n 5 3.7 3.3\n\n, , variable = L_full[2]\n\n chain\niteration 1 2\n 1 1.4 1.3\n 2 2.3 3.1\n 3 1.9 1.0\n 4 1.8 2.6\n 5 2.2 1.7\n\n, , variable = L_full[3]\n\n chain\niteration 1 2\n 1 -8.6 -11.5\n 2 -7.8 -7.1\n 3 -9.4 -10.2\n 4 -11.9 -8.1\n 5 -7.8 -8.7\n\n# ... with 995 more iterations\n\n\nIf we know the name of the Stan parameter, we can look at the trace plot to see how the quality of the Markov Chain Monte Carlo (MCMC) sampling used to fit the model. A good trace plot shows a bouncy line that is stable around an average value. For more info, see the Stan documentation.\n\nstan_trace(sen_est,par='L_full[1]')\n\n\n\n\n\n\n\n\nFinally we can also extract all of the posterior iterations to do additional calculations that average over posterior uncertainty by changing the aggregate option in summary. In the following code, I access the individual posterior iterations for the item/bill parameters, including difficulty (average probability of voting yes), discrimination (how strongly the item/bill loads on either end of the ideal point scale) and the midpoints (position where someone with that ideal point would be indifferent to voting yes/no).\n\nitem_all <- summary(sen_est,pars='items', aggregate=F)\nknitr::kable(head(item_all))\n\n\n\n\n\n\n\n\n\n\n\n\nPosterior_Sample\nItem Name\nItem Type\nPredicted Outcome\nParameter\nIteration\n\n\n\n\n-2.996433\n4\nNon-Inflated Item Midpoint\n1\nA function of other parameters\n1\n\n\n-0.513094\n4\nNon-Inflated Item Midpoint\n1\nA function of other parameters\n2\n\n\n-2.521416\n4\nNon-Inflated Item Midpoint\n1\nA function of other parameters\n3\n\n\n-2.157285\n4\nNon-Inflated Item Midpoint\n1\nA function of other parameters\n4\n\n\n-2.455105\n4\nNon-Inflated Item Midpoint\n1\nA function of other parameters\n5\n\n\n-2.343950\n4\nNon-Inflated Item Midpoint\n1\nA function of other parameters\n6", + "text": "Parameter Values\nWe can obtain summary estimates of all the ideal points and item/bill discrimination/difficulty parameters using the summary function that provides the median value of the parameters in addition to a specified posterior density interval (i.e., 5%-95%). For example, we can extract summaries for the ideal points:\n\nideal_pts_sum <- summary(sen_est,pars='ideal_pts')\n\nJoining with `by = join_by(id_num)`\n\ntt(head(ideal_pts_sum))\n\n\n\n \n\n \n \n \n \n \n \n Person\n Group\n Time_Point\n Low Posterior Interval\n Posterior Median\n High Posterior Interval\n Parameter Name\n \n \n \n \n \n WYDEN, Ronald Lee \n D\n 1\n 5.908937\n 7.201095\n 8.719860\n L_full[100]\n \n \n BOXER, Barbara \n D\n 1\n 6.780327\n 8.465760\n 10.712110\n L_full[10] \n \n \n BROWN, Sherrod \n D\n 1\n 7.289706\n 9.221625\n 11.874305\n L_full[11] \n \n \n BURR, Richard M. \n R\n 1\n -6.645283\n -5.665140\n -4.792147\n L_full[12] \n \n \n CANTWELL, Maria E. \n D\n 1\n 6.941406\n 8.661010\n 10.781860\n L_full[13] \n \n \n CAPITO, Shelley Moore\n R\n 1\n -5.783458\n -4.992145\n -4.276122\n L_full[14] \n \n \n \n \n\n\n\nParameter Name is the name of the parameter in the underlying Stan code, which can be useful f you want to peruse the fitted Stan model (and can be accessed as given in the code below). The name of the parameters for ideal points in the Stan model is L_full (as seen in the summary from above).\n\nstan_obj <- sen_est@stan_samples\n# show the \nstan_obj$draws(c(\"L_full[1]\",\n 'L_full[2]',\n 'L_full[3]'))\n\n# A draws_array: 1000 iterations, 2 chains, and 3 variables\n, , variable = L_full[1]\n\n chain\niteration 1 2\n 1 -4.0 -4.3\n 2 -4.3 -4.1\n 3 -4.1 -3.8\n 4 -4.6 -4.0\n 5 -3.9 -3.7\n\n, , variable = L_full[2]\n\n chain\niteration 1 2\n 1 -2.3 -1.6\n 2 -2.2 -1.9\n 3 -2.5 -2.9\n 4 -2.5 -1.4\n 5 -2.5 -3.1\n\n, , variable = L_full[3]\n\n chain\niteration 1 2\n 1 5.8 8.8\n 2 11.3 8.3\n 3 7.6 10.2\n 4 7.6 6.8\n 5 8.0 9.1\n\n# ... with 995 more iterations\n\n\nIf we know the name of the Stan parameter, we can look at the trace plot to see how the quality of the Markov Chain Monte Carlo (MCMC) sampling used to fit the model. A good trace plot shows a bouncy line that is stable around an average value. For more info, see the Stan documentation.\n\nstan_trace(sen_est,par='L_full[1]')\n\n\n\n\n\n\n\n\nFinally we can also extract all of the posterior iterations to do additional calculations that average over posterior uncertainty by changing the aggregate option in summary. In the following code, I access the individual posterior iterations for the item/bill parameters, including difficulty (average probability of voting yes), discrimination (how strongly the item/bill loads on either end of the ideal point scale) and the midpoints (position where someone with that ideal point would be indifferent to voting yes/no).\n\nitem_all <- summary(sen_est,pars='items', aggregate=F)\ntt(head(item_all))\n\n\n\n \n\n \n \n \n \n \n \n Posterior_Sample\n Item Name\n Item Type\n Predicted Outcome\n Parameter\n Iteration\n \n \n \n \n \n 1.606639\n 4\n Non-Inflated Item Midpoint\n 1\n A function of other parameters\n 1\n \n \n 1.511766\n 4\n Non-Inflated Item Midpoint\n 1\n A function of other parameters\n 2\n \n \n 1.028057\n 4\n Non-Inflated Item Midpoint\n 1\n A function of other parameters\n 3\n \n \n 1.976161\n 4\n Non-Inflated Item Midpoint\n 1\n A function of other parameters\n 4\n \n \n 1.550986\n 4\n Non-Inflated Item Midpoint\n 1\n A function of other parameters\n 5\n \n \n 1.377775\n 4\n Non-Inflated Item Midpoint\n 1\n A function of other parameters\n 6", "crumbs": [ "Articles", "Introduction to Idealstan" @@ -68,7 +68,7 @@ "href": "vignettes/Package_Introduction.html#hierarchical-covariates", "title": "Introduction to Idealstan", "section": "Hierarchical Covariates", - "text": "Hierarchical Covariates\nNote: ideal point marginal effects have yet to be implemented as a separate function. In this section I demonstrate how to estimate these effects using R code.\nFinally, we can also fit a model where we include a covariate that varies by person/legislator. To do so, we need to pass a one-sided formula to the id_make function to prepare the data accordingly. By way of example, we will include a model where we include an interaction between party ID (party_code) and the legislator’s age to see if younger/older legislators are more or less conservative. Because this is a static model, the effect of the covariate is averaged over all of the bills in the dataset and all the legislators in the dataset without taking into account the order or time period of the bills.\nIt is important to note that for static ideal point models, covariates are only defined over the legislators/persons who are not being used as constraints in the model, such as John Barasso and Elizabeth Warren in this model.\n\nsenate114$age <- 2018 - senate114$born\n# center the variable\nsenate114$age <- senate114$age - mean(senate114$age)\n# put in units of 10 years\nsenate114$age <- senate114$age / 10\n\n# doing this will improve estimation speed (variables mean-centered and with an SD\n# not much bigger than 1 or 2)\n\nsenate_data <- id_make(senate114,outcome_disc = 'cast_code',\n person_id = 'bioname',\n item_id = 'rollnumber',\n group_id= 'party_code',\n time_id='date',\n person_cov = ~party_code*age)\n\nsen_est_cov <- id_estimate(senate_data,\n model_type = 1,\n fixtype='prefix',\n nchains=2,\n ncores=8,\n restrict_ind_high = \"BARRASSO, John A.\",\n restrict_ind_low=\"WARREN, Elizabeth\",\n seed=84520)\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 10.2 seconds.\n[1] \"Estimating model with full Stan MCMC sampler.\"\n\n\nInit values were only set for a subset of parameters. \nMissing init values for the following parameters:\n - chain 1: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm3, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw\n - chain 2: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm3, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw\n\nTo disable this message use options(cmdstanr_warn_inits = FALSE).\n\n\nRunning MCMC with 2 parallel chains, with 4 thread(s) per chain...\n\nChain 2 finished in 592.9 seconds.\nChain 1 finished in 593.8 seconds.\n\nBoth chains finished successfully.\nMean chain execution time: 593.4 seconds.\nTotal execution time: 594.1 seconds.\n\n\nAs discussed in the associated working paper (https://osf.io/preprints/osf/8j2bt), ideal point marginal effects can be derived from idealstan models in which the raw relationship between the hierarchical covariates and the actual outcomes (in this case, votes) can be shown at the item (vote) level. There are two functions that can be used to calculate and display ideal point marginal effects. The first, id_me, shown in the chunks, below, will produce data frames with summaries ideal point marginal effects given a covariate and also data frames with one row per posterior draw that are useful for further analysis or aggregation.\nIn the example below, ideal point marginal effects are calculated for the \"age\" covariate, first for the whole dataset and then for all distinct values of \"group_id\", which is party ID in our data. This latter calculation is especially useful as we interaction age with group_id, and by calculating marginal effects for each distinct subset of group_id we can learn what the conditional marginal effect is by party ID.\n\n # calculate marginal effects for age subset by item\n\n marg_effs <- id_me(sen_est_cov,covariate=\"age\")\n\nCreating predictions\n\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\nDifferencing\n\n\nJoining with `by = join_by(item_id)`\n\n head(marg_effs$ideal_effects) %>% \n tt\n\n\n\n \n\n \n \n \n \n \n \n draws\n item_id\n person_id\n estimate\n group_id\n item_orig\n person_orig\n model_id\n \n \n \n \n \n 1\n 1\n 1\n 0.0049192952\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 2\n 1\n 1\n 0.0003805561\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 3\n 1\n 1\n 0.0011962110\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 4\n 1\n 1\n 0.0032083563\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 5\n 1\n 1\n 0.0071981862\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 6\n 1\n 1\n 0.0175821741\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n \n \n\n\n head(marg_effs$sum_ideal_effects) %>% \n tt\n\n\n\n \n\n \n \n \n \n \n \n item_id\n item_orig\n model_id\n mean_est\n low_est\n high_est\n item_discrimination\n \n \n \n \n \n 1\n 4 \n 1\n -0.019325899\n -0.127125345\n 0.005264348\n 0.6737565\n \n \n 2\n 5 \n 1\n -0.001696310\n -0.038862286\n 0.033107971\n 0.5783955\n \n \n 3\n 7 \n 1\n -0.005639773\n -0.035121110\n 0.014181149\n 0.7212400\n \n \n 4\n 8 \n 1\n 0.024363041\n -0.006493817\n 0.148384316\n -0.5858625\n \n \n 5\n 9 \n 1\n -0.006413201\n -0.065204188\n 0.032053323\n 0.4316120\n \n \n 6\n 11\n 1\n -0.018866769\n -0.081474922\n 0.017572876\n -0.3350580\n \n \n \n \n\n\n\n\n # now group marginal effects by group_id (party ID)\n\n marg_effs_grouped <- id_me(sen_est_cov,covariate=\"age\",\n group_effects=\"group_id\")\n\nCreating predictions\n\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\nDifferencing\n\n\nGrouping marginal effect summaries by group_id\n\n\nJoining with `by = join_by(item_id)`\n\n marg_effs_grouped$sum_ideal_effects %>% \n arrange(item_id, group_id) %>% \n slice(1:10) %>% \n tt\n\n\n\n \n\n \n \n \n \n \n \n group_id\n item_id\n item_orig\n model_id\n mean_est\n low_est\n high_est\n item_discrimination\n \n \n \n \n \n D\n 1\n 4\n 1\n -0.043283252\n -7.617911e-02\n -0.021564054\n 0.6737565\n \n \n R\n 1\n 4\n 1\n 0.001728437\n 9.152197e-05\n 0.005387632\n 0.6737565\n \n \n I\n 1\n 4\n 1\n -0.164655068\n -5.395945e-01\n 0.217850402\n 0.6737565\n \n \n D\n 2\n 5\n 1\n -0.015525753\n -3.250633e-02\n -0.003625894\n 0.5783955\n \n \n R\n 2\n 5\n 1\n 0.011176008\n 2.326406e-03\n 0.025459885\n 0.5783955\n \n \n I\n 2\n 5\n 1\n -0.034827213\n -1.720185e-01\n 0.044333672\n 0.5783955\n \n \n D\n 3\n 7\n 1\n -0.019038183\n -3.703802e-02\n -0.005856791\n 0.7212400\n \n \n R\n 3\n 7\n 1\n 0.006786453\n 8.963596e-04\n 0.019558981\n 0.7212400\n \n \n I\n 3\n 7\n 1\n -0.041874126\n -1.781197e-01\n 0.042756959\n 0.7212400\n \n \n D\n 4\n 8\n 1\n 0.054077835\n 2.330002e-02\n 0.091203099\n -0.5858625\n \n \n \n \n\n\n\nIn addition to the data frames of the results, the id_plot_cov can take the same arguments, calculate the ideal point marginal effects and then plot them. If we pass a grouping variable, the id_plot_cov function will plot marginal effects in distinct facets for each level of the grouping variable. If there are multiple model ID types, the function will produce distinct facets for each model ID type (note that only one kind of facetting can be used for a given plot).\n\n # plot the result\n \n sen_est_cov %>% \n id_plot_cov(calc_param=\"age\",group_effects=\"group_id\",\n label_high=\"Conservative\",\n label_low=\"Liberal\")\n\nCreating predictions\n\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\nWarning in max(Y_cont): no non-missing arguments to max; returning -Inf\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\nDifferencing\n\n\nGrouping marginal effect summaries by group_id\n\n\nJoining with `by = join_by(item_id)`\n\n\n\n\n\n\n\n\n\nBecause these covariates are on the ideal point scale, the meaning of the scale in terms of party ideology must be kept in mind in order to interpret the plot. The way to interpret these plots is that older Democrats tend to be more likely to vote for conservative bills, while younger Democrats vote more for liberal bills. The relationship does not hold true for Republicans, who are roughly equally as likely to vote for liberal or conservative bills regardless of age. Keeping the direction of the scale in mind–which is shown on the plot as the colour of the item discrimination for each vote–is crucial for understanding hierarchical covariates in ideal point models.\nWe can also extract the covariate summary values using the summary function:\n\ncov_sum <- summary(sen_est_cov,pars='person_cov')\ntt(cov_sum)\n\n\n\n \n\n \n \n \n \n \n \n Covariate\n Posterior Median\n Posterior High Interval\n Posterior Low Interval\n Parameter\n \n \n \n \n \n party_codeR \n 14.4114000\n 15.5292350\n 13.235560\n legis_x\n \n \n party_codeI \n -0.0402673\n 6.0862770\n -6.466765\n legis_x\n \n \n age \n -1.6332200\n -0.8166661\n -2.446573\n legis_x\n \n \n party_codeR:age\n 2.4787250\n 3.4572140\n 1.428219\n legis_x\n \n \n party_codeI:age\n -1.7233150\n 4.4371645\n -7.166542\n legis_x", + "text": "Hierarchical Covariates\nNote: ideal point marginal effects have yet to be implemented as a separate function. In this section I demonstrate how to estimate these effects using R code.\nFinally, we can also fit a model where we include a covariate that varies by person/legislator. To do so, we need to pass a one-sided formula to the id_make function to prepare the data accordingly. By way of example, we will include a model where we include an interaction between party ID (party_code) and the legislator’s age to see if younger/older legislators are more or less conservative. Because this is a static model, the effect of the covariate is averaged over all of the bills in the dataset and all the legislators in the dataset without taking into account the order or time period of the bills.\nIt is important to note that for static ideal point models, covariates are only defined over the legislators/persons who are not being used as constraints in the model, such as John Barasso and Elizabeth Warren in this model.\n\nsenate114$age <- 2018 - senate114$born\n# center the variable\nsenate114$age <- senate114$age - mean(senate114$age)\n# put in units of 10 years\nsenate114$age <- senate114$age / 10\n\n# doing this will improve estimation speed (variables mean-centered and with an SD\n# not much bigger than 1 or 2)\n\nsenate_data <- id_make(senate114,outcome_disc = 'cast_code',\n person_id = 'bioname',\n item_id = 'rollnumber',\n group_id= 'party_code',\n time_id='date',\n person_cov = ~party_code*age)\n\nsen_est_cov <- id_estimate(senate_data,\n model_type = 1,\n fixtype='prefix',\n nchains=2,\n ncores=8,\n restrict_ind_high = \"BARRASSO, John A.\",\n restrict_ind_low=\"WARREN, Elizabeth\",\n seed=84520)\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 5.5 seconds.\n[1] \"Estimating model with full Stan MCMC sampler.\"\nRunning MCMC with 2 parallel chains, with 4 thread(s) per chain...\n\nChain 2 finished in 256.4 seconds.\nChain 1 finished in 256.6 seconds.\n\nBoth chains finished successfully.\nMean chain execution time: 256.5 seconds.\nTotal execution time: 256.8 seconds.\n\n\nAs discussed in the associated working paper (https://osf.io/preprints/osf/8j2bt), ideal point marginal effects can be derived from idealstan models in which the raw relationship between the hierarchical covariates and the actual outcomes (in this case, votes) can be shown at the item (vote) level. There are two functions that can be used to calculate and display ideal point marginal effects. The first, id_me, shown in the chunks, below, will produce data frames with summaries ideal point marginal effects given a covariate and also data frames with one row per posterior draw that are useful for further analysis or aggregation.\nIn the example below, ideal point marginal effects are calculated for the \"age\" covariate, first for the whole dataset and then for all distinct values of \"group_id\", which is party ID in our data. This latter calculation is especially useful as we interaction age with group_id, and by calculating marginal effects for each distinct subset of group_id we can learn what the conditional marginal effect is by party ID.\n\n # calculate marginal effects for age subset by item\n\n marg_effs <- id_me(sen_est_cov,covariate=\"age\")\n\nCreating predictions\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\nDifferencing\n\n\nJoining with `by = join_by(item_id)`\n\n head(marg_effs$ideal_effects) %>% \n tt\n\n\n\n \n\n \n \n \n \n \n \n draws\n item_id\n person_id\n estimate\n group_id\n item_orig\n person_orig\n model_id\n \n \n \n \n \n 1\n 1\n 1\n 3.050097e-05\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 2\n 1\n 1\n 3.113286e-04\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 3\n 1\n 1\n 6.084729e-03\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 4\n 1\n 1\n 8.515025e-04\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 5\n 1\n 1\n 3.301149e-03\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n 6\n 1\n 1\n 4.367442e-04\n R\n 4\n ALEXANDER, Lamar\n 1\n \n \n \n \n\n\n head(marg_effs$sum_ideal_effects) %>% \n tt\n\n\n\n \n\n \n \n \n \n \n \n item_id\n item_orig\n model_id\n mean_est\n low_est\n high_est\n item_discrimination\n \n \n \n \n \n 1\n 4 \n 1\n -0.027324609\n -0.19376592\n 0.005557074\n -0.6573580\n \n \n 2\n 5 \n 1\n -0.003546904\n -0.05185579\n 0.037121004\n -0.5594220\n \n \n 3\n 7 \n 1\n -0.008581398\n -0.05267362\n 0.016401029\n -0.7241575\n \n \n 4\n 8 \n 1\n 0.030378577\n -0.00656919\n 0.203952527\n 0.5657380\n \n \n 5\n 9 \n 1\n -0.010908422\n -0.09720920\n 0.034804994\n -0.4180350\n \n \n 6\n 11\n 1\n -0.020290320\n -0.09146070\n 0.023107847\n 0.3245960\n \n \n \n \n\n\n\n\n # now group marginal effects by group_id (party ID)\n\n marg_effs_grouped <- id_me(sen_est_cov,covariate=\"age\",\n group_effects=\"group_id\")\n\nCreating predictions\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\nDifferencing\n\n\nGrouping marginal effect summaries by group_id\n\n\nJoining with `by = join_by(item_id)`\n\n marg_effs_grouped$sum_ideal_effects %>% \n arrange(item_id, group_id) %>% \n slice(1:10) %>% \n tt\n\n\n\n \n\n \n \n \n \n \n \n group_id\n item_id\n item_orig\n model_id\n mean_est\n low_est\n high_est\n item_discrimination\n \n \n \n \n \n D\n 1\n 4\n 1\n -0.059669410\n -0.1061344485\n -0.030980545\n -0.6573580\n \n \n R\n 1\n 4\n 1\n 0.001842369\n 0.0001115782\n 0.004954489\n -0.6573580\n \n \n I\n 1\n 4\n 1\n -0.175759403\n -0.5527863128\n 0.097773912\n -0.6573580\n \n \n D\n 2\n 5\n 1\n -0.021396470\n -0.0445927354\n -0.004632567\n -0.5594220\n \n \n R\n 2\n 5\n 1\n 0.011258984\n 0.0015062504\n 0.023842689\n -0.5594220\n \n \n I\n 2\n 5\n 1\n -0.040033881\n -0.1370294461\n 0.012257794\n -0.5594220\n \n \n D\n 3\n 7\n 1\n -0.028223857\n -0.0536652758\n -0.007861273\n -0.7241575\n \n \n R\n 3\n 7\n 1\n 0.005514060\n 0.0004894154\n 0.014164724\n -0.7241575\n \n \n I\n 3\n 7\n 1\n -0.043940857\n -0.1725620105\n 0.016527400\n -0.7241575\n \n \n D\n 4\n 8\n 1\n 0.070496166\n 0.0377855263\n 0.104861559\n 0.5657380\n \n \n \n \n\n\n\nIn addition to the data frames of the results, the id_plot_cov can take the same arguments, calculate the ideal point marginal effects and then plot them. If we pass a grouping variable, the id_plot_cov function will plot marginal effects in distinct facets for each level of the grouping variable. If there are multiple model ID types, the function will produce distinct facets for each model ID type (note that only one kind of facetting can be used for a given plot).\n\n # plot the result\n \n sen_est_cov %>% \n id_plot_cov(calc_param=\"age\",group_effects=\"group_id\",\n label_high=\"Conservative\",\n label_low=\"Liberal\")\n\nCreating predictions\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\n[1] \"Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples.\"\n[1] \"Adding in hierarchical covariates values to the time-varying person scores.\"\n[1] \"Collapsing covariates to person and time IDs.\"\n[1] \"Done!\"\n[1] \"Now on model 1\"\n\n\nDifferencing\n\n\nGrouping marginal effect summaries by group_id\n\n\nJoining with `by = join_by(item_id)`\n\n\n\n\n\n\n\n\n\nBecause these covariates are on the ideal point scale, the meaning of the scale in terms of party ideology must be kept in mind in order to interpret the plot. The way to interpret these plots is that older Democrats tend to be more likely to vote for conservative bills, while younger Democrats vote more for liberal bills. The relationship does not hold true for Republicans, who are roughly equally as likely to vote for liberal or conservative bills regardless of age. Keeping the direction of the scale in mind–which is shown on the plot as the colour of the item discrimination for each vote–is crucial for understanding hierarchical covariates in ideal point models.\nWe can also extract the covariate summary values using the summary function:\n\ncov_sum <- summary(sen_est_cov,pars='person_cov')\ntt(cov_sum)\n\n\n\n \n\n \n \n \n \n \n \n Covariate\n Posterior Median\n Posterior High Interval\n Posterior Low Interval\n Parameter\n \n \n \n \n \n party_codeR \n -15.5384000\n -14.451030\n -16.697360\n legis_x\n \n \n party_codeI \n -0.6862375\n 5.981570\n -6.834136\n legis_x\n \n \n age \n 2.3011950\n 3.067987\n 1.463249\n legis_x\n \n \n party_codeR:age\n -3.2372250\n -2.184633\n -4.234465\n legis_x\n \n \n party_codeI:age\n 1.1277700\n 6.660751\n -5.019880\n legis_x", "crumbs": [ "Articles", "Introduction to Idealstan" @@ -453,7 +453,7 @@ "href": "man/id_plot_cov.html", "title": "idealstan", "section": "", - "text": "This function will calculate marginal effects, or the first derivative of the IRT/ideal point model with respect to the hierarchical covariate, separately for the two poles of the latent variable. These two marginal effects permit the interpretation of the effect of the covariate on with respect to either end of the latent variable.\n\n\n\nid_plot_cov(\n object,\n calc_param = NULL,\n label_high = \"High\",\n label_low = \"Low\",\n cov_type = \"person_cov\",\n plot_model_id = NULL,\n pred_outcome = NULL,\n high_quantile = 0.95,\n low_quantile = 0.05,\n new_cov_names = NULL,\n ...\n)\n\n\n\n\n\n\n\nobject\n\n\nA fitted idealstan object\n\n\n\n\ncalc_param\n\n\nWhether to calculate ideal point marginal effects for a given covariate. If NULL, the default, the function will instead produce a plot of the raw coefficients from the ideal point model. If passing the name of a covariate, should be a character value of a column in the data passed to the id_make function.\n\n\n\n\nlabel_high\n\n\nWhat label to use on the plot for the high end of the latent scale\n\n\n\n\nlabel_low\n\n\nWhat label to use on the plot for the low end of the latent scale\n\n\n\n\ncov_type\n\n\nEither ‘person_cov’ for person or group-level hierarchical parameters, ‘discrim_reg_cov’ for bill/item discrimination parameters from regular (non-inflated) model, and ‘discrim_infl_cov’ for bill/item discrimination parameters from inflated model.\n\n\n\n\nplot_model_id\n\n\nThe integer of the model ID to plot. If NULL and there are multiple model types, facet_wrap will be used to produce multiple plots with one for each model type.\n\n\n\n\npred_outcome\n\n\nFor discrete models with more than 2 categories, or binary models with missing data, which outcome to predict. This should be the value that matches what the outcome was coded as in the data passed to id_make.\n\n\n\n\nhigh_quantile\n\n\nThe upper limit of the posterior density to use for calculating credible intervals\n\n\n\n\nlow_quantile\n\n\nThe lower limit of the posterior density to use for calculating credible intervals\n\n\n\n\nnew_cov_names\n\n\nA character vector of length equal to the number of covariates (plus 1 for the intercept) to change the default labels. To see the default labels, use the plot function with this option blank. The character vector should be of th form used by\n\n\n\n\n…\n\n\nAdditional argument passed on to id_me\n\n\n\n\nfilter_cov\n\n\nA character vector of coefficients from covariate plots to exclude from plotting (should be the names of coefficients as they appear in the plots)\n\n\n\n\n\n\nBecause the marginal effects are always with respect to a given outcome/response, the outcome to be predicted must be specified in pred_outcome. If it is not specified, the function will prompt you to select one of the outcome’s values in the data.\nThe ends of the latent variable can be specified via the label_low and label_high options, which will use those labels in the ensuing plot.\nTo exclude parameters from the plot, use the filter_cov option. Note that the parameters must be specified using the underlying model syntax (however they are labeled in the plot). You can also change the names of parameters using the new_cov_names option.\nNote that the function produces a ggplot2 object, which can be further modified with ggplot2 functions.\n\n\n\nA ggplot2 plot that can be further customized with ggplot2 functions if need be.", + "text": "This function will calculate and plot the ideal point marginal effects, or the first derivative of the IRT/ideal point model with respect to the hierarchical covariate, for each item in the model. The function id_me is used to first calculate the ideal point marginal effects.\n\n\n\nid_plot_cov(\n object,\n calc_param = NULL,\n label_high = \"High\",\n label_low = \"Low\",\n group_effects = NULL,\n plot_model_id = NULL,\n pred_outcome = NULL,\n lb = 0.05,\n upb = 0.95,\n facet_ncol = 2,\n cov_type = \"person_cov\",\n ...\n)\n\n\n\n\n\n\n\nobject\n\n\nA fitted idealstan object\n\n\n\n\ncalc_param\n\n\nWhether to calculate ideal point marginal effects for a given covariate. If NULL, the default, the function will instead produce a plot of the raw coefficients from the ideal point model. If passing the name of a covariate, should be a character value of a column in the data passed to the id_make function.\n\n\n\n\nlabel_high\n\n\nWhat label to use on the plot for the high end of the latent scale\n\n\n\n\nlabel_low\n\n\nWhat label to use on the plot for the low end of the latent scale\n\n\n\n\nplot_model_id\n\n\nThe integer of the model ID to plot. If NULL and there are multiple model types, facet_wrap will be used to produce multiple plots with one for each model type.\n\n\n\n\npred_outcome\n\n\nFor discrete models with more than 2 categories, or binary models with missing data, which outcome to predict. This should be the value that matches what the outcome was coded as in the data passed to id_make.\n\n\n\n\nlb\n\n\nThe lower limit of the posterior density to use for calculating credible intervals\n\n\n\n\nupb\n\n\nThe upper limit of the posterior density to use for calculating credible intervals\n\n\n\n\nfacet_ncol\n\n\nIf facetting by multiple models or grouped factors, sets the number of columns in the multiple plots\n\n\n\n\ncov_type\n\n\nEither ‘person_cov’ for person or group-level hierarchical parameters, ‘discrim_reg_cov’ for bill/item discrimination parameters from regular (non-inflated) model, and ‘discrim_infl_cov’ for bill/item discrimination parameters from inflated model.\n\n\n\n\n…\n\n\nAdditional argument passed on to id_me\n\n\n\n\n\n\nThe ends of the latent variable can be specified via the label_low and label_high options, which will use those labels for item discrimination.\nNote that the function produces a ggplot2 object, which can be further modified with ggplot2 functions.\n\n\n\nA ggplot2 plot that can be further customized with ggplot2 functions if need be.", "crumbs": [ "Reference", "id_plot_cov" @@ -464,7 +464,7 @@ "href": "man/id_plot_cov.html#marginal-effects-plot-for-hierarchical-covariates", "title": "idealstan", "section": "", - "text": "This function will calculate marginal effects, or the first derivative of the IRT/ideal point model with respect to the hierarchical covariate, separately for the two poles of the latent variable. These two marginal effects permit the interpretation of the effect of the covariate on with respect to either end of the latent variable.\n\n\n\nid_plot_cov(\n object,\n calc_param = NULL,\n label_high = \"High\",\n label_low = \"Low\",\n cov_type = \"person_cov\",\n plot_model_id = NULL,\n pred_outcome = NULL,\n high_quantile = 0.95,\n low_quantile = 0.05,\n new_cov_names = NULL,\n ...\n)\n\n\n\n\n\n\n\nobject\n\n\nA fitted idealstan object\n\n\n\n\ncalc_param\n\n\nWhether to calculate ideal point marginal effects for a given covariate. If NULL, the default, the function will instead produce a plot of the raw coefficients from the ideal point model. If passing the name of a covariate, should be a character value of a column in the data passed to the id_make function.\n\n\n\n\nlabel_high\n\n\nWhat label to use on the plot for the high end of the latent scale\n\n\n\n\nlabel_low\n\n\nWhat label to use on the plot for the low end of the latent scale\n\n\n\n\ncov_type\n\n\nEither ‘person_cov’ for person or group-level hierarchical parameters, ‘discrim_reg_cov’ for bill/item discrimination parameters from regular (non-inflated) model, and ‘discrim_infl_cov’ for bill/item discrimination parameters from inflated model.\n\n\n\n\nplot_model_id\n\n\nThe integer of the model ID to plot. If NULL and there are multiple model types, facet_wrap will be used to produce multiple plots with one for each model type.\n\n\n\n\npred_outcome\n\n\nFor discrete models with more than 2 categories, or binary models with missing data, which outcome to predict. This should be the value that matches what the outcome was coded as in the data passed to id_make.\n\n\n\n\nhigh_quantile\n\n\nThe upper limit of the posterior density to use for calculating credible intervals\n\n\n\n\nlow_quantile\n\n\nThe lower limit of the posterior density to use for calculating credible intervals\n\n\n\n\nnew_cov_names\n\n\nA character vector of length equal to the number of covariates (plus 1 for the intercept) to change the default labels. To see the default labels, use the plot function with this option blank. The character vector should be of th form used by\n\n\n\n\n…\n\n\nAdditional argument passed on to id_me\n\n\n\n\nfilter_cov\n\n\nA character vector of coefficients from covariate plots to exclude from plotting (should be the names of coefficients as they appear in the plots)\n\n\n\n\n\n\nBecause the marginal effects are always with respect to a given outcome/response, the outcome to be predicted must be specified in pred_outcome. If it is not specified, the function will prompt you to select one of the outcome’s values in the data.\nThe ends of the latent variable can be specified via the label_low and label_high options, which will use those labels in the ensuing plot.\nTo exclude parameters from the plot, use the filter_cov option. Note that the parameters must be specified using the underlying model syntax (however they are labeled in the plot). You can also change the names of parameters using the new_cov_names option.\nNote that the function produces a ggplot2 object, which can be further modified with ggplot2 functions.\n\n\n\nA ggplot2 plot that can be further customized with ggplot2 functions if need be.", + "text": "This function will calculate and plot the ideal point marginal effects, or the first derivative of the IRT/ideal point model with respect to the hierarchical covariate, for each item in the model. The function id_me is used to first calculate the ideal point marginal effects.\n\n\n\nid_plot_cov(\n object,\n calc_param = NULL,\n label_high = \"High\",\n label_low = \"Low\",\n group_effects = NULL,\n plot_model_id = NULL,\n pred_outcome = NULL,\n lb = 0.05,\n upb = 0.95,\n facet_ncol = 2,\n cov_type = \"person_cov\",\n ...\n)\n\n\n\n\n\n\n\nobject\n\n\nA fitted idealstan object\n\n\n\n\ncalc_param\n\n\nWhether to calculate ideal point marginal effects for a given covariate. If NULL, the default, the function will instead produce a plot of the raw coefficients from the ideal point model. If passing the name of a covariate, should be a character value of a column in the data passed to the id_make function.\n\n\n\n\nlabel_high\n\n\nWhat label to use on the plot for the high end of the latent scale\n\n\n\n\nlabel_low\n\n\nWhat label to use on the plot for the low end of the latent scale\n\n\n\n\nplot_model_id\n\n\nThe integer of the model ID to plot. If NULL and there are multiple model types, facet_wrap will be used to produce multiple plots with one for each model type.\n\n\n\n\npred_outcome\n\n\nFor discrete models with more than 2 categories, or binary models with missing data, which outcome to predict. This should be the value that matches what the outcome was coded as in the data passed to id_make.\n\n\n\n\nlb\n\n\nThe lower limit of the posterior density to use for calculating credible intervals\n\n\n\n\nupb\n\n\nThe upper limit of the posterior density to use for calculating credible intervals\n\n\n\n\nfacet_ncol\n\n\nIf facetting by multiple models or grouped factors, sets the number of columns in the multiple plots\n\n\n\n\ncov_type\n\n\nEither ‘person_cov’ for person or group-level hierarchical parameters, ‘discrim_reg_cov’ for bill/item discrimination parameters from regular (non-inflated) model, and ‘discrim_infl_cov’ for bill/item discrimination parameters from inflated model.\n\n\n\n\n…\n\n\nAdditional argument passed on to id_me\n\n\n\n\n\n\nThe ends of the latent variable can be specified via the label_low and label_high options, which will use those labels for item discrimination.\nNote that the function produces a ggplot2 object, which can be further modified with ggplot2 functions.\n\n\n\nA ggplot2 plot that can be further customized with ggplot2 functions if need be.", "crumbs": [ "Reference", "id_plot_cov" @@ -574,7 +574,7 @@ "href": "man/id_me-idealstan-method.html", "title": "idealstan", "section": "", - "text": "This function allows you to calculate ideal point marginal effects for a given person-level hierarchical covariate.\n\n\n\n## S4 method for signature 'idealstan'\nid_me(\n object,\n covariate = NULL,\n pred_outcome = NULL,\n eps = 1e-04,\n draws = 100,\n cores = 1,\n lb = 0.05,\n upb = 0.95\n)\n\n\n\n\n\n\n\nobject\n\n\nA fitted idealstan model\n\n\n\n\ncovariate\n\n\nThe character value for a covariate passed to the ‘id_make’ function before model fitting. Only one covariate can be processed at a time.\n\n\n\n\npred_outcome\n\n\nNumeric value for level of outcome to predict for ordinal responses. Defaults to top level.\n\n\n\n\neps\n\n\nThe value used for numerical differentiation. Default is 1e-4. Usually does not need to be changed.\n\n\n\n\ndraws\n\n\nThe total number of draws to use when calculating the marginal effects. Defaults to 100. Use option \"all\" to use all available MCMC draws.\n\n\n\n\ncores\n\n\nThe total number of cores to use when calculating the marginal effects. Defaults to 1.\n\n\n\n\nlb\n\n\nThe quantile for the lower bound of the aggregated effects (default is 0.05)\n\n\n\n\nupb\n\n\nThe quantile for the upper bound of the aggregated effects (default is 0.95)\n\n\n\n\n\n\nThis function will calculate item-level ideal point marginal effects for a given covariate that was passed to the ‘id_make’ function using the ‘person_cov’ option. The function will iterate over all items in the model and use numerical differentiation to calculate responses in the scale of the outcome for each item. Note: if the covariate is binary (i.e., only has two values), then the function will calculate the difference between these two values instead of using numerical differentation.\n\n\n\nA list with two objects, ideal_effects with one estimate of the marginal effect per item and posterior draw and sum_ideal_effects with one row per item with that item’s median ideal point marginal effect with the quantiles defined by the upb and lb parameters.", + "text": "This function allows you to calculate ideal point marginal effects for a given person-level hierarchical covariate.\n\n\n\n## S4 method for signature 'idealstan'\nid_me(\n object,\n covariate = NULL,\n group_effects = NULL,\n pred_outcome = NULL,\n eps = 1e-04,\n draws = 100,\n cores = 1,\n lb = 0.05,\n upb = 0.95\n)\n\n\n\n\n\n\n\nobject\n\n\nA fitted idealstan model\n\n\n\n\ncovariate\n\n\nThe character value for a covariate passed to the ‘id_make’ function before model fitting. Only one covariate can be processed at a time.\n\n\n\n\ngroup_effects\n\n\ncharacter value of a covariate included in the formula passed to ‘id_make’ for which marginal effect summaries should be grouped by. Useful when looking at the marginal effect of an interaction. Note that grouping by a covariate with many values will result in slow performance.\n\n\n\n\npred_outcome\n\n\nNumeric value for level of outcome to predict for ordinal responses. Defaults to top level.\n\n\n\n\neps\n\n\nThe value used for numerical differentiation. Default is 1e-4. Usually does not need to be changed.\n\n\n\n\ndraws\n\n\nThe total number of draws to use when calculating the marginal effects. Defaults to 100. Use option \"all\" to use all available MCMC draws.\n\n\n\n\ncores\n\n\nThe total number of cores to use when calculating the marginal effects. Defaults to 1.\n\n\n\n\nlb\n\n\nThe quantile for the lower bound of the aggregated effects (default is 0.05)\n\n\n\n\nupb\n\n\nThe quantile for the upper bound of the aggregated effects (default is 0.95)\n\n\n\n\n\n\nThis function will calculate item-level ideal point marginal effects for a given covariate that was passed to the ‘id_make’ function using the ‘person_cov’ option. The function will iterate over all items in the model and use numerical differentiation to calculate responses in the scale of the outcome for each item. Note: if the covariate is binary (i.e., only has two values), then the function will calculate the difference between these two values instead of using numerical differentation.\n\n\n\nA list with two objects, ideal_effects with one estimate of the marginal effect per item and posterior draw and sum_ideal_effects with one row per item with that item’s median ideal point marginal effect with the quantiles defined by the upb and lb parameters.", "crumbs": [ "Reference", "id_me-idealstan-method" @@ -585,7 +585,7 @@ "href": "man/id_me-idealstan-method.html#calculate-ideal-point-marginal-effects", "title": "idealstan", "section": "", - "text": "This function allows you to calculate ideal point marginal effects for a given person-level hierarchical covariate.\n\n\n\n## S4 method for signature 'idealstan'\nid_me(\n object,\n covariate = NULL,\n pred_outcome = NULL,\n eps = 1e-04,\n draws = 100,\n cores = 1,\n lb = 0.05,\n upb = 0.95\n)\n\n\n\n\n\n\n\nobject\n\n\nA fitted idealstan model\n\n\n\n\ncovariate\n\n\nThe character value for a covariate passed to the ‘id_make’ function before model fitting. Only one covariate can be processed at a time.\n\n\n\n\npred_outcome\n\n\nNumeric value for level of outcome to predict for ordinal responses. Defaults to top level.\n\n\n\n\neps\n\n\nThe value used for numerical differentiation. Default is 1e-4. Usually does not need to be changed.\n\n\n\n\ndraws\n\n\nThe total number of draws to use when calculating the marginal effects. Defaults to 100. Use option \"all\" to use all available MCMC draws.\n\n\n\n\ncores\n\n\nThe total number of cores to use when calculating the marginal effects. Defaults to 1.\n\n\n\n\nlb\n\n\nThe quantile for the lower bound of the aggregated effects (default is 0.05)\n\n\n\n\nupb\n\n\nThe quantile for the upper bound of the aggregated effects (default is 0.95)\n\n\n\n\n\n\nThis function will calculate item-level ideal point marginal effects for a given covariate that was passed to the ‘id_make’ function using the ‘person_cov’ option. The function will iterate over all items in the model and use numerical differentiation to calculate responses in the scale of the outcome for each item. Note: if the covariate is binary (i.e., only has two values), then the function will calculate the difference between these two values instead of using numerical differentation.\n\n\n\nA list with two objects, ideal_effects with one estimate of the marginal effect per item and posterior draw and sum_ideal_effects with one row per item with that item’s median ideal point marginal effect with the quantiles defined by the upb and lb parameters.", + "text": "This function allows you to calculate ideal point marginal effects for a given person-level hierarchical covariate.\n\n\n\n## S4 method for signature 'idealstan'\nid_me(\n object,\n covariate = NULL,\n group_effects = NULL,\n pred_outcome = NULL,\n eps = 1e-04,\n draws = 100,\n cores = 1,\n lb = 0.05,\n upb = 0.95\n)\n\n\n\n\n\n\n\nobject\n\n\nA fitted idealstan model\n\n\n\n\ncovariate\n\n\nThe character value for a covariate passed to the ‘id_make’ function before model fitting. Only one covariate can be processed at a time.\n\n\n\n\ngroup_effects\n\n\ncharacter value of a covariate included in the formula passed to ‘id_make’ for which marginal effect summaries should be grouped by. Useful when looking at the marginal effect of an interaction. Note that grouping by a covariate with many values will result in slow performance.\n\n\n\n\npred_outcome\n\n\nNumeric value for level of outcome to predict for ordinal responses. Defaults to top level.\n\n\n\n\neps\n\n\nThe value used for numerical differentiation. Default is 1e-4. Usually does not need to be changed.\n\n\n\n\ndraws\n\n\nThe total number of draws to use when calculating the marginal effects. Defaults to 100. Use option \"all\" to use all available MCMC draws.\n\n\n\n\ncores\n\n\nThe total number of cores to use when calculating the marginal effects. Defaults to 1.\n\n\n\n\nlb\n\n\nThe quantile for the lower bound of the aggregated effects (default is 0.05)\n\n\n\n\nupb\n\n\nThe quantile for the upper bound of the aggregated effects (default is 0.95)\n\n\n\n\n\n\nThis function will calculate item-level ideal point marginal effects for a given covariate that was passed to the ‘id_make’ function using the ‘person_cov’ option. The function will iterate over all items in the model and use numerical differentiation to calculate responses in the scale of the outcome for each item. Note: if the covariate is binary (i.e., only has two values), then the function will calculate the difference between these two values instead of using numerical differentation.\n\n\n\nA list with two objects, ideal_effects with one estimate of the marginal effect per item and posterior draw and sum_ideal_effects with one row per item with that item’s median ideal point marginal effect with the quantiles defined by the upb and lb parameters.", "crumbs": [ "Reference", "id_me-idealstan-method" @@ -772,7 +772,7 @@ "href": "vignettes/Time_Series.html#random-walk-model", "title": "Time-Varying Ideal Points", "section": "Random-Walk Model", - "text": "Random-Walk Model\nTo fit the random walk model, we first create data in which we pass the name of the column of dates for each bill/item to the time_id option of id_make. One important thing to note about this model is that we code missing values as 'Absent', but we leave NA values in the outcome. These NA values will be dropped before running the model. They represent periods of time when legislators were not in office, and hence it is reasonable to exclude these periods of time from analysis.\n\n# Absent to missing\n\ndelaware$outcome[delaware$outcome==\"Absent\"] <- NA\n\n# adjust data to 0/1\n\ndelaware$outcome <- as.numeric(delaware$outcome==\"Yes\")\n\ndelaware_data <- id_make(delaware,outcome_disc = 'outcome',\n person_id = 'person_id',\n item_id = 'item_id',\n group_id= 'group_id',\n time_id='time_id')\n\nWe then pass this object to the id_estimate function and specify 'random_walk' in the vary_ideal_pts option. We also use model_type=2 to select a binary model (yes/no votes) that adjust for the missing data (legislator absences). We pass the names of two rollcall votes to restrict their item discrimination parameters for identification (i.e. we constrain one vote with all Republicans voting for to be positive and one vote with all Democrats voting for to be negative). To do so, we need to set the const_type argument to \"items\" and pass the name of bills to the restrict_ind_high and restrict_ind_low options. Using bills (or whatever indicators are in the data) that have a clear split in the votes between parties will help achieve identification, as well as using bills that are far apart in time.\nOne problem with time-varying models is that they introduce additional identification issues with the ideal point scores. Theoretically, if over-time variance is high enough, ideal point scores can oscillate from positive to negative. In these cases, you can add additional items to constrain via the restrict_ind_high and restrict_ind_low options or use a simpler time-series model like a spline with few degrees.\n\n# parallel processing over persons/legislators specified with\n# ncores = 16 and nchains = 2\n# this will equal 8 cores per chain.\n# of course your machine must have 16 cores for \n# that number to be useful\n\ndel_est <- id_estimate(delaware_data,\n model_type = 1,\n fixtype='prefix',const_type=\"items\",\n nchains = 2,use_vb = T,\n ncores = 8,\n vary_ideal_pts='random_walk',\n restrict_ind_high = 305,\n restrict_ind_low= 276,\n seed=84520,\n id_refresh=0)\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 8.5 seconds.\n[1] \"Estimating model with Pathfinder for inference (approximation of true posterior).\"\n\n\nPareto k value (35) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. \nFinished in 9.0 seconds.\n\n\nIt is important to note that the warnings about importance resampling and the approximation do matter and a run with the Hamiltonian Markov Chain sampler should be used before final inferences by setting use_vb=TRUE. The approximation is only useful for exploratory model development.\nGiven the fitted model, we can now plot the ideal points. We will turn off the option for showing the uncertainty interval as there are a lot of lines, one for each legislator:\n\nid_plot_legis_dyn(del_est,use_ci = T) +\n scale_color_manual(values=c(R='red',\n D='blue',\n X='green'),\n name=\"Party\") +\n ggtitle(\"Yearly Ideal Point Scores for Delaware Legislature\")\n\n\n\n\n\n\n\n\nThis plot does now show very much that is particularly interesting. Most of the ideal points are not changing over time, although it is important to note that polarization is increasing over time–both within parties and between parties as some legislators move to the extremes.\n\nWe can also look at the variance of the ideal points to see which of the legislators had the highest variance in their ideal points:\n\nid_plot_legis_var(del_est) + ggtitle('Variances of Time-Varying Ideal Points in Delaware State Legislature',subtitle='Higher Variances Indicate Less Stable Ideal Points') +\n scale_color_manual(values=c(R='red',\n D='blue',\n X='green'))\n\n\n\n\n\n\n\n\nWe can access the actual estimates of the variances by passing the return_data=TRUE option to the plot function:\n\nout_d <- id_plot_legis_var(del_est,return_data = T)\nknitr::kable(head(out_d$plot_data))\n\n\n\n\n\n\n\n\n\n\n\n\n\nlegis\nlow_pt\nhigh_pt\nmedian_pt\nid_num\nperson_id\ngroup_id\n\n\n\n\ntime_var_free[100]\n0.6819100\n0.6819100\n0.6819100\n100\nPettyjohn, Brian Guy 137\nR\n\n\ntime_var_free[101]\n0.0577349\n0.0577349\n0.0577349\n101\nPlant, Al Sr. 76\nD\n\n\ntime_var_free[102]\n0.2079570\n0.2079570\n0.2079570\n102\nPlant, Hazel 77\nD\n\n\ntime_var_free[103]\n0.1906220\n0.1906220\n0.1906220\n103\nPoore, Nicole 138\nD\n\n\ntime_var_free[104]\n0.3805770\n0.3805770\n0.3805770\n104\nPostles, Charles S. 78\nR\n\n\ntime_var_free[105]\n0.3066450\n0.3066450\n0.3066450\n105\nPotter, Charles Jr. 79\nD", + "text": "Random-Walk Model\nTo fit the random walk model, we first create data in which we pass the name of the column of dates for each bill/item to the time_id option of id_make. One important thing to note about this model is that we code missing values as 'Absent', but we leave NA values in the outcome. These NA values will be dropped before running the model. They represent periods of time when legislators were not in office, and hence it is reasonable to exclude these periods of time from analysis.\n\n# Absent to missing\n\ndelaware$outcome[delaware$outcome==\"Absent\"] <- NA\n\n# adjust data to 0/1\n\ndelaware$outcome <- as.numeric(delaware$outcome==\"Yes\")\n\ndelaware_data <- id_make(delaware,outcome_disc = 'outcome',\n person_id = 'person_id',\n item_id = 'item_id',\n group_id= 'group_id',\n time_id='time_id')\n\nWe then pass this object to the id_estimate function and specify 'random_walk' in the vary_ideal_pts option. We also use model_type=2 to select a binary model (yes/no votes) that adjust for the missing data (legislator absences). We pass the names of two rollcall votes to restrict their item discrimination parameters for identification (i.e. we constrain one vote with all Republicans voting for to be positive and one vote with all Democrats voting for to be negative). To do so, we need to set the const_type argument to \"items\" and pass the name of bills to the restrict_ind_high and restrict_ind_low options. Using bills (or whatever indicators are in the data) that have a clear split in the votes between parties will help achieve identification, as well as using bills that are far apart in time.\nOne problem with time-varying models is that they introduce additional identification issues with the ideal point scores. Theoretically, if over-time variance is high enough, ideal point scores can oscillate from positive to negative. In these cases, you can add additional items to constrain via the restrict_ind_high and restrict_ind_low options or use a simpler time-series model like a spline with few degrees.\n\n# parallel processing over persons/legislators specified with\n# ncores = 16 and nchains = 2\n# this will equal 8 cores per chain.\n# of course your machine must have 16 cores for \n# that number to be useful\n\ndel_est <- id_estimate(delaware_data,\n model_type = 1,\n fixtype='prefix',const_type=\"items\",\n nchains = 2,use_vb = T,\n ncores = 8,\n vary_ideal_pts='random_walk',\n restrict_ind_high = 305,\n restrict_ind_low= 276,\n seed=84520,\n id_refresh=0)\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 7.5 seconds.\n[1] \"Estimating model with Pathfinder for inference (approximation of true posterior).\"\n\n\nPareto k value (41) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. \nFinished in 8.7 seconds.\n\n\nIt is important to note that the warnings about importance resampling and the approximation do matter and a run with the Hamiltonian Markov Chain sampler should be used before final inferences by setting use_vb=TRUE. The approximation is only useful for exploratory model development.\nGiven the fitted model, we can now plot the ideal points. We will turn off the option for showing the uncertainty interval as there are a lot of lines, one for each legislator:\n\nid_plot_legis_dyn(del_est,use_ci = T) +\n scale_color_manual(values=c(R='red',\n D='blue',\n X='green'),\n name=\"Party\") +\n ggtitle(\"Yearly Ideal Point Scores for Delaware Legislature\")\n\n\n\n\n\n\n\n\nThis plot does now show very much that is particularly interesting. Most of the ideal points are not changing over time, although it is important to note that polarization is increasing over time–both within parties and between parties as some legislators move to the extremes.\n\nWe can also look at the variance of the ideal points to see which of the legislators had the highest variance in their ideal points:\n\nid_plot_legis_var(del_est) + ggtitle('Variances of Time-Varying Ideal Points in Delaware State Legislature',subtitle='Higher Variances Indicate Less Stable Ideal Points') +\n scale_color_manual(values=c(R='red',\n D='blue',\n X='green'))\n\n\n\n\n\n\n\n\nWe can access the actual estimates of the variances by passing the return_data=TRUE option to the plot function:\n\nout_d <- id_plot_legis_var(del_est,return_data = T)\nknitr::kable(head(out_d$plot_data))\n\n\n\n\n\n\n\n\n\n\n\n\n\nlegis\nlow_pt\nhigh_pt\nmedian_pt\nid_num\nperson_id\ngroup_id\n\n\n\n\ntime_var_free[100]\n0.6745350\n0.6745350\n0.6745350\n100\nPettyjohn, Brian Guy 137\nR\n\n\ntime_var_free[101]\n0.0536705\n0.0536705\n0.0536705\n101\nPlant, Al Sr. 76\nD\n\n\ntime_var_free[102]\n0.2083990\n0.2083990\n0.2083990\n102\nPlant, Hazel 77\nD\n\n\ntime_var_free[103]\n0.1720390\n0.1720390\n0.1720390\n103\nPoore, Nicole 138\nD\n\n\ntime_var_free[104]\n0.3825970\n0.3825970\n0.3825970\n104\nPostles, Charles S. 78\nR\n\n\ntime_var_free[105]\n0.3129320\n0.3129320\n0.3129320\n105\nPotter, Charles Jr. 79\nD", "crumbs": [ "Articles", "Time-Varying Ideal Points" @@ -783,7 +783,7 @@ "href": "vignettes/Time_Series.html#spline-model", "title": "Time-Varying Ideal Points", "section": "Spline Model", - "text": "Spline Model\nWe now fit a form of splines for the legislator trajectories by passing 'splines' to vary_ideal_pts. This model has two main control parameters - spline_degree and spline_knots. The first is equal to the number of polynomial coefficients or “bends” in the time series – for a value of 2 the model is quadratic, with 3 it is a sigmoid (three bends), with 4 there is an additional possible bend in the time series, and so on. We will fit a restrictive time-varying model with 0 knots (equivalent to a single polynomial function) and only 2 degrees for the polynomial function:\n\ndel_est_spline <- id_estimate(delaware_data,\n model_type = 1,\n fixtype='prefix',const_type=\"items\",\n nchains=2,\n ncores=8,spline_knots = NULL,spline_degree = 2,\n vary_ideal_pts='splines',use_vb=TRUE,\n restrict_ind_high = 305,\n restrict_ind_low=276,\n seed=84520)\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 5.9 seconds.\n[1] \"Estimating model with Pathfinder for inference (approximation of true posterior).\"\n\n\nPareto k value (29) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. \nFinished in 6.5 seconds.\n\nid_plot_legis_dyn(del_est_spline,use_ci = F) +\n scale_color_manual(values=c(R='red',\n D='blue',\n X='green'))\n\n\n\n\n\n\n\n\nThese ideal points are similar to the random walk estimates and show the limited variation possible in a 2-degree polynomial function (essentially a quadratic function). For one session, this model would appear adequate at capturing monthly changes in legislator trajectories.\nFinally, we can also examine the individual ideal points by each time point using the summary function:\n\nsummary(del_est_spline,pars='ideal_pts') %>% \n head %>% \n knitr::kable(.)\n\n\n\n\n\n\n\n\n\n\n\n\n\nPerson\nGroup\nTime_Point\nLow Posterior Interval\nPosterior Median\nHigh Posterior Interval\nParameter Name\n\n\n\n\nNA\nNA\nNA\n0.433686\n0.433686\n0.433686\nL_tp1[1,100]\n\n\nPlant, Al Sr. 76\nD\n1995-01-01\n-6.352500\n-6.352500\n-6.352500\nL_tp1[1,101]\n\n\nNA\nNA\nNA\n-5.640150\n-5.640150\n-5.640150\nL_tp1[1,102]\n\n\nNA\nNA\nNA\n-0.123376\n-0.123376\n-0.123376\nL_tp1[1,103]\n\n\nNA\nNA\nNA\n-0.453890\n-0.453890\n-0.453890\nL_tp1[1,104]\n\n\nNA\nNA\nNA\n-0.518331\n-0.518331\n-0.518331\nL_tp1[1,105]", + "text": "Spline Model\nWe now fit a form of splines for the legislator trajectories by passing 'splines' to vary_ideal_pts. This model has two main control parameters - spline_degree and spline_knots. The first is equal to the number of polynomial coefficients or “bends” in the time series – for a value of 2 the model is quadratic, with 3 it is a sigmoid (three bends), with 4 there is an additional possible bend in the time series, and so on. We will fit a restrictive time-varying model with 0 knots (equivalent to a single polynomial function) and only 2 degrees for the polynomial function:\n\ndel_est_spline <- id_estimate(delaware_data,\n model_type = 1,\n fixtype='prefix',const_type=\"items\",\n nchains=2,\n ncores=8,spline_knots = NULL,spline_degree = 2,\n vary_ideal_pts='splines',use_vb=TRUE,\n restrict_ind_high = 305,\n restrict_ind_low=276,\n seed=84520)\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 5.8 seconds.\n[1] \"Estimating model with Pathfinder for inference (approximation of true posterior).\"\n\n\nPareto k value (31) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. \nFinished in 7.3 seconds.\n\nid_plot_legis_dyn(del_est_spline,use_ci = F) +\n scale_color_manual(values=c(R='red',\n D='blue',\n X='green'))\n\n\n\n\n\n\n\n\nThese ideal points are similar to the random walk estimates and show the limited variation possible in a 2-degree polynomial function (essentially a quadratic function). For one session, this model would appear adequate at capturing monthly changes in legislator trajectories.\nFinally, we can also examine the individual ideal points by each time point using the summary function:\n\nsummary(del_est_spline,pars='ideal_pts') %>% \n head %>% \n knitr::kable(.)\n\n\n\n\n\n\n\n\n\n\n\n\n\nPerson\nGroup\nTime_Point\nLow Posterior Interval\nPosterior Median\nHigh Posterior Interval\nParameter Name\n\n\n\n\nNA\nNA\nNA\n1.590490\n1.590490\n1.590490\nL_tp1[1,100]\n\n\nPlant, Al Sr. 76\nD\n1995-01-01\n-6.750600\n-6.750600\n-6.750600\nL_tp1[1,101]\n\n\nNA\nNA\nNA\n-5.226830\n-5.226830\n-5.226830\nL_tp1[1,102]\n\n\nNA\nNA\nNA\n-0.341960\n-0.341960\n-0.341960\nL_tp1[1,103]\n\n\nNA\nNA\nNA\n-0.133957\n-0.133957\n-0.133957\nL_tp1[1,104]\n\n\nNA\nNA\nNA\n-0.376860\n-0.376860\n-0.376860\nL_tp1[1,105]", "crumbs": [ "Articles", "Time-Varying Ideal Points" @@ -794,7 +794,7 @@ "href": "vignettes/Time_Series.html#group-level-time-varying-ideal-points", "title": "Time-Varying Ideal Points", "section": "Group-level Time-varying Ideal Points", - "text": "Group-level Time-varying Ideal Points\nFinally, we can also change the model’s parameters to look at group-level, i.e. party-level, ideal points. To do so we need to specify the use_groups=T option in the id_estimate function, and we change the restricted parameters to parties:\n\ndel_est_rw3 <- id_estimate(delaware_data,\n fixtype='prefix',const_type=\"items\",\n nchains=2,use_groups = T,\n ncores=8,use_vb=TRUE,\n restrict_ind_high = 305,\n restrict_ind_low=276,\n vary_ideal_pts='random_walk',\n seed=84520)\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 103.6 seconds.\n[1] \"Estimating model with Pathfinder for inference (approximation of true posterior).\"\n\n\nPareto k value (15) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. \nFinished in 82.5 seconds.\n\nid_plot_legis_dyn(del_est_rw3,\n include=c('D','R')) + scale_colour_manual(values=c(R='red',\n D='blue',\n I='green'),\n name=\"Parties\")\n\n\n\n\n\n\n\n\nWe can also overlay a bill/item midpoint to see where the line of indifference in voting is relative to party positions. In a dynamic ideal point model, the bill/item midpoint will be a straight line as the bill-item midpoint was only voted on in one time point, and hence has only one parameter:\n\nid_plot_legis_dyn(del_est_rw3,item_plot='342',\n text_size_label = 5,\n include=c('D','R')) + scale_colour_manual(values=c(R='red',\n D='blue',\n I='green'),\n name=\"Parties\") +\n ggtitle('Time-Varying Party-level Ideal Points for the Delaware State Legislature',\n subtitle = 'Midpoint (Line of Indifference to Voting) for 342nd Roll-call Vote as Dotted Line') +\n guides(color='none') +\n annotate(geom='text',\n x = ymd('2016-01-01'),\n y=-1,\n label='Confirmation Vote for Wilhelmina Wright as U.S. District Judge')\n\n\n\n\n\n\n\n\nAs this plot shows, the line of indifference is very close to the Republican party, implying that the vote split the Republican party while Democrats voted as a bloc. Empirically that is very close to the observed votes; all 27 Democrats voted to confirm the judge while 7 out of 6 Republicans did so.\nI will now estimate an additional Gaussian process model to use as comparison points to the random-walk model for parties:\n\ndel_est_gp1 <- id_estimate(delaware_data,\n fixtype='prefix',const_type=\"items\",\n nchains=2,use_groups=T,\n ncores=8,use_vb=TRUE,\n restrict_ind_high = 305,\n restrict_ind_low=276,\n vary_ideal_pts='GP',\n seed=84520)\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 192.9 seconds.\n[1] \"Estimating model with Pathfinder for inference (approximation of true posterior).\"\n\n\nPareto k value (15) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. \nFinished in 1070.2 seconds.\n\n\nWe can then examine the distributions for both models as plots:\n\nid_plot_legis_dyn(del_est_rw3,include=c('D','R'))\n\n\n\n\n\n\n\nid_plot_legis_dyn(del_est_gp1,include=c('D','R'))\n\n\n\n\n\n\n\n\nThis plot shows that are substantial divergences between the different models (each plot is faceted by group_id). The GP model shows a lot more bounce over time relative to the random walk model, which is implausible given the latent trait we are trying to estimate is legislator ideology. In this case, we should prefer simpler models, such as random walks or splines, to estimate a more slowly-changing latent variable. Estimation with HMC rather than the variational approximation could also help.\nWe could also consider adjusting GP-specific parameters to force a more restrictive fit, though that type of prior adjustment depends on the particular dataset and context. These parameters are given defaults that restrict movement in the ideal points to help ensure identification. As such, they tend to be fairly conservative, but they can be made even more so when necessary. The table below shows these parameters’ values.\n\nParameters in the Gaussian Process Time-Series Model\n\n\n\n\n\n\nParameter\nDescription\n\n\n\n\ngp_sd_par\nThis parameter represents residual variation in the series that the GP does not account for. As such, its default is a very low value, as increasing it will generally increase oscillation in the series.\n\n\ngp_num_diff\nThis parameter is a multiplier that is used to set the prior for the length-scale of the GP. Loosely speaking, the length-scale determines the number of times that the time-series can cross zero, and so lowering this parameter will decrease the length-scale and subsequently increase the number of times the series can cross zero. The length-scale is given a prior equal to the difference between the maximum and minimum length of the time series in whatever units it is recorded in (days, weeks, etc) times the parameter gp_num_diff. The second numeric value of this parameter represents the standard deviation of the log-normal prior of the length scale. Increasing the standard deviation will put more weight on the data in determining the amount of flexibility in the time series.\n\n\ngp_m_sd_par\nThis parameter has two values that set the GP’s marginal standard deviation. This parameter loosely represents the amount of time-series variation in the series. The first numeric value represents the hard upper limit for this parameter to prevent the series oscillating. The second numeric value is equal to the shape of an inverse-gamma prior defined over the interval between 0 and the first numeric value (the hard upper limit). It is a weakly informative prior that pulls values away from zero to prevent divergences. Increasing the first numeric value (the upper limit) will increase marginal standard deviation, while the second numeric value can increase marginal standard deviation by decreasing its value, resulting in a flatter inverse-gamma prior.", + "text": "Group-level Time-varying Ideal Points\nFinally, we can also change the model’s parameters to look at group-level, i.e. party-level, ideal points. To do so we need to specify the use_groups=T option in the id_estimate function, and we change the restricted parameters to parties:\n\ndel_est_rw3 <- id_estimate(delaware_data,\n fixtype='prefix',const_type=\"items\",\n nchains=2,use_groups = T,\n ncores=8,use_vb=TRUE,\n restrict_ind_high = 305,\n restrict_ind_low=276,\n vary_ideal_pts='random_walk',\n seed=84520)\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 103.6 seconds.\n[1] \"Estimating model with Pathfinder for inference (approximation of true posterior).\"\n\n\nPareto k value (17) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. \nFinished in 101.4 seconds.\n\nid_plot_legis_dyn(del_est_rw3,\n include=c('D','R')) + scale_colour_manual(values=c(R='red',\n D='blue',\n I='green'),\n name=\"Parties\")\n\n\n\n\n\n\n\n\nWe can also overlay a bill/item midpoint to see where the line of indifference in voting is relative to party positions. In a dynamic ideal point model, the bill/item midpoint will be a straight line as the bill-item midpoint was only voted on in one time point, and hence has only one parameter:\n\nid_plot_legis_dyn(del_est_rw3,item_plot='342',\n text_size_label = 5,\n include=c('D','R')) + scale_colour_manual(values=c(R='red',\n D='blue',\n I='green'),\n name=\"Parties\") +\n ggtitle('Time-Varying Party-level Ideal Points for the Delaware State Legislature',\n subtitle = 'Midpoint (Line of Indifference to Voting) for 342nd Roll-call Vote as Dotted Line') +\n guides(color='none') +\n annotate(geom='text',\n x = ymd('2016-01-01'),\n y=-1,\n label='Confirmation Vote for Wilhelmina Wright as U.S. District Judge')\n\n\n\n\n\n\n\n\nAs this plot shows, the line of indifference is very close to the Republican party, implying that the vote split the Republican party while Democrats voted as a bloc. Empirically that is very close to the observed votes; all 27 Democrats voted to confirm the judge while 7 out of 6 Republicans did so.\nI will now estimate an additional Gaussian process model to use as comparison points to the random-walk model for parties:\n\ndel_est_gp1 <- id_estimate(delaware_data,\n fixtype='prefix',const_type=\"items\",\n nchains=2,use_groups=T,\n ncores=8,use_vb=TRUE,\n restrict_ind_high = 305,\n restrict_ind_low=276,\n vary_ideal_pts='GP',\n seed=84520)\n\n[1] \"Running pathfinder to find starting values\"\nFinished in 94.2 seconds.\n[1] \"Estimating model with Pathfinder for inference (approximation of true posterior).\"\n\n\nPareto k value (18) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. \nFinished in 70.5 seconds.\n\n\nWe can then examine the distributions for both models as plots:\n\nid_plot_legis_dyn(del_est_rw3,include=c('D','R'))\n\n\n\n\n\n\n\nid_plot_legis_dyn(del_est_gp1,include=c('D','R'))\n\n\n\n\n\n\n\n\nThis plot shows that are substantial divergences between the different models (each plot is faceted by group_id). The GP model shows a lot more bounce over time relative to the random walk model, which is implausible given the latent trait we are trying to estimate is legislator ideology. In this case, we should prefer simpler models, such as random walks or splines, to estimate a more slowly-changing latent variable. Estimation with HMC rather than the variational approximation could also help.\nWe could also consider adjusting GP-specific parameters to force a more restrictive fit, though that type of prior adjustment depends on the particular dataset and context. These parameters are given defaults that restrict movement in the ideal points to help ensure identification. As such, they tend to be fairly conservative, but they can be made even more so when necessary. The table below shows these parameters’ values.\n\nParameters in the Gaussian Process Time-Series Model\n\n\n\n\n\n\nParameter\nDescription\n\n\n\n\ngp_sd_par\nThis parameter represents residual variation in the series that the GP does not account for. As such, its default is a very low value, as increasing it will generally increase oscillation in the series.\n\n\ngp_num_diff\nThis parameter is a multiplier that is used to set the prior for the length-scale of the GP. Loosely speaking, the length-scale determines the number of times that the time-series can cross zero, and so lowering this parameter will decrease the length-scale and subsequently increase the number of times the series can cross zero. The length-scale is given a prior equal to the difference between the maximum and minimum length of the time series in whatever units it is recorded in (days, weeks, etc) times the parameter gp_num_diff. The second numeric value of this parameter represents the standard deviation of the log-normal prior of the length scale. Increasing the standard deviation will put more weight on the data in determining the amount of flexibility in the time series.\n\n\ngp_m_sd_par\nThis parameter has two values that set the GP’s marginal standard deviation. This parameter loosely represents the amount of time-series variation in the series. The first numeric value represents the hard upper limit for this parameter to prevent the series oscillating. The second numeric value is equal to the shape of an inverse-gamma prior defined over the interval between 0 and the first numeric value (the hard upper limit). It is a weakly informative prior that pulls values away from zero to prevent divergences. Increasing the first numeric value (the upper limit) will increase marginal standard deviation, while the second numeric value can increase marginal standard deviation by decreasing its value, resulting in a flatter inverse-gamma prior.", "crumbs": [ "Articles", "Time-Varying Ideal Points" diff --git a/docs/vignettes/Package_Introduction.html b/docs/vignettes/Package_Introduction.html index 4fbaa09..46072f2 100755 --- a/docs/vignettes/Package_Introduction.html +++ b/docs/vignettes/Package_Introduction.html @@ -463,10 +463,10 @@

Introduction to Idealstan

----++++ @@ -595,25 +595,20 @@

Installation Ins

Simulation of Ordinal IRT with Missing Data

To begin with, we can simulate data from an ordinal ideal-point model in which there are three possible responses corresponding to a legislator voting: yes, abstain and no. An additional category is also simulated that indicates whether a legislator shows up to vote or is absent, which traditional IRT models would record as missing data and would drop from the estimation. This package can instead utilize missing data via a hurdle model in which the censoring of the vote/score data is estimated as a function of individual item/bill intercepts and discrimination parameters for the decision to be absent or present. In other words, if the missing data is a reflection of the person’s ideal point, such as more conservative legislators refusing to show up to vote, than the model will make use of this missing data to infer additional information about the legislators’ ideal points.

The function id_sim_gen() allows you to simulate data from any of the sixteen models currently implemented in idealstan (see previous list). To include missing data, specify the inflate option as TRUE. For example, here we sample data from an ordinal graded response model:

-
-
ord_ideal_sim <- id_sim_gen(model='ordinal_grm',inflate = T)
-
-
Warning: `data_frame()` was deprecated in tibble 1.1.0.
-ℹ Please use `tibble()` instead.
-ℹ The deprecated feature was likely used in the idealstan package.
-  Please report the issue at <https://github.com/saudiwin/idealstan/issues>.
-
-
tt(head(ord_ideal_sim@score_matrix))
+
+
ord_ideal_sim <- id_sim_gen(model='ordinal_grm',inflate = T)
+
+tt(head(ord_ideal_sim@score_matrix))
-
+
@@ -716,7 +711,7 @@

Table 1 as the model_id argument in the id_estimate function or, in the case of multiple models/item types, pass a column model_id to the id_make function that specifies the model ID for each row in the data. This latter option is useful when you have items of mixed types, such as binary, ordinal and/or continuous items. The function id_make also includes the ability to incorporate hierarchical (person or item-level) covariates, as discussed below.

To speed up processing, all of the models shown in Table 1 make use of multiple core parallel computation. To use this option, the specified number of available cores in the ncores option must exceed the number of MCMC chains nchains. cmdstanr will automatically assign cores by dividing the number of chains by the number of cores. In all of the examples in this vignette, I use a machine with 8 cores and estimate 2 chains, so there are 4 cores per chain. By default, id_estimate parallelizes over persons, although that can be changed to items with the map_over_id option (only works with static models).

The package has options for identification that are similar to other IRT packages in which the IDs of legislators/persons to constrain are specified to the id_estimate function. For example, we can use the true values of the simulated legislators to constrain one legislator/person with the highest simulated ideal point and one legislator/person with the lowest ideal point. Each constrained parameter must be fixed to a specific value, preferably at either end of the ideal point spectrum, to identify the model. In particular, two pieces of information are necessary: a value for the high ideal point, and the difference between the high and low points. In this example I pre-specify which parameters to constrain based on the simulated data as restrict_ind_high and restrict_ind_low, and use the actual values to pin the parameters to specific values with fix_high and fix_low.

-
-
true_legis <- ord_ideal_sim@simul_data$true_person
-high_leg <- sort(true_legis,decreasing = TRUE,index.return=TRUE)
-low_leg <- sort(true_legis,index.return=TRUE)
-
-ord_ideal_est <- id_estimate(idealdata=ord_ideal_sim,
-                             model_type=6,
-                             fixtype='prefix',
-                             restrict_ind_high = as.character(high_leg$ix[1]),
-                             restrict_ind_low=as.character(low_leg$ix[1]),
-                             fix_high = sort(true_legis,decreasing = TRUE)[1],
-                             fix_low = sort(true_legis,decreasing = FALSE)[1],
-                             id_refresh=500,
-                             ncores=8,
-                             nchains=2)
-
-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-
+
+
true_legis <- ord_ideal_sim@simul_data$true_person
+high_leg <- sort(true_legis,decreasing = TRUE,index.return=TRUE)
+low_leg <- sort(true_legis,index.return=TRUE)
+
+ord_ideal_est <- id_estimate(idealdata=ord_ideal_sim,
+                             model_type=6,
+                             fixtype='prefix',
+                             restrict_ind_high = as.character(high_leg$ix[1]),
+                             restrict_ind_low=as.character(low_leg$ix[1]),
+                             fix_high = sort(true_legis,decreasing = TRUE)[1],
+                             fix_low = sort(true_legis,decreasing = FALSE)[1],
+                             id_refresh=500,
+                             ncores=8,
+                             nchains=2)
[1] "Running pathfinder to find starting values"
-Path [1] :Initial log joint density = -1572.319503 
+Path [1] :Initial log joint density = -1577.176212 
 Path [1] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
-             93      -7.521e+02      2.715e-03   4.924e-03    4.981e-01  1.000e+00      2326 -9.485e+02 -9.485e+02                   
-Path [1] :Best Iter: [88] ELBO (-931.144330) evaluations: (2326) 
-Finished in  0.8 seconds.
-[1] "Estimating model with full Stan MCMC sampler."
-
-
-
Init values were only set for a subset of parameters. 
-Missing init values for the following parameters:
- - chain 1: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw
- - chain 2: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw
-
-To disable this message use options(cmdstanr_warn_inits = FALSE).
-
-
-
Running MCMC with 2 parallel chains, with 4 thread(s) per chain...
+             87      -8.501e+02      4.265e-04   3.971e-03    7.494e-01  7.494e-01      2176 -1.065e+03 -1.065e+03                   
+Path [1] :Best Iter: [85] ELBO (-1059.338643) evaluations: (2176) 
+Finished in  0.5 seconds.
+[1] "Estimating model with full Stan MCMC sampler."
+Running MCMC with 2 parallel chains, with 4 thread(s) per chain...
 
 Chain 1 Iteration:    1 / 2000 [  0%]  (Warmup)
@@ -817,13 +798,13 @@

-
Chain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -115.417, but should be greater than the previous element, -115.417 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from
+
Chain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -11.3421, but should be greater than the previous element, -11.3421 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from

Chain 1 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from
-
Chain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)
+
Chain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)
Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
@@ -841,13 +822,13 @@

-
Chain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -72.5968, but should be greater than the previous element, -72.5968 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from
+
Chain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -163.557, but should be greater than the previous element, -163.557 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from

Chain 2 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from
-
Chain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)
+
Chain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)
Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
@@ -859,59 +840,56 @@

-
Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
+
Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:

-
Chain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is 1.48349, but should be greater than the previous element, 1.48349 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from
+
Chain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -14.201, but should be greater than the previous element, -14.201 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from
-
Chain 1 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from
+
Chain 2 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from
-
Chain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)
+
Chain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)
-
Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
+
Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
-
Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
+
Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
-
Chain 1
+
Chain 2 
Chain 2 Iteration:  500 / 2000 [ 25%]  (Warmup) 
 Chain 1 Iteration:  500 / 2000 [ 25%]  (Warmup) 
-Chain 2 Iteration: 1000 / 2000 [ 50%]  (Warmup) 
-Chain 2 Iteration: 1001 / 2000 [ 50%]  (Sampling) 
 Chain 1 Iteration: 1000 / 2000 [ 50%]  (Warmup) 
 Chain 1 Iteration: 1001 / 2000 [ 50%]  (Sampling) 
+Chain 2 Iteration: 1000 / 2000 [ 50%]  (Warmup) 
+Chain 2 Iteration: 1001 / 2000 [ 50%]  (Sampling) 
 Chain 1 Iteration: 1500 / 2000 [ 75%]  (Sampling) 
 Chain 2 Iteration: 1500 / 2000 [ 75%]  (Sampling) 
 Chain 1 Iteration: 2000 / 2000 [100%]  (Sampling) 
-Chain 1 finished in 46.7 seconds.
 Chain 2 Iteration: 2000 / 2000 [100%]  (Sampling) 
-Chain 2 finished in 49.3 seconds.
+Chain 1 finished in 21.8 seconds.
+Chain 2 finished in 21.7 seconds.
 
 Both chains finished successfully.
-Mean chain execution time: 48.0 seconds.
-Total execution time: 49.6 seconds.
+Mean chain execution time: 21.8 seconds. +Total execution time: 21.9 seconds.

We can then check and see how well the Stan estimation engine was able to capture the “true” values used in the simulation by plotting the true ideal points relative to the estimated ones:

-
-
id_plot_legis(ord_ideal_est,show_true = TRUE)
-
-
Warning: Dropping 'draws_df' class as required metadata was removed.
-
+
+
id_plot_legis(ord_ideal_est,show_true = TRUE)
Joining with `by = join_by(id_num)`
 Joining with `by = join_by(id_num)`
-
+
-

+

@@ -919,133 +897,110 @@

-
ord_ideal_est <- id_estimate(idealdata=ord_ideal_sim,
-                             model_type=6,
-                             id_refresh=2000,fixtype="vb_full",
-                             ncores=8,
-                           nchains=2)
-
-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-
+
+
ord_ideal_est <- id_estimate(idealdata=ord_ideal_sim,
+                             model_type=6,
+                             id_refresh=2000,fixtype="vb_full",
+                             ncores=8,
+                           nchains=2)
[1] "(First Step): Estimating model with Pathfinder (variational inference) to identify modes to constrain."
-Path [1] :Initial log joint density = -2121.033157 
+Path [1] :Initial log joint density = -1927.222174 
 Path [1] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
-             99      -7.605e+02      6.214e-03   2.023e-02    1.000e+00  1.000e+00      2476 -9.697e+02 -9.697e+02                   
-Path [1] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
-            109      -7.605e+02      7.750e-04   3.252e-03    7.237e-01  7.237e-01      2726 -9.639e+02 -9.639e+02                   
-Path [1] :Best Iter: [100] ELBO (-957.463122) evaluations: (2726) 
-Finished in  0.9 seconds.
-
-
-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
+ 98 -8.586e+02 1.010e-03 4.650e-03 1.000e+00 1.000e+00 2451 -1.074e+03 -1.074e+03 +Path [1] :Best Iter: [95] ELBO (-1068.256459) evaluations: (2451) +Finished in 0.5 seconds. 
[1] "Running pathfinder to find starting values"
-Path [1] :Initial log joint density = -1561.800868 
+Path [1] :Initial log joint density = -1533.547548 
 Path [1] : Iter      log prob        ||dx||      ||grad||     alpha      alpha0      # evals       ELBO    Best ELBO        Notes  
-            103      -7.411e+02      9.196e-04   5.285e-03    1.000e+00  1.000e+00      2576 -9.406e+02 -9.406e+02                   
-Path [1] :Best Iter: [94] ELBO (-936.862674) evaluations: (2576) 
-Finished in  0.9 seconds.
-[1] "Estimating model with full Stan MCMC sampler."
-
-
-
Init values were only set for a subset of parameters. 
-Missing init values for the following parameters:
- - chain 1: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw
- - chain 2: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw
-
-To disable this message use options(cmdstanr_warn_inits = FALSE).
-
-
-
Running MCMC with 2 parallel chains, with 4 thread(s) per chain...
+            107      -8.459e+02      6.874e-04   2.590e-03    1.000e+00  1.000e+00      2676 -1.071e+03 -1.071e+03                   
+Path [1] :Best Iter: [101] ELBO (-1052.747760) evaluations: (2676) 
+Finished in  0.5 seconds.
+[1] "Estimating model with full Stan MCMC sampler."
+Running MCMC with 2 parallel chains, with 4 thread(s) per chain...
 
-Chain 1 Iteration:    1 / 2000 [  0%]  (Warmup)
+Chain 1 Iteration: 1 / 2000 [ 0%] (Warmup) +Chain 2 Iteration: 1 / 2000 [ 0%] (Warmup)
-
Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
+
Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
-
Chain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -20.578, but should be greater than the previous element, -20.578 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from
+
Chain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -261.141, but should be greater than the previous element, -261.141 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from
-
Chain 1 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from
+
Chain 2 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from
-
Chain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)
+
Chain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)
-
Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
+
Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
-
Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
+
Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
-
Chain 1
-
-
-
Chain 2 Iteration:    1 / 2000 [  0%]  (Warmup)
+
Chain 2
-
Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
+
Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
-
Chain 1 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -5.64329, but should be greater than the previous element, -5.64329 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from
+
Chain 2 Exception: Exception: ordered_logistic: Cut-points is not a valid ordered vector. The element at 2 is -11.4019, but should be greater than the previous element, -11.4019 (in '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/model_types_mm_map_persons.stan', line 378, column 6, included from
-
Chain 1 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from
+
Chain 2 '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/idealstan/stan_files//chunks/map_func.stan', line 408, column 0, included from
-
Chain 1 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/Rtmp0BtqfJ/model-a8ac48becdd9.stan', line 639, column 2 to line 745, column 21)
+
Chain 2 '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 44, column 0) (in '/var/folders/4d/m4b3zyn966d7ctnd4hz4zvfh0000gs/T/RtmpSSVA47/model-dd1a1549e887.stan', line 639, column 2 to line 745, column 21)
-
Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
+
Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
-
Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
+
Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
-
Chain 1
+
Chain 2 
Chain 2 Iteration: 1001 / 2000 [ 50%]  (Sampling) 
 Chain 1 Iteration: 1001 / 2000 [ 50%]  (Sampling) 
-Chain 1 Iteration: 2000 / 2000 [100%]  (Sampling) 
-Chain 1 finished in 42.7 seconds.
 Chain 2 Iteration: 2000 / 2000 [100%]  (Sampling) 
-Chain 2 finished in 44.8 seconds.
+Chain 2 finished in 25.7 seconds.
+Chain 1 Iteration: 2000 / 2000 [100%]  (Sampling) 
+Chain 1 finished in 26.6 seconds.
 
 Both chains finished successfully.
-Mean chain execution time: 43.7 seconds.
-Total execution time: 44.9 seconds.
+Mean chain execution time: 26.1 seconds. +Total execution time: 26.7 seconds.

We can see from the plot of the Rhats, which is an MCMC convergence diagnostic, that all the Rhats are below 1.1, which is a good (though not perfect) sign that the model is fully identified:

-
-
id_plot_rhats(ord_ideal_est)
+
+
id_plot_rhats(ord_ideal_est)
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
-
+
-

+

-
id_plot_legis(ord_ideal_est,show_true = T)
-
-
Warning: Dropping 'draws_df' class as required metadata was removed.
-
+
id_plot_legis(ord_ideal_est,show_true = T)
Joining with `by = join_by(id_num)`
 Joining with `by = join_by(id_num)`
-
+
-

+

@@ -1057,20 +1012,20 @@

Empirical Example: U.S. Senate

This package was developed for datasets that are in a long format, i.e., one row per person/legislator, item/bill, and any other covariates. This data format departs from the traditional way of storing/using IRT/ideal point data, which is more commonly stored in a wide format with legislators/persons in the rows and items/bills in the columns.

To demonstrate how the package functions empirically, I include in the package a partial voting record of the 114th Senate (excluding rollcall votes without significant disagreement) from the website www.voteview.com. We can convert this data, which is provided in a long data frame, to an idealdata object suitable for estimation by using the id_make function. Because the intention is to fit a binary outcome model (yes or no votes on bills), I recode the outcome to be 0 for no votes and 1 for yes votes as idealstan expects binary outcomes to be coded this way.

We can first take a look at the raw data:

-
-
data('senate114')
-
-tt(select(head(senate114),1:8))
+
+
data('senate114')
+
+tt(select(head(senate114),1:8))
-

+
@@ -1200,7 +1155,7 @@

Empirical Example: U.S. Senate

-
table(senate114$cast_code)
+
table(senate114$cast_code)

     No    Yes Absent 
@@ -1212,17 +1167,17 @@ 
Empirical Example: U.S. Senate

 
To create an idealdata object for modeling from our long data frame, we pass it to the id_make function and specify the names of the columns that correspond to person IDs, item IDs, group IDs (i.e., party), time IDs and the discrete outcome, although only person, item and outcome are required for the function to work for a static model. Because this is a discrete model, we pass the column name for the outcome to the outcome_disc argument. If we also had items with multiple outcome distributions, we would need to specify the model_id column with the correct model number for each item (see Table 1) and put all continuous (real) data in a separate column which we could pass to the outcome_cont argument.

 
Note that all missing data should be coded as NA before passing it to id_make.

 
There are many other columns in the senate114 data. These can be used as person or item/bill covariates, as is discussed at the end of the vignette, but are essentially ignored unless specified to the id_make function.

-

-
# set missing (Absent) to NA
-senate114$cast_code <- ifelse(senate114$cast_code=="Absent",NA,senate114$cast_code)
-# recode outcome to 0/1
-senate114$cast_code <- senate114$cast_code -  1
-
-senate_data <- id_make(senate114,outcome_disc = 'cast_code',
-                       person_id = 'bioname',
-                       item_id = 'rollnumber',
-                       group_id= 'party_code',
-                       time_id='date')

+

+
# set missing (Absent) to NA
+senate114$cast_code <- ifelse(senate114$cast_code=="Absent",NA,senate114$cast_code)
+# recode outcome to 0/1
+senate114$cast_code <- senate114$cast_code -  1
+
+senate_data <- id_make(senate114,outcome_disc = 'cast_code',
+                       person_id = 'bioname',
+                       item_id = 'rollnumber',
+                       group_id= 'party_code',
+                       time_id='date')

 

 
We can then run a binary IRT ideal point model in which absences on particular bills are treated as a “hurdle” that the legislator must overcome in order to show up to vote. To do so, we specify model_type=2, which signifies a binary IRT model with missing-data (absence) inflation (see list in Table 1). In essence, the model is calculating a separate ideal point position for each bill/item that represents the bill’s importance to different senators. Only if a bill is relatively salient will a legislator choose to show up and vote.

 
This same missing-data mechanism also applies more broadly to situations of social choice. Any time that missing data might be a function of ideal points–people with certain ideal points are likely to avoid giving an answer–then these values should be marked as NA in the data and an inflated model type should be used. Otherwise, the missing data will be ignored during estimation.

@@ -1231,107 +1186,69 @@ 
Empirical Example: U.S. Senate

 
It is important to note that the model can also be identified by fixing item (bill) discrimination parameters by setting the const_type argument to "items". Then the values for restrict_ind_high and restrict_ind_low should be set to the character values of names for items in the data. Identifying the model based on item discrimination can have some excellent properties as it leaves all of the person ideal points to float. It is also very useful with time-varying models where fixing person ideal points can be very challenging.

 
 
To make the model fit faster, I set nchains at 2 and ncores at 8, which will allow for 4 cores to be used per chain for parallel processing (assuming of course the computer has access to 8 cores).

-

-
sen_est <- id_estimate(senate_data,
-                model_type = 1,ncores=8,nchains=2,
-                fixtype='prefix',
-                 restrict_ind_high = "WARREN, Elizabeth",
-                 restrict_ind_low="BARRASSO, John A.",
-            seed=84520)

-

-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-Warning in max(Y_cont): no non-missing arguments to max; returning -Inf

-

+

+
sen_est <- id_estimate(senate_data,
+                model_type = 1,ncores=8,nchains=2,
+                fixtype='prefix',
+                 restrict_ind_high = "WARREN, Elizabeth",
+                 restrict_ind_low="BARRASSO, John A.",
+            seed=84520)

 

 
[1] "Running pathfinder to find starting values"
-Finished in  6.2 seconds.
-[1] "Estimating model with full Stan MCMC sampler."

-

-

-
Init values were only set for a subset of parameters. 
-Missing init values for the following parameters:
- - chain 1: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm3, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw
- - chain 2: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm3, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw
-
-To disable this message use options(cmdstanr_warn_inits = FALSE).

-

-

-
Running MCMC with 2 parallel chains, with 4 thread(s) per chain...
+Finished in  2.8 seconds.
+[1] "Estimating model with full Stan MCMC sampler."
+Running MCMC with 2 parallel chains, with 4 thread(s) per chain...
 
-Chain 1 finished in 280.0 seconds.
-Chain 2 finished in 295.6 seconds.
+Chain 1 finished in 130.5 seconds.
+Chain 2 finished in 131.2 seconds.
 
 Both chains finished successfully.
-Mean chain execution time: 287.8 seconds.
-Total execution time: 295.8 seconds.

-

-

-
Warning: The ESS has been capped to avoid unstable estimates.

-

-

-
Warning: The ESS has been capped to avoid unstable estimates.
-Warning: The ESS has been capped to avoid unstable estimates.

-

-
id_plot_legis(sen_est,person_ci_alpha=0.2) +
-  scale_color_manual(values=c(D='blue',R='red',I='green')) +
-  ggtitle('Ideal Points of the 114th Senate')

-

-
Warning: Dropping 'draws_df' class as required metadata was removed.

+Mean chain execution time: 130.9 seconds.
+Total execution time: 131.5 seconds.
+
id_plot_legis(sen_est,person_ci_alpha=0.2) +
+  scale_color_manual(values=c(D='blue',R='red',I='green')) +
+  ggtitle('Ideal Points of the 114th Senate')
Joining with `by = join_by(id_num)`
-
+
-

+

The id_plot function has many other options which are documented in the help files. One notable option, though, is to plot bill midpoints along with the legislator ideal points. The midpoints show the line of equiprobability, i.e., at what ideal point is a legislator with that ideal point indifferent to voting on a bill (or answering an item correctly). To plot a bill midpoint overlay, simply include the character ID of the bill (equivalent to the column name of the bill in the rollcall vote matrix) as the item_plot option:

-
-
id_plot_legis(sen_est,person_ci_alpha=0.1,item_plot='94') +
-  scale_color_manual(values=c(D='blue',R='red',I='green')) +
-  ggtitle('Ideal Points of the 114th Senate with Vote 94 Midpoint')
-
-
Warning: Dropping 'draws_df' class as required metadata was removed.
-
+
+
id_plot_legis(sen_est,person_ci_alpha=0.1,item_plot='94') +
+  scale_color_manual(values=c(D='blue',R='red',I='green')) +
+  ggtitle('Ideal Points of the 114th Senate with Vote 94 Midpoint')
Joining with `by = join_by(id_num)`
-
-
Warning: attributes are not identical across measure variables; they will be
-dropped
-
-
+
-

+

The 50th bill in the 114 Senate shows very high discrimination: the bill midpoint is right in the middle of the ideal point distribution, with most Democrats voting yes and most Republicans voting no. The two rug lines at the bottom of the plot show the high density posterior interval for the bill midpoint, and as can be seen, the uncertainty only included those legislators near the very center of the distribution.

To look at the bill’s absence midpoints, simply change the item_plot_type parameter to the id_plot function:

-
-
id_plot_legis(sen_est,person_ci_alpha=0.1,item_plot='225',
-        item_plot_type='inflated') + 
-  scale_color_manual(values=c(D='blue',R='red',I='green'))
-
-
Warning: Dropping 'draws_df' class as required metadata was removed.
-
+
+
id_plot_legis(sen_est,person_ci_alpha=0.1,item_plot='225',
+        item_plot_type='inflated') + 
+  scale_color_manual(values=c(D='blue',R='red',I='green'))
Joining with `by = join_by(id_num)`
-
-
Warning: attributes are not identical across measure variables; they will be
-dropped
-
-
+
-

+

@@ -1340,28 +1257,22 @@

Empirical Example: U.S. Senate

Parameter Values

We can obtain summary estimates of all the ideal points and item/bill discrimination/difficulty parameters using the summary function that provides the median value of the parameters in addition to a specified posterior density interval (i.e., 5%-95%). For example, we can extract summaries for the ideal points:

-
-
ideal_pts_sum <- summary(sen_est,pars='ideal_pts')
-
-
Warning: Dropping 'draws_df' class as required metadata was removed.
-
+
+
ideal_pts_sum <- summary(sen_est,pars='ideal_pts')
Joining with `by = join_by(id_num)`
-
-
Warning: Unknown or uninitialised column: `time_id`.
-
-
tt(head(ideal_pts_sum))
+
tt(head(ideal_pts_sum))
-
+
@@ -1428,54 +1339,54 @@

Parameter Values

- - - + + + - - - + + + - - - + + + - - - + + + - - - + + + - - - + + + @@ -1485,133 +1396,184 @@

Parameter Values

Parameter Name is the name of the parameter in the underlying Stan code, which can be useful f you want to peruse the fitted Stan model (and can be accessed as given in the code below). The name of the parameters for ideal points in the Stan model is L_full (as seen in the summary from above).

-
-
stan_obj <- sen_est@stan_samples
-# show the 
-stan_obj$draws(c("L_full[1]",
-                        'L_full[2]',
-                        'L_full[3]'))
+
+
stan_obj <- sen_est@stan_samples
+# show the 
+stan_obj$draws(c("L_full[1]",
+                        'L_full[2]',
+                        'L_full[3]'))
# A draws_array: 1000 iterations, 2 chains, and 3 variables
 , , variable = L_full[1]
 
          chain
-iteration   1   2
-        1 3.8 3.6
-        2 3.3 4.3
-        3 4.4 3.3
-        4 4.2 4.5
-        5 3.7 3.3
+iteration    1    2
+        1 -4.0 -4.3
+        2 -4.3 -4.1
+        3 -4.1 -3.8
+        4 -4.6 -4.0
+        5 -3.9 -3.7
 
 , , variable = L_full[2]
 
          chain
-iteration   1   2
-        1 1.4 1.3
-        2 2.3 3.1
-        3 1.9 1.0
-        4 1.8 2.6
-        5 2.2 1.7
+iteration    1    2
+        1 -2.3 -1.6
+        2 -2.2 -1.9
+        3 -2.5 -2.9
+        4 -2.5 -1.4
+        5 -2.5 -3.1
 
 , , variable = L_full[3]
 
          chain
-iteration     1     2
-        1  -8.6 -11.5
-        2  -7.8  -7.1
-        3  -9.4 -10.2
-        4 -11.9  -8.1
-        5  -7.8  -8.7
+iteration    1    2
+        1  5.8  8.8
+        2 11.3  8.3
+        3  7.6 10.2
+        4  7.6  6.8
+        5  8.0  9.1
 
 # ... with 995 more iterations

If we know the name of the Stan parameter, we can look at the trace plot to see how the quality of the Markov Chain Monte Carlo (MCMC) sampling used to fit the model. A good trace plot shows a bouncy line that is stable around an average value. For more info, see the Stan documentation.

-
-
stan_trace(sen_est,par='L_full[1]')
+
+
stan_trace(sen_est,par='L_full[1]')
-
+
-

+

Finally we can also extract all of the posterior iterations to do additional calculations that average over posterior uncertainty by changing the aggregate option in summary. In the following code, I access the individual posterior iterations for the item/bill parameters, including difficulty (average probability of voting yes), discrimination (how strongly the item/bill loads on either end of the ideal point scale) and the midpoints (position where someone with that ideal point would be indifferent to voting yes/no).

-
-
item_all <- summary(sen_est,pars='items', aggregate=F)
-knitr::kable(head(item_all))
+
+
item_all <- summary(sen_est,pars='items', aggregate=F)
+tt(head(item_all))
-
WYDEN, Ronald Lee D 1 -9.158463-7.509925-6.155738 5.908937 7.201095 8.719860 L_full[100]
BOXER, Barbara D 1-10.985220-8.691115-7.031368 6.780327 8.46576010.712110 L_full[10]
BROWN, Sherrod D 1-11.973265-9.486375-7.520037 7.289706 9.22162511.874305 L_full[11]
BURR, Richard M. R 1 4.917415 5.856475 6.882041-6.645283-5.665140-4.792147 L_full[12]
CANTWELL, Maria E. D 1-11.067110-8.880885-7.215407 6.941406 8.66101010.781860 L_full[13]
CAPITO, Shelley Moore R 1 4.408447 5.175785 6.017246-5.783458-4.992145-4.276122 L_full[14]
-------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Posterior_SampleItem NameItem TypePredicted OutcomeParameterIteration
-2.9964334Non-Inflated Item Midpoint1A function of other parameters1
-0.5130944Non-Inflated Item Midpoint1A function of other parameters2
-2.5214164Non-Inflated Item Midpoint1A function of other parameters3
-2.1572854Non-Inflated Item Midpoint1A function of other parameters4
-2.4551054Non-Inflated Item Midpoint1A function of other parameters5
-2.3439504Non-Inflated Item Midpoint1A function of other parameters6
+ + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Posterior_SampleItem NameItem TypePredicted OutcomeParameterIteration
1.6066394Non-Inflated Item Midpoint1A function of other parameters1
1.5117664Non-Inflated Item Midpoint1A function of other parameters2
1.0280574Non-Inflated Item Midpoint1A function of other parameters3
1.9761614Non-Inflated Item Midpoint1A function of other parameters4
1.5509864Non-Inflated Item Midpoint1A function of other parameters5
1.3777754Non-Inflated Item Midpoint1A function of other parameters6
+
+
@@ -1620,72 +1582,54 @@

Hierarchical Covar

Note: ideal point marginal effects have yet to be implemented as a separate function. In this section I demonstrate how to estimate these effects using R code.

Finally, we can also fit a model where we include a covariate that varies by person/legislator. To do so, we need to pass a one-sided formula to the id_make function to prepare the data accordingly. By way of example, we will include a model where we include an interaction between party ID (party_code) and the legislator’s age to see if younger/older legislators are more or less conservative. Because this is a static model, the effect of the covariate is averaged over all of the bills in the dataset and all the legislators in the dataset without taking into account the order or time period of the bills.

It is important to note that for static ideal point models, covariates are only defined over the legislators/persons who are not being used as constraints in the model, such as John Barasso and Elizabeth Warren in this model.

-
-
senate114$age <- 2018 - senate114$born
-# center the variable
-senate114$age <- senate114$age - mean(senate114$age)
-# put in units of 10 years
-senate114$age <- senate114$age / 10
-
-# doing this will improve estimation speed (variables mean-centered and with an SD
-# not much bigger than 1 or 2)
-
-senate_data <- id_make(senate114,outcome_disc = 'cast_code',
-                       person_id = 'bioname',
-                       item_id = 'rollnumber',
-                       group_id= 'party_code',
-                       time_id='date',
-                       person_cov = ~party_code*age)
-
-sen_est_cov <- id_estimate(senate_data,
-                model_type = 1,
-                fixtype='prefix',
-                nchains=2,
-                ncores=8,
-                 restrict_ind_high = "BARRASSO, John A.",
-                 restrict_ind_low="WARREN, Elizabeth",
-            seed=84520)
-
-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-
+
+
senate114$age <- 2018 - senate114$born
+# center the variable
+senate114$age <- senate114$age - mean(senate114$age)
+# put in units of 10 years
+senate114$age <- senate114$age / 10
+
+# doing this will improve estimation speed (variables mean-centered and with an SD
+# not much bigger than 1 or 2)
+
+senate_data <- id_make(senate114,outcome_disc = 'cast_code',
+                       person_id = 'bioname',
+                       item_id = 'rollnumber',
+                       group_id= 'party_code',
+                       time_id='date',
+                       person_cov = ~party_code*age)
+
+sen_est_cov <- id_estimate(senate_data,
+                model_type = 1,
+                fixtype='prefix',
+                nchains=2,
+                ncores=8,
+                 restrict_ind_high = "BARRASSO, John A.",
+                 restrict_ind_low="WARREN, Elizabeth",
+            seed=84520)
[1] "Running pathfinder to find starting values"
-Finished in  10.2 seconds.
-[1] "Estimating model with full Stan MCMC sampler."
-
-
-
Init values were only set for a subset of parameters. 
-Missing init values for the following parameters:
- - chain 1: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm3, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw
- - chain 2: m_sd_free, gp_sd_free, ls_int, ls_int_abs, L_tp1_var, L_AR1, steps_votes3, steps_votes4, steps_votes5, steps_votes6, steps_votes7, steps_votes8, steps_votes9, steps_votes10, steps_votes_grm3, steps_votes_grm4, steps_votes_grm5, steps_votes_grm6, steps_votes_grm7, steps_votes_grm8, steps_votes_grm9, steps_votes_grm10, ordbeta_cut, phi, extra_sd, time_var_gp_free, time_var_free, a_raw
+Finished in  5.5 seconds.
+[1] "Estimating model with full Stan MCMC sampler."
+Running MCMC with 2 parallel chains, with 4 thread(s) per chain...
 
-To disable this message use options(cmdstanr_warn_inits = FALSE).
-
-
-
Running MCMC with 2 parallel chains, with 4 thread(s) per chain...
-
-Chain 2 finished in 592.9 seconds.
-Chain 1 finished in 593.8 seconds.
+Chain 2 finished in 256.4 seconds.
+Chain 1 finished in 256.6 seconds.
 
 Both chains finished successfully.
-Mean chain execution time: 593.4 seconds.
-Total execution time: 594.1 seconds.
+Mean chain execution time: 256.5 seconds. +Total execution time: 256.8 seconds.

As discussed in the associated working paper (https://osf.io/preprints/osf/8j2bt), ideal point marginal effects can be derived from idealstan models in which the raw relationship between the hierarchical covariates and the actual outcomes (in this case, votes) can be shown at the item (vote) level. There are two functions that can be used to calculate and display ideal point marginal effects. The first, id_me, shown in the chunks, below, will produce data frames with summaries ideal point marginal effects given a covariate and also data frames with one row per posterior draw that are useful for further analysis or aggregation.

In the example below, ideal point marginal effects are calculated for the "age" covariate, first for the whole dataset and then for all distinct values of "group_id", which is party ID in our data. This latter calculation is especially useful as we interaction age with group_id, and by calculating marginal effects for each distinct subset of group_id we can learn what the conditional marginal effect is by party ID.

-
-
  # calculate marginal effects for age subset by item
-
-  marg_effs <- id_me(sen_est_cov,covariate="age")
+
+
  # calculate marginal effects for age subset by item
+
+  marg_effs <- id_me(sen_est_cov,covariate="age")
Creating predictions
-
-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-
[1] "Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples."
 [1] "Adding in hierarchical covariates values to the time-varying person scores."
@@ -1693,10 +1637,6 @@ 
Hierarchical Covar
 [1] "Done!"
 [1] "Now on model 1"
-
-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-
[1] "Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples."
 [1] "Adding in hierarchical covariates values to the time-varying person scores."
@@ -1710,18 +1650,18 @@ 
Hierarchical Covar
 

 
Joining with `by = join_by(item_id)`

 

-
  head(marg_effs$ideal_effects) %>% 
-    tt

+
  head(marg_effs$ideal_effects) %>% 
+    tt

 

 
 
     
 
     
     

-      
+      

@@ -1790,7 +1730,7 @@ 
Hierarchical Covar
                   

-                  
+                  
@@ -1800,7 +1740,7 @@ 
Hierarchical Covar
                   

-                  
+                  
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Hierarchical Covar
                   

-                  
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Hierarchical Covar
                   

-                  
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Hierarchical Covar
                   

-                  
+                  
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Hierarchical Covar
                   

-                  
+                  
@@ -1851,18 +1791,18 @@ 
Hierarchical Covar
     
 
 
-
  head(marg_effs$sum_ideal_effects) %>% 
-    tt

+
  head(marg_effs$sum_ideal_effects) %>% 
+    tt

 

 
 
     
 
     
     

-      

         
         
               
1
                   1
                   10.00491929523.050097e-05
                   R
                   4
                   ALEXANDER, Lamar2
                   1
                   10.00038055613.113286e-04
                   R
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                   ALEXANDER, Lamar3
                   1
                   10.00119621106.084729e-03
                   R
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                   ALEXANDER, Lamar4
                   1
                   10.00320835638.515025e-04
                   R
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                   ALEXANDER, Lamar5
                   1
                   10.00719818623.301149e-03
                   R
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                   ALEXANDER, Lamar6
                   1
                   10.01758217414.367442e-04
                   R
                   4
                   ALEXANDER, Lamar

+      

@@ -1929,55 +1869,55 @@ 
Hierarchical Covar
                   

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                   1-0.019325899-0.1271253450.005264348 0.6737565-0.027324609-0.193765920.005557074-0.6573580
                 

                 

                   2
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                   1-0.001696310-0.0388622860.033107971 0.5783955-0.003546904-0.051855790.037121004-0.5594220
                 

                 

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                   1-0.005639773-0.0351211100.014181149 0.7212400-0.008581398-0.052673620.016401029-0.7241575
                 

                 

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                   1 0.024363041-0.0064938170.148384316-0.5858625 0.030378577-0.006569190.203952527 0.5657380
                 

                 

                   5
                   9 
                   1-0.006413201-0.0652041880.032053323 0.4316120-0.010908422-0.097209200.034804994-0.4180350
                 

                 

                   6
                   11
                   1-0.018866769-0.0814749220.017572876-0.3350580-0.020290320-0.091460700.023107847 0.3245960
                 

         
       

@@ -1985,18 +1925,14 @@ 
Hierarchical Covar
 
 

 

-

-
  # now group marginal effects by group_id (party ID)
-
-  marg_effs_grouped <- id_me(sen_est_cov,covariate="age",
-                     group_effects="group_id")

+

+
  # now group marginal effects by group_id (party ID)
+
+  marg_effs_grouped <- id_me(sen_est_cov,covariate="age",
+                     group_effects="group_id")

 

 
Creating predictions

 

-

-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-Warning in max(Y_cont): no non-missing arguments to max; returning -Inf

-

 

 
[1] "Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples."
 [1] "Adding in hierarchical covariates values to the time-varying person scores."
@@ -2004,10 +1940,6 @@ 
Hierarchical Covar
 [1] "Done!"
 [1] "Now on model 1"

 

-

-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-Warning in max(Y_cont): no non-missing arguments to max; returning -Inf

-

 

 
[1] "Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples."
 [1] "Adding in hierarchical covariates values to the time-varying person scores."
@@ -2024,20 +1956,20 @@ 
Hierarchical Covar
 

 
Joining with `by = join_by(item_id)`

 

-
  marg_effs_grouped$sum_ideal_effects %>% 
-    arrange(item_id, group_id) %>% 
-    slice(1:10) %>% 
-    tt

+
  marg_effs_grouped$sum_ideal_effects %>% 
+    arrange(item_id, group_id) %>% 
+    slice(1:10) %>% 
+    tt

 

 
 
     
 
     
     

-      
+      

@@ -2107,100 +2039,100 @@ 
Hierarchical Covar
                   

-                  
-                  
-                  
-                  
+                  
+                  
+                  
+                  
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+                  
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+                  
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-                  
+                  
+                  
+                  
+                  

         
         
               
1
                   4
                   1-0.043283252-7.617911e-02-0.021564054 0.6737565-0.059669410-0.1061344485-0.030980545-0.6573580
                 

                 

                   R
                   1
                   4
                   1 0.001728437 9.152197e-05 0.005387632 0.6737565 0.001842369 0.0001115782 0.004954489-0.6573580
                 

                 

                   I
                   1
                   4
                   1-0.164655068-5.395945e-01 0.217850402 0.6737565-0.175759403-0.5527863128 0.097773912-0.6573580
                 

                 

                   D
                   2
                   5
                   1-0.015525753-3.250633e-02-0.003625894 0.5783955-0.021396470-0.0445927354-0.004632567-0.5594220
                 

                 

                   R
                   2
                   5
                   1 0.011176008 2.326406e-03 0.025459885 0.5783955 0.011258984 0.0015062504 0.023842689-0.5594220
                 

                 

                   I
                   2
                   5
                   1-0.034827213-1.720185e-01 0.044333672 0.5783955-0.040033881-0.1370294461 0.012257794-0.5594220
                 

                 

                   D
                   3
                   7
                   1-0.019038183-3.703802e-02-0.005856791 0.7212400-0.028223857-0.0536652758-0.007861273-0.7241575
                 

                 

                   R
                   3
                   7
                   1 0.006786453 8.963596e-04 0.019558981 0.7212400 0.005514060 0.0004894154 0.014164724-0.7241575
                 

                 

                   I
                   3
                   7
                   1-0.041874126-1.781197e-01 0.042756959 0.7212400-0.043940857-0.1725620105 0.016527400-0.7241575
                 

                 

                   D
                   4
                   8
                   1 0.054077835 2.330002e-02 0.091203099-0.5858625 0.070496166 0.0377855263 0.104861559 0.5657380
                 

         
       

@@ -2209,20 +2141,16 @@ 
Hierarchical Covar
 

 

 
In addition to the data frames of the results, the id_plot_cov can take the same arguments, calculate the ideal point marginal effects and then plot them. If we pass a grouping variable, the id_plot_cov function will plot marginal effects in distinct facets for each level of the grouping variable. If there are multiple model ID types, the function will produce distinct facets for each model ID type (note that only one kind of facetting can be used for a given plot).

-

-
   # plot the result
-   
-   sen_est_cov %>% 
-     id_plot_cov(calc_param="age",group_effects="group_id",
-                 label_high="Conservative",
-                 label_low="Liberal")

+

+
   # plot the result
+   
+   sen_est_cov %>% 
+     id_plot_cov(calc_param="age",group_effects="group_id",
+                 label_high="Conservative",
+                 label_low="Liberal")

 

 
Creating predictions

 

-

-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-Warning in max(Y_cont): no non-missing arguments to max; returning -Inf

-

 

 
[1] "Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples."
 [1] "Adding in hierarchical covariates values to the time-varying person scores."
@@ -2230,10 +2158,6 @@ 
Hierarchical Covar
 [1] "Done!"
 [1] "Now on model 1"

 

-

-
Warning in max(Y_cont): no non-missing arguments to max; returning -Inf
-Warning in max(Y_cont): no non-missing arguments to max; returning -Inf

-

 

 
[1] "Processing posterior replications for 23352 scores using 100 posterior samples out of a total of 2000 samples."
 [1] "Adding in hierarchical covariates values to the time-varying person scores."
@@ -2251,28 +2175,28 @@ 
Hierarchical Covar
 
Joining with `by = join_by(item_id)`

 

 

-

+

 

-

+

 

 

 

 

 
Because these covariates are on the ideal point scale, the meaning of the scale in terms of party ideology must be kept in mind in order to interpret the plot. The way to interpret these plots is that older Democrats tend to be more likely to vote for conservative bills, while younger Democrats vote more for liberal bills. The relationship does not hold true for Republicans, who are roughly equally as likely to vote for liberal or conservative bills regardless of age. Keeping the direction of the scale in mind–which is shown on the plot as the colour of the item discrimination for each vote–is crucial for understanding hierarchical covariates in ideal point models.

 
We can also extract the covariate summary values using the summary function:

-

-
cov_sum <- summary(sen_est_cov,pars='person_cov')
-tt(cov_sum)

+

+
cov_sum <- summary(sen_est_cov,pars='person_cov')
+tt(cov_sum)

 

 
 
     
 
     
     

-      
+      

@@ -2333,37 +2257,37 @@ 
Hierarchical Covar
         

-                  
-                  
-                  
+                  
+                  
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+                  
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+                  
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@@ -734,12 +734,12 @@ 
Spline Model

             seed=84520)
 

 
[1] "Running pathfinder to find starting values"
-Finished in  5.9 seconds.
+Finished in  5.8 seconds.
 [1] "Estimating model with Pathfinder for inference (approximation of true posterior)."

 

 

-
Pareto k value (29) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. 
-Finished in  6.5 seconds.

+
Pareto k value (31) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. 
+Finished in  7.3 seconds.

 

 
id_plot_legis_dyn(del_est_spline,use_ci = F) +
   scale_color_manual(values=c(R='red',
@@ -786,54 +786,54 @@ 
Spline Model

 

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@@ -859,8 +859,8 @@ 
Grou
 [1] "Estimating model with Pathfinder for inference (approximation of true posterior)."
 
 

-
Pareto k value (15) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. 
-Finished in  82.5 seconds.

+
Pareto k value (17) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. 
+Finished in  101.4 seconds.

 

 
id_plot_legis_dyn(del_est_rw3,
                   include=c('D','R')) + scale_colour_manual(values=c(R='red',
@@ -911,12 +911,12 @@ 
Grou
             seed=84520)

 

 
[1] "Running pathfinder to find starting values"
-Finished in  192.9 seconds.
+Finished in  94.2 seconds.
 [1] "Estimating model with Pathfinder for inference (approximation of true posterior)."

 

 

-
Pareto k value (15) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. 
-Finished in  1070.2 seconds.

+
Pareto k value (18) is greater than 0.7. Importance resampling was not able to improve the approximation, which may indicate that the approximation itself is poor. 
+Finished in  70.5 seconds.

 

 
 
We can then examine the distributions for both models as plots:

diff --git a/docs/vignettes/Time_Series_files/figure-html/ar1_1-1.png b/docs/vignettes/Time_Series_files/figure-html/ar1_1-1.png
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diff --git a/docs/vignettes/Time_Series_files/libs/bootstrap/bootstrap-icons.css b/docs/vignettes/Time_Series_files/libs/bootstrap/bootstrap-icons.css
new file mode 100644
index 0000000..285e444
--- /dev/null
+++ b/docs/vignettes/Time_Series_files/libs/bootstrap/bootstrap-icons.css
@@ -0,0 +1,2078 @@
+/*!
+ * Bootstrap Icons v1.11.1 (https://icons.getbootstrap.com/)
+ * Copyright 2019-2023 The Bootstrap Authors
+ * Licensed under MIT (https://github.com/twbs/icons/blob/main/LICENSE)
+ */
+
+@font-face {
+  font-display: block;
+  font-family: "bootstrap-icons";
+  src: 
+url("./bootstrap-icons.woff?2820a3852bdb9a5832199cc61cec4e65") format("woff");
+}
+
+.bi::before,
+[class^="bi-"]::before,
+[class*=" bi-"]::before {
+  display: inline-block;
+  font-family: bootstrap-icons !important;
+  font-style: normal;
+  font-weight: normal !important;
+  font-variant: normal;
+  text-transform: none;
+  line-height: 1;
+  vertical-align: -.125em;
+  -webkit-font-smoothing: antialiased;
+  -moz-osx-font-smoothing: grayscale;
+}
+
+.bi-123::before { content: "\f67f"; }
+.bi-alarm-fill::before { content: "\f101"; }
+.bi-alarm::before { content: "\f102"; }
+.bi-align-bottom::before { content: "\f103"; }
+.bi-align-center::before { content: "\f104"; }
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diff --git a/docs/vignettes/Time_Series_files/libs/bootstrap/bootstrap.min.css b/docs/vignettes/Time_Series_files/libs/bootstrap/bootstrap.min.css
new file mode 100644
index 0000000..eb5daa3
--- /dev/null
+++ b/docs/vignettes/Time_Series_files/libs/bootstrap/bootstrap.min.css
@@ -0,0 +1,12 @@
+/*!
+ * Bootstrap  v5.3.1 (https://getbootstrap.com/)
+ * Copyright 2011-2023 The Bootstrap Authors
+ * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)
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992px){.navbar-expand-lg{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand-lg .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-lg .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-lg .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-lg .navbar-nav-scroll{overflow:visible}.navbar-expand-lg .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-lg .navbar-toggler{display:none}.navbar-expand-lg .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-lg .offcanvas .offcanvas-header{display:none}.navbar-expand-lg .offcanvas 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.offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-xxl .offcanvas .offcanvas-header{display:none}.navbar-expand-xxl .offcanvas .offcanvas-body{display:flex;display:-webkit-flex;flex-grow:0;-webkit-flex-grow:0;padding:0;overflow-y:visible}}.navbar-expand{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand .navbar-nav-scroll{overflow:visible}.navbar-expand .navbar-collapse{display:flex !important;display:-webkit-flex 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var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media(prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(33, 37, 41, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(33, 37, 41, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #0d6efd;--bs-pagination-bg: #ffffff;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.375rem;--bs-pagination-hover-color: #0a58ca;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #0a58ca;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-pagination-active-color: #ffffff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: rgba(33, 37, 41, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.25rem}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #ffffff;--bs-badge-border-radius: 0.375rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 1px solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.375rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.375rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #ffffff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #212529;--bs-list-group-bg: #ffffff;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.375rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(33, 37, 41, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #212529;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(33, 37, 41, 0.75);--bs-list-group-disabled-bg: #ffffff;--bs-list-group-active-color: #ffffff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") 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";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: 0.5;--bs-btn-close-hover-opacity: 0.75;--bs-btn-close-focus-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: 0.25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:rgba(0,0,0,0) var(--bs-btn-close-bg) center/1em auto 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1px}.bslib-value-box{border-width:var(--bslib-value-box-border-width-auto-no, var(--bslib-value-box-border-width-baseline));container-name:bslib-value-box;container-type:inline-size}.bslib-value-box.card{box-shadow:var(--bslib-value-box-shadow)}.bslib-value-box.border-auto{border-width:var(--bslib-value-box-border-width-auto-yes, var(--bslib-value-box-border-width-baseline))}.bslib-value-box.default{--bslib-value-box-bg-default: var(--bs-card-bg, #ffffff);--bslib-value-box-border-color-default: var(--bs-card-border-color, rgba(0, 0, 0, 0.175));color:var(--bslib-value-box-color);background-color:var(--bslib-value-box-bg, var(--bslib-value-box-bg-default));border-color:var(--bslib-value-box-border-color, var(--bslib-value-box-border-color-default))}.bslib-value-box .value-box-grid{display:grid;grid-template-areas:"left right";align-items:center;overflow:hidden}.bslib-value-box .value-box-showcase{height:100%;max-height:var(---bslib-value-box-showcase-max-h, 100%)}.bslib-value-box 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.value-box-title:empty::after{content:" "}.bslib-value-box .value-box-value{font-size:calc(1.29rem + 0.48vw);margin-top:0;margin-bottom:.5rem;font-weight:500;line-height:1.2}@media(min-width: 1200px){.bslib-value-box .value-box-value{font-size:1.65rem}}.bslib-value-box .value-box-value:empty::after{content:" "}.bslib-value-box .value-box-showcase{align-items:center;justify-content:center;margin-top:auto;margin-bottom:auto;padding:1rem}.bslib-value-box .value-box-showcase .bi,.bslib-value-box .value-box-showcase .fa,.bslib-value-box .value-box-showcase .fab,.bslib-value-box .value-box-showcase .fas,.bslib-value-box .value-box-showcase .far{opacity:.85;min-width:50px;max-width:125%}.bslib-value-box .value-box-showcase .bi,.bslib-value-box .value-box-showcase .fa,.bslib-value-box .value-box-showcase .fab,.bslib-value-box .value-box-showcase .fas,.bslib-value-box .value-box-showcase .far{font-size:4rem}.bslib-value-box.showcase-top-right .value-box-grid{grid-template-columns:1fr var(---bslib-value-box-showcase-w, 50%)}.bslib-value-box.showcase-top-right .value-box-grid .value-box-showcase{grid-area:right;margin-left:auto;align-self:start;align-items:end;padding-left:0;padding-bottom:0}.bslib-value-box.showcase-top-right .value-box-grid .value-box-area{grid-area:left;align-self:end}.bslib-value-box.showcase-top-right[data-full-screen=true] .value-box-grid{grid-template-columns:auto var(---bslib-value-box-showcase-w-fs, 1fr)}.bslib-value-box.showcase-top-right[data-full-screen=true] .value-box-grid>div{align-self:center}.bslib-value-box.showcase-top-right:not([data-full-screen=true]) .value-box-showcase{margin-top:0}@container bslib-value-box (max-width: 300px){.bslib-value-box.showcase-top-right:not([data-full-screen=true]) .value-box-grid .value-box-showcase{padding-left:1rem}}.bslib-value-box.showcase-left-center .value-box-grid{grid-template-columns:var(---bslib-value-box-showcase-w, 30%) auto}.bslib-value-box.showcase-left-center[data-full-screen=true] .value-box-grid{grid-template-columns:var(---bslib-value-box-showcase-w-fs, 1fr) auto}.bslib-value-box.showcase-left-center:not([data-fill-screen=true]) .value-box-grid .value-box-showcase{grid-area:left}.bslib-value-box.showcase-left-center:not([data-fill-screen=true]) .value-box-grid .value-box-area{grid-area:right}.bslib-value-box.showcase-bottom .value-box-grid{grid-template-columns:1fr;grid-template-rows:1fr var(---bslib-value-box-showcase-h, auto);grid-template-areas:"top" "bottom";overflow:hidden}.bslib-value-box.showcase-bottom .value-box-grid .value-box-showcase{grid-area:bottom;padding:0;margin:0}.bslib-value-box.showcase-bottom .value-box-grid .value-box-area{grid-area:top}.bslib-value-box.showcase-bottom[data-full-screen=true] .value-box-grid{grid-template-rows:1fr var(---bslib-value-box-showcase-h-fs, 2fr)}.bslib-value-box.showcase-bottom[data-full-screen=true] .value-box-grid .value-box-showcase{padding:1rem}[data-bs-theme=dark] .bslib-value-box{--bslib-value-box-shadow: 0 0.5rem 1rem rgb(0 0 0 / 50%)}@media(min-width: 576px){.nav:not(.nav-hidden){display:flex !important;display:-webkit-flex !important}.nav:not(.nav-hidden):not(.nav-stacked):not(.flex-column){float:none !important}.nav:not(.nav-hidden):not(.nav-stacked):not(.flex-column)>.bslib-nav-spacer{margin-left:auto !important}.nav:not(.nav-hidden):not(.nav-stacked):not(.flex-column)>.form-inline{margin-top:auto;margin-bottom:auto}.nav:not(.nav-hidden).nav-stacked{flex-direction:column;-webkit-flex-direction:column;height:100%}.nav:not(.nav-hidden).nav-stacked>.bslib-nav-spacer{margin-top:auto !important}}.bslib-card{overflow:auto}.bslib-card .card-body+.card-body{padding-top:0}.bslib-card .card-body{overflow:auto}.bslib-card .card-body p{margin-top:0}.bslib-card .card-body p:last-child{margin-bottom:0}.bslib-card .card-body{max-height:var(--bslib-card-body-max-height, none)}.bslib-card[data-full-screen=true]>.card-body{max-height:var(--bslib-card-body-max-height-full-screen, none)}.bslib-card .card-header .form-group{margin-bottom:0}.bslib-card .card-header .selectize-control{margin-bottom:0}.bslib-card .card-header .selectize-control .item{margin-right:1.15rem}.bslib-card .card-footer{margin-top:auto}.bslib-card .bslib-navs-card-title{display:flex;flex-wrap:wrap;justify-content:space-between;align-items:center}.bslib-card .bslib-navs-card-title .nav{margin-left:auto}.bslib-card .bslib-sidebar-layout:not([data-bslib-sidebar-border=true]){border:none}.bslib-card .bslib-sidebar-layout:not([data-bslib-sidebar-border-radius=true]){border-top-left-radius:0;border-top-right-radius:0}[data-full-screen=true]{position:fixed;inset:3.5rem 1rem 1rem;height:auto !important;max-height:none !important;width:auto !important;z-index:1070}.bslib-full-screen-enter{display:none;position:absolute;bottom:var(--bslib-full-screen-enter-bottom, 0.2rem);right:var(--bslib-full-screen-enter-right, 0);top:var(--bslib-full-screen-enter-top);left:var(--bslib-full-screen-enter-left);color:var(--bslib-color-fg, var(--bs-card-color));background-color:var(--bslib-color-bg, var(--bs-card-bg, var(--bs-body-bg)));border:var(--bs-card-border-width) solid var(--bslib-color-fg, var(--bs-card-border-color));box-shadow:0 2px 4px rgba(0,0,0,.15);margin:.2rem .4rem;padding:.55rem !important;font-size:.8rem;cursor:pointer;opacity:.7;z-index:1070}.bslib-full-screen-enter:hover{opacity:1}.card[data-full-screen=false]:hover>*>.bslib-full-screen-enter{display:block}.bslib-has-full-screen .card:hover>*>.bslib-full-screen-enter{display:none}@media(max-width: 575.98px){.bslib-full-screen-enter{display:none !important}}.bslib-full-screen-exit{position:relative;top:1.35rem;font-size:.9rem;cursor:pointer;text-decoration:none;display:flex;float:right;margin-right:2.15rem;align-items:center;color:rgba(var(--bs-body-bg-rgb), 0.8)}.bslib-full-screen-exit:hover{color:rgba(var(--bs-body-bg-rgb), 1)}.bslib-full-screen-exit svg{margin-left:.5rem;font-size:1.5rem}#bslib-full-screen-overlay{position:fixed;inset:0;background-color:rgba(var(--bs-body-color-rgb), 0.6);backdrop-filter:blur(2px);-webkit-backdrop-filter:blur(2px);z-index:1069;animation:bslib-full-screen-overlay-enter 400ms cubic-bezier(0.6, 0.02, 0.65, 1) forwards}@keyframes bslib-full-screen-overlay-enter{0%{opacity:0}100%{opacity:1}}.bslib-grid{display:grid !important;gap:var(--bslib-spacer, 1rem);height:var(--bslib-grid-height)}.bslib-grid.grid{grid-template-columns:repeat(var(--bs-columns, 12), minmax(0, 1fr));grid-template-rows:unset;grid-auto-rows:var(--bslib-grid--row-heights);--bslib-grid--row-heights--xs: unset;--bslib-grid--row-heights--sm: unset;--bslib-grid--row-heights--md: unset;--bslib-grid--row-heights--lg: unset;--bslib-grid--row-heights--xl: unset;--bslib-grid--row-heights--xxl: unset}.bslib-grid.grid.bslib-grid--row-heights--xs{--bslib-grid--row-heights: 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+*
+* ansi colors from IPython notebook's
+*
+* we also add `bright-[color]-` synonyms for the `-[color]-intense` classes since
+* that seems to be what ansi_up emits
+*
+*/.ansi-black-fg{color:#3e424d}.ansi-black-bg{background-color:#3e424d}.ansi-black-intense-black,.ansi-bright-black-fg{color:#282c36}.ansi-black-intense-black,.ansi-bright-black-bg{background-color:#282c36}.ansi-red-fg{color:#e75c58}.ansi-red-bg{background-color:#e75c58}.ansi-red-intense-red,.ansi-bright-red-fg{color:#b22b31}.ansi-red-intense-red,.ansi-bright-red-bg{background-color:#b22b31}.ansi-green-fg{color:#00a250}.ansi-green-bg{background-color:#00a250}.ansi-green-intense-green,.ansi-bright-green-fg{color:#007427}.ansi-green-intense-green,.ansi-bright-green-bg{background-color:#007427}.ansi-yellow-fg{color:#ddb62b}.ansi-yellow-bg{background-color:#ddb62b}.ansi-yellow-intense-yellow,.ansi-bright-yellow-fg{color:#b27d12}.ansi-yellow-intense-yellow,.ansi-bright-yellow-bg{background-color:#b27d12}.ansi-blue-fg{color:#208ffb}.ansi-blue-bg{background-color:#208ffb}.ansi-blue-intense-blue,.ansi-bright-blue-fg{color:#0065ca}.ansi-blue-intense-blue,.ansi-bright-blue-bg{background-color:#0065ca}.ansi-magenta-fg{color:#d160c4}.ansi-magenta-bg{background-color:#d160c4}.ansi-magenta-intense-magenta,.ansi-bright-magenta-fg{color:#a03196}.ansi-magenta-intense-magenta,.ansi-bright-magenta-bg{background-color:#a03196}.ansi-cyan-fg{color:#60c6c8}.ansi-cyan-bg{background-color:#60c6c8}.ansi-cyan-intense-cyan,.ansi-bright-cyan-fg{color:#258f8f}.ansi-cyan-intense-cyan,.ansi-bright-cyan-bg{background-color:#258f8f}.ansi-white-fg{color:#c5c1b4}.ansi-white-bg{background-color:#c5c1b4}.ansi-white-intense-white,.ansi-bright-white-fg{color:#a1a6b2}.ansi-white-intense-white,.ansi-bright-white-bg{background-color:#a1a6b2}.ansi-default-inverse-fg{color:#fff}.ansi-default-inverse-bg{background-color:#000}.ansi-bold{font-weight:bold}.ansi-underline{text-decoration:underline}:root{--quarto-body-bg: 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H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=On.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}N.on(document,yn,'[data-bs-toggle="modal"]',(function(t){const e=z.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),N.one(e,pn,(t=>{t.defaultPrevented||N.one(e,fn,(()=>{a(this)&&this.focus()}))}));const i=z.findOne(".modal.show");i&&On.getInstance(i).hide(),On.getOrCreateInstance(e).toggle(this)})),R(On),m(On);const xn=".bs.offcanvas",kn=".data-api",Ln=`load${xn}${kn}`,Sn="show",Dn="showing",$n="hiding",In=".offcanvas.show",Nn=`show${xn}`,Pn=`shown${xn}`,Mn=`hide${xn}`,jn=`hidePrevented${xn}`,Fn=`hidden${xn}`,Hn=`resize${xn}`,Wn=`click${xn}${kn}`,Bn=`keydown.dismiss${xn}`,zn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class qn extends W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"
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")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Gn)}_setContent(t,e,i){const n=z.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?o(e)?this._putElementInTemplate(r(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return g(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const Zn=new Set(["sanitize","allowList","sanitizeFn"]),ts="fade",es="show",is=".modal",ns="hide.bs.modal",ss="hover",os="focus",rs={AUTO:"auto",TOP:"top",RIGHT:p()?"left":"right",BOTTOM:"bottom",LEFT:p()?"right":"left"},as={allowList:Vn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'',title:"",trigger:"hover focus"},ls={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class cs extends W{constructor(t,e){if(void 0===vi)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,e),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return as}static get DefaultType(){return ls}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),N.off(this._element.closest(is),ns,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=N.trigger(this._element,this.constructor.eventName("show")),e=(c(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,"mouseover",h);this._activeTrigger.click=!1,this._activeTrigger[os]=!1,this._activeTrigger[ss]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),N.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ts,es),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(ts),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new Jn({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{".tooltip-inner":this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(ts)}_isShown(){return this.tip&&this.tip.classList.contains(es)}_createPopper(t){const e=g(this._config.placement,[this,t,this._element]),i=rs[e.toUpperCase()];return 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R(ro),m(ro),{Alert:Q,Button:Y,Carousel:xt,Collapse:Bt,Dropdown:qi,Modal:On,Offcanvas:qn,Popover:us,ScrollSpy:Es,Tab:Vs,Toast:ro,Tooltip:cs}}));
+//# sourceMappingURL=bootstrap.bundle.min.js.map
\ No newline at end of file
diff --git a/docs/vignettes/Time_Series_files/libs/clipboard/clipboard.min.js b/docs/vignettes/Time_Series_files/libs/clipboard/clipboard.min.js
new file mode 100644
index 0000000..1103f81
--- /dev/null
+++ b/docs/vignettes/Time_Series_files/libs/clipboard/clipboard.min.js
@@ -0,0 +1,7 @@
+/*!
+ * clipboard.js v2.0.11
+ * https://clipboardjs.com/
+ *
+ * Licensed MIT © Zeno Rocha
+ */
+!function(t,e){"object"==typeof exports&&"object"==typeof module?module.exports=e():"function"==typeof define&&define.amd?define([],e):"object"==typeof exports?exports.ClipboardJS=e():t.ClipboardJS=e()}(this,function(){return n={686:function(t,e,n){"use strict";n.d(e,{default:function(){return b}});var e=n(279),i=n.n(e),e=n(370),u=n.n(e),e=n(817),r=n.n(e);function c(t){try{return document.execCommand(t)}catch(t){return}}var a=function(t){t=r()(t);return c("cut"),t};function o(t,e){var n,o,t=(n=t,o="rtl"===document.documentElement.getAttribute("dir"),(t=document.createElement("textarea")).style.fontSize="12pt",t.style.border="0",t.style.padding="0",t.style.margin="0",t.style.position="absolute",t.style[o?"right":"left"]="-9999px",o=window.pageYOffset||document.documentElement.scrollTop,t.style.top="".concat(o,"px"),t.setAttribute("readonly",""),t.value=n,t);return e.container.appendChild(t),e=r()(t),c("copy"),t.remove(),e}var f=function(t){var e=1.anchorjs-link,.anchorjs-link:focus{opacity:1}",A.sheet.cssRules.length),A.sheet.insertRule("[data-anchorjs-icon]::after{content:attr(data-anchorjs-icon)}",A.sheet.cssRules.length),A.sheet.insertRule('@font-face{font-family:anchorjs-icons;src:url(data:n/a;base64,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) format("truetype")}',A.sheet.cssRules.length)),h=document.querySelectorAll("[id]"),t=[].map.call(h,function(A){return A.id}),i=0;i\]./()*\\\n\t\b\v\u00A0]/g,"-").replace(/-{2,}/g,"-").substring(0,this.options.truncate).replace(/^-+|-+$/gm,"").toLowerCase()},this.hasAnchorJSLink=function(A){var e=A.firstChild&&-1<(" "+A.firstChild.className+" ").indexOf(" anchorjs-link "),A=A.lastChild&&-1<(" "+A.lastChild.className+" ").indexOf(" anchorjs-link ");return e||A||!1}}});
+// @license-end
\ No newline at end of file
diff --git a/docs/vignettes/Time_Series_files/libs/quarto-html/popper.min.js b/docs/vignettes/Time_Series_files/libs/quarto-html/popper.min.js
new file mode 100644
index 0000000..e3726d7
--- /dev/null
+++ b/docs/vignettes/Time_Series_files/libs/quarto-html/popper.min.js
@@ -0,0 +1,6 @@
+/**
+ * @popperjs/core v2.11.7 - MIT License
+ */
+
+!function(e,t){"object"==typeof exports&&"undefined"!=typeof module?t(exports):"function"==typeof define&&define.amd?define(["exports"],t):t((e="undefined"!=typeof globalThis?globalThis:e||self).Popper={})}(this,(function(e){"use strict";function t(e){if(null==e)return window;if("[object Window]"!==e.toString()){var t=e.ownerDocument;return t&&t.defaultView||window}return e}function n(e){return e instanceof t(e).Element||e instanceof Element}function r(e){return e instanceof t(e).HTMLElement||e instanceof HTMLElement}function o(e){return"undefined"!=typeof ShadowRoot&&(e instanceof t(e).ShadowRoot||e instanceof ShadowRoot)}var i=Math.max,a=Math.min,s=Math.round;function f(){var e=navigator.userAgentData;return null!=e&&e.brands&&Array.isArray(e.brands)?e.brands.map((function(e){return e.brand+"/"+e.version})).join(" "):navigator.userAgent}function c(){return!/^((?!chrome|android).)*safari/i.test(f())}function p(e,o,i){void 0===o&&(o=!1),void 0===i&&(i=!1);var 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+
diff --git a/docs/vignettes/Time_Series_files/libs/quarto-html/quarto-syntax-highlighting.css b/docs/vignettes/Time_Series_files/libs/quarto-html/quarto-syntax-highlighting.css
new file mode 100644
index 0000000..b30ce57
--- /dev/null
+++ b/docs/vignettes/Time_Series_files/libs/quarto-html/quarto-syntax-highlighting.css
@@ -0,0 +1,205 @@
+/* quarto syntax highlight colors */
+:root {
+  --quarto-hl-ot-color: #003B4F;
+  --quarto-hl-at-color: #657422;
+  --quarto-hl-ss-color: #20794D;
+  --quarto-hl-an-color: #5E5E5E;
+  --quarto-hl-fu-color: #4758AB;
+  --quarto-hl-st-color: #20794D;
+  --quarto-hl-cf-color: #003B4F;
+  --quarto-hl-op-color: #5E5E5E;
+  --quarto-hl-er-color: #AD0000;
+  --quarto-hl-bn-color: #AD0000;
+  --quarto-hl-al-color: #AD0000;
+  --quarto-hl-va-color: #111111;
+  --quarto-hl-bu-color: inherit;
+  --quarto-hl-ex-color: inherit;
+  --quarto-hl-pp-color: #AD0000;
+  --quarto-hl-in-color: #5E5E5E;
+  --quarto-hl-vs-color: #20794D;
+  --quarto-hl-wa-color: #5E5E5E;
+  --quarto-hl-do-color: #5E5E5E;
+  --quarto-hl-im-color: #00769E;
+  --quarto-hl-ch-color: #20794D;
+  --quarto-hl-dt-color: #AD0000;
+  --quarto-hl-fl-color: #AD0000;
+  --quarto-hl-co-color: #5E5E5E;
+  --quarto-hl-cv-color: #5E5E5E;
+  --quarto-hl-cn-color: #8f5902;
+  --quarto-hl-sc-color: #5E5E5E;
+  --quarto-hl-dv-color: #AD0000;
+  --quarto-hl-kw-color: #003B4F;
+}
+
+/* other quarto variables */
+:root {
+  --quarto-font-monospace: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace;
+}
+
+pre > code.sourceCode > span {
+  color: #003B4F;
+}
+
+code span {
+  color: #003B4F;
+}
+
+code.sourceCode > span {
+  color: #003B4F;
+}
+
+div.sourceCode,
+div.sourceCode pre.sourceCode {
+  color: #003B4F;
+}
+
+code span.ot {
+  color: #003B4F;
+  font-style: inherit;
+}
+
+code span.at {
+  color: #657422;
+  font-style: inherit;
+}
+
+code span.ss {
+  color: #20794D;
+  font-style: inherit;
+}
+
+code span.an {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.fu {
+  color: #4758AB;
+  font-style: inherit;
+}
+
+code span.st {
+  color: #20794D;
+  font-style: inherit;
+}
+
+code span.cf {
+  color: #003B4F;
+  font-weight: bold;
+  font-style: inherit;
+}
+
+code span.op {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.er {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.bn {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.al {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.va {
+  color: #111111;
+  font-style: inherit;
+}
+
+code span.bu {
+  font-style: inherit;
+}
+
+code span.ex {
+  font-style: inherit;
+}
+
+code span.pp {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.in {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.vs {
+  color: #20794D;
+  font-style: inherit;
+}
+
+code span.wa {
+  color: #5E5E5E;
+  font-style: italic;
+}
+
+code span.do {
+  color: #5E5E5E;
+  font-style: italic;
+}
+
+code span.im {
+  color: #00769E;
+  font-style: inherit;
+}
+
+code span.ch {
+  color: #20794D;
+  font-style: inherit;
+}
+
+code span.dt {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.fl {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.co {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.cv {
+  color: #5E5E5E;
+  font-style: italic;
+}
+
+code span.cn {
+  color: #8f5902;
+  font-style: inherit;
+}
+
+code span.sc {
+  color: #5E5E5E;
+  font-style: inherit;
+}
+
+code span.dv {
+  color: #AD0000;
+  font-style: inherit;
+}
+
+code span.kw {
+  color: #003B4F;
+  font-weight: bold;
+  font-style: inherit;
+}
+
+.prevent-inlining {
+  content: " {
+  // Find any conflicting margin elements and add margins to the
+  // top to prevent overlap
+  const marginChildren = window.document.querySelectorAll(
+    ".column-margin.column-container > *, .margin-caption, .aside"
+  );
+
+  let lastBottom = 0;
+  for (const marginChild of marginChildren) {
+    if (marginChild.offsetParent !== null) {
+      // clear the top margin so we recompute it
+      marginChild.style.marginTop = null;
+      const top = marginChild.getBoundingClientRect().top + window.scrollY;
+      if (top < lastBottom) {
+        const marginChildStyle = window.getComputedStyle(marginChild);
+        const marginBottom = parseFloat(marginChildStyle["marginBottom"]);
+        const margin = lastBottom - top + marginBottom;
+        marginChild.style.marginTop = `${margin}px`;
+      }
+      const styles = window.getComputedStyle(marginChild);
+      const marginTop = parseFloat(styles["marginTop"]);
+      lastBottom = top + marginChild.getBoundingClientRect().height + marginTop;
+    }
+  }
+};
+
+window.document.addEventListener("DOMContentLoaded", function (_event) {
+  // Recompute the position of margin elements anytime the body size changes
+  if (window.ResizeObserver) {
+    const resizeObserver = new window.ResizeObserver(
+      throttle(() => {
+        layoutMarginEls();
+        if (
+          window.document.body.getBoundingClientRect().width < 990 &&
+          isReaderMode()
+        ) {
+          quartoToggleReader();
+        }
+      }, 50)
+    );
+    resizeObserver.observe(window.document.body);
+  }
+
+  const tocEl = window.document.querySelector('nav.toc-active[role="doc-toc"]');
+  const sidebarEl = window.document.getElementById("quarto-sidebar");
+  const leftTocEl = window.document.getElementById("quarto-sidebar-toc-left");
+  const marginSidebarEl = window.document.getElementById(
+    "quarto-margin-sidebar"
+  );
+  // function to determine whether the element has a previous sibling that is active
+  const prevSiblingIsActiveLink = (el) => {
+    const sibling = el.previousElementSibling;
+    if (sibling && sibling.tagName === "A") {
+      return sibling.classList.contains("active");
+    } else {
+      return false;
+    }
+  };
+
+  // fire slideEnter for bootstrap tab activations (for htmlwidget resize behavior)
+  function fireSlideEnter(e) {
+    const event = window.document.createEvent("Event");
+    event.initEvent("slideenter", true, true);
+    window.document.dispatchEvent(event);
+  }
+  const tabs = window.document.querySelectorAll('a[data-bs-toggle="tab"]');
+  tabs.forEach((tab) => {
+    tab.addEventListener("shown.bs.tab", fireSlideEnter);
+  });
+
+  // fire slideEnter for tabby tab activations (for htmlwidget resize behavior)
+  document.addEventListener("tabby", fireSlideEnter, false);
+
+  // Track scrolling and mark TOC links as active
+  // get table of contents and sidebar (bail if we don't have at least one)
+  const tocLinks = tocEl
+    ? [...tocEl.querySelectorAll("a[data-scroll-target]")]
+    : [];
+  const makeActive = (link) => tocLinks[link].classList.add("active");
+  const removeActive = (link) => tocLinks[link].classList.remove("active");
+  const removeAllActive = () =>
+    [...Array(tocLinks.length).keys()].forEach((link) => removeActive(link));
+
+  // activate the anchor for a section associated with this TOC entry
+  tocLinks.forEach((link) => {
+    link.addEventListener("click", () => {
+      if (link.href.indexOf("#") !== -1) {
+        const anchor = link.href.split("#")[1];
+        const heading = window.document.querySelector(
+          `[data-anchor-id="${anchor}"]`
+        );
+        if (heading) {
+          // Add the class
+          heading.classList.add("reveal-anchorjs-link");
+
+          // function to show the anchor
+          const handleMouseout = () => {
+            heading.classList.remove("reveal-anchorjs-link");
+            heading.removeEventListener("mouseout", handleMouseout);
+          };
+
+          // add a function to clear the anchor when the user mouses out of it
+          heading.addEventListener("mouseout", handleMouseout);
+        }
+      }
+    });
+  });
+
+  const sections = tocLinks.map((link) => {
+    const target = link.getAttribute("data-scroll-target");
+    if (target.startsWith("#")) {
+      return window.document.getElementById(decodeURI(`${target.slice(1)}`));
+    } else {
+      return window.document.querySelector(decodeURI(`${target}`));
+    }
+  });
+
+  const sectionMargin = 200;
+  let currentActive = 0;
+  // track whether we've initialized state the first time
+  let init = false;
+
+  const updateActiveLink = () => {
+    // The index from bottom to top (e.g. reversed list)
+    let sectionIndex = -1;
+    if (
+      window.innerHeight + window.pageYOffset >=
+      window.document.body.offsetHeight
+    ) {
+      // This is the no-scroll case where last section should be the active one
+      sectionIndex = 0;
+    } else {
+      // This finds the last section visible on screen that should be made active
+      sectionIndex = [...sections].reverse().findIndex((section) => {
+        if (section) {
+          return window.pageYOffset >= section.offsetTop - sectionMargin;
+        } else {
+          return false;
+        }
+      });
+    }
+    if (sectionIndex > -1) {
+      const current = sections.length - sectionIndex - 1;
+      if (current !== currentActive) {
+        removeAllActive();
+        currentActive = current;
+        makeActive(current);
+        if (init) {
+          window.dispatchEvent(sectionChanged);
+        }
+        init = true;
+      }
+    }
+  };
+
+  const inHiddenRegion = (top, bottom, hiddenRegions) => {
+    for (const region of hiddenRegions) {
+      if (top <= region.bottom && bottom >= region.top) {
+        return true;
+      }
+    }
+    return false;
+  };
+
+  const categorySelector = "header.quarto-title-block .quarto-category";
+  const activateCategories = (href) => {
+    // Find any categories
+    // Surround them with a link pointing back to:
+    // #category=Authoring
+    try {
+      const categoryEls = window.document.querySelectorAll(categorySelector);
+      for (const categoryEl of categoryEls) {
+        const categoryText = categoryEl.textContent;
+        if (categoryText) {
+          const link = `${href}#category=${encodeURIComponent(categoryText)}`;
+          const linkEl = window.document.createElement("a");
+          linkEl.setAttribute("href", link);
+          for (const child of categoryEl.childNodes) {
+            linkEl.append(child);
+          }
+          categoryEl.appendChild(linkEl);
+        }
+      }
+    } catch {
+      // Ignore errors
+    }
+  };
+  function hasTitleCategories() {
+    return window.document.querySelector(categorySelector) !== null;
+  }
+
+  function offsetRelativeUrl(url) {
+    const offset = getMeta("quarto:offset");
+    return offset ? offset + url : url;
+  }
+
+  function offsetAbsoluteUrl(url) {
+    const offset = getMeta("quarto:offset");
+    const baseUrl = new URL(offset, window.location);
+
+    const projRelativeUrl = url.replace(baseUrl, "");
+    if (projRelativeUrl.startsWith("/")) {
+      return projRelativeUrl;
+    } else {
+      return "/" + projRelativeUrl;
+    }
+  }
+
+  // read a meta tag value
+  function getMeta(metaName) {
+    const metas = window.document.getElementsByTagName("meta");
+    for (let i = 0; i < metas.length; i++) {
+      if (metas[i].getAttribute("name") === metaName) {
+        return metas[i].getAttribute("content");
+      }
+    }
+    return "";
+  }
+
+  async function findAndActivateCategories() {
+    const currentPagePath = offsetAbsoluteUrl(window.location.href);
+    const response = await fetch(offsetRelativeUrl("listings.json"));
+    if (response.status == 200) {
+      return response.json().then(function (listingPaths) {
+        const listingHrefs = [];
+        for (const listingPath of listingPaths) {
+          const pathWithoutLeadingSlash = listingPath.listing.substring(1);
+          for (const item of listingPath.items) {
+            if (
+              item === currentPagePath ||
+              item === currentPagePath + "index.html"
+            ) {
+              // Resolve this path against the offset to be sure
+              // we already are using the correct path to the listing
+              // (this adjusts the listing urls to be rooted against
+              // whatever root the page is actually running against)
+              const relative = offsetRelativeUrl(pathWithoutLeadingSlash);
+              const baseUrl = window.location;
+              const resolvedPath = new URL(relative, baseUrl);
+              listingHrefs.push(resolvedPath.pathname);
+              break;
+            }
+          }
+        }
+
+        // Look up the tree for a nearby linting and use that if we find one
+        const nearestListing = findNearestParentListing(
+          offsetAbsoluteUrl(window.location.pathname),
+          listingHrefs
+        );
+        if (nearestListing) {
+          activateCategories(nearestListing);
+        } else {
+          // See if the referrer is a listing page for this item
+          const referredRelativePath = offsetAbsoluteUrl(document.referrer);
+          const referrerListing = listingHrefs.find((listingHref) => {
+            const isListingReferrer =
+              listingHref === referredRelativePath ||
+              listingHref === referredRelativePath + "index.html";
+            return isListingReferrer;
+          });
+
+          if (referrerListing) {
+            // Try to use the referrer if possible
+            activateCategories(referrerListing);
+          } else if (listingHrefs.length > 0) {
+            // Otherwise, just fall back to the first listing
+            activateCategories(listingHrefs[0]);
+          }
+        }
+      });
+    }
+  }
+  if (hasTitleCategories()) {
+    findAndActivateCategories();
+  }
+
+  const findNearestParentListing = (href, listingHrefs) => {
+    if (!href || !listingHrefs) {
+      return undefined;
+    }
+    // Look up the tree for a nearby linting and use that if we find one
+    const relativeParts = href.substring(1).split("/");
+    while (relativeParts.length > 0) {
+      const path = relativeParts.join("/");
+      for (const listingHref of listingHrefs) {
+        if (listingHref.startsWith(path)) {
+          return listingHref;
+        }
+      }
+      relativeParts.pop();
+    }
+
+    return undefined;
+  };
+
+  const manageSidebarVisiblity = (el, placeholderDescriptor) => {
+    let isVisible = true;
+    let elRect;
+
+    return (hiddenRegions) => {
+      if (el === null) {
+        return;
+      }
+
+      // Find the last element of the TOC
+      const lastChildEl = el.lastElementChild;
+
+      if (lastChildEl) {
+        // Converts the sidebar to a menu
+        const convertToMenu = () => {
+          for (const child of el.children) {
+            child.style.opacity = 0;
+            child.style.overflow = "hidden";
+            child.style.pointerEvents = "none";
+          }
+
+          nexttick(() => {
+            const toggleContainer = window.document.createElement("div");
+            toggleContainer.style.width = "100%";
+            toggleContainer.classList.add("zindex-over-content");
+            toggleContainer.classList.add("quarto-sidebar-toggle");
+            toggleContainer.classList.add("headroom-target"); // Marks this to be managed by headeroom
+            toggleContainer.id = placeholderDescriptor.id;
+            toggleContainer.style.position = "fixed";
+
+            const toggleIcon = window.document.createElement("i");
+            toggleIcon.classList.add("quarto-sidebar-toggle-icon");
+            toggleIcon.classList.add("bi");
+            toggleIcon.classList.add("bi-caret-down-fill");
+
+            const toggleTitle = window.document.createElement("div");
+            const titleEl = window.document.body.querySelector(
+              placeholderDescriptor.titleSelector
+            );
+            if (titleEl) {
+              toggleTitle.append(
+                titleEl.textContent || titleEl.innerText,
+                toggleIcon
+              );
+            }
+            toggleTitle.classList.add("zindex-over-content");
+            toggleTitle.classList.add("quarto-sidebar-toggle-title");
+            toggleContainer.append(toggleTitle);
+
+            const toggleContents = window.document.createElement("div");
+            toggleContents.classList = el.classList;
+            toggleContents.classList.add("zindex-over-content");
+            toggleContents.classList.add("quarto-sidebar-toggle-contents");
+            for (const child of el.children) {
+              if (child.id === "toc-title") {
+                continue;
+              }
+
+              const clone = child.cloneNode(true);
+              clone.style.opacity = 1;
+              clone.style.pointerEvents = null;
+              clone.style.display = null;
+              toggleContents.append(clone);
+            }
+            toggleContents.style.height = "0px";
+            const positionToggle = () => {
+              // position the element (top left of parent, same width as parent)
+              if (!elRect) {
+                elRect = el.getBoundingClientRect();
+              }
+              toggleContainer.style.left = `${elRect.left}px`;
+              toggleContainer.style.top = `${elRect.top}px`;
+              toggleContainer.style.width = `${elRect.width}px`;
+            };
+            positionToggle();
+
+            toggleContainer.append(toggleContents);
+            el.parentElement.prepend(toggleContainer);
+
+            // Process clicks
+            let tocShowing = false;
+            // Allow the caller to control whether this is dismissed
+            // when it is clicked (e.g. sidebar navigation supports
+            // opening and closing the nav tree, so don't dismiss on click)
+            const clickEl = placeholderDescriptor.dismissOnClick
+              ? toggleContainer
+              : toggleTitle;
+
+            const closeToggle = () => {
+              if (tocShowing) {
+                toggleContainer.classList.remove("expanded");
+                toggleContents.style.height = "0px";
+                tocShowing = false;
+              }
+            };
+
+            // Get rid of any expanded toggle if the user scrolls
+            window.document.addEventListener(
+              "scroll",
+              throttle(() => {
+                closeToggle();
+              }, 50)
+            );
+
+            // Handle positioning of the toggle
+            window.addEventListener(
+              "resize",
+              throttle(() => {
+                elRect = undefined;
+                positionToggle();
+              }, 50)
+            );
+
+            window.addEventListener("quarto-hrChanged", () => {
+              elRect = undefined;
+            });
+
+            // Process the click
+            clickEl.onclick = () => {
+              if (!tocShowing) {
+                toggleContainer.classList.add("expanded");
+                toggleContents.style.height = null;
+                tocShowing = true;
+              } else {
+                closeToggle();
+              }
+            };
+          });
+        };
+
+        // Converts a sidebar from a menu back to a sidebar
+        const convertToSidebar = () => {
+          for (const child of el.children) {
+            child.style.opacity = 1;
+            child.style.overflow = null;
+            child.style.pointerEvents = null;
+          }
+
+          const placeholderEl = window.document.getElementById(
+            placeholderDescriptor.id
+          );
+          if (placeholderEl) {
+            placeholderEl.remove();
+          }
+
+          el.classList.remove("rollup");
+        };
+
+        if (isReaderMode()) {
+          convertToMenu();
+          isVisible = false;
+        } else {
+          // Find the top and bottom o the element that is being managed
+          const elTop = el.offsetTop;
+          const elBottom =
+            elTop + lastChildEl.offsetTop + lastChildEl.offsetHeight;
+
+          if (!isVisible) {
+            // If the element is current not visible reveal if there are
+            // no conflicts with overlay regions
+            if (!inHiddenRegion(elTop, elBottom, hiddenRegions)) {
+              convertToSidebar();
+              isVisible = true;
+            }
+          } else {
+            // If the element is visible, hide it if it conflicts with overlay regions
+            // and insert a placeholder toggle (or if we're in reader mode)
+            if (inHiddenRegion(elTop, elBottom, hiddenRegions)) {
+              convertToMenu();
+              isVisible = false;
+            }
+          }
+        }
+      }
+    };
+  };
+
+  const tabEls = document.querySelectorAll('a[data-bs-toggle="tab"]');
+  for (const tabEl of tabEls) {
+    const id = tabEl.getAttribute("data-bs-target");
+    if (id) {
+      const columnEl = document.querySelector(
+        `${id} .column-margin, .tabset-margin-content`
+      );
+      if (columnEl)
+        tabEl.addEventListener("shown.bs.tab", function (event) {
+          const el = event.srcElement;
+          if (el) {
+            const visibleCls = `${el.id}-margin-content`;
+            // walk up until we find a parent tabset
+            let panelTabsetEl = el.parentElement;
+            while (panelTabsetEl) {
+              if (panelTabsetEl.classList.contains("panel-tabset")) {
+                break;
+              }
+              panelTabsetEl = panelTabsetEl.parentElement;
+            }
+
+            if (panelTabsetEl) {
+              const prevSib = panelTabsetEl.previousElementSibling;
+              if (
+                prevSib &&
+                prevSib.classList.contains("tabset-margin-container")
+              ) {
+                const childNodes = prevSib.querySelectorAll(
+                  ".tabset-margin-content"
+                );
+                for (const childEl of childNodes) {
+                  if (childEl.classList.contains(visibleCls)) {
+                    childEl.classList.remove("collapse");
+                  } else {
+                    childEl.classList.add("collapse");
+                  }
+                }
+              }
+            }
+          }
+
+          layoutMarginEls();
+        });
+    }
+  }
+
+  // Manage the visibility of the toc and the sidebar
+  const marginScrollVisibility = manageSidebarVisiblity(marginSidebarEl, {
+    id: "quarto-toc-toggle",
+    titleSelector: "#toc-title",
+    dismissOnClick: true,
+  });
+  const sidebarScrollVisiblity = manageSidebarVisiblity(sidebarEl, {
+    id: "quarto-sidebarnav-toggle",
+    titleSelector: ".title",
+    dismissOnClick: false,
+  });
+  let tocLeftScrollVisibility;
+  if (leftTocEl) {
+    tocLeftScrollVisibility = manageSidebarVisiblity(leftTocEl, {
+      id: "quarto-lefttoc-toggle",
+      titleSelector: "#toc-title",
+      dismissOnClick: true,
+    });
+  }
+
+  // Find the first element that uses formatting in special columns
+  const conflictingEls = window.document.body.querySelectorAll(
+    '[class^="column-"], [class*=" column-"], aside, [class*="margin-caption"], [class*=" margin-caption"], [class*="margin-ref"], [class*=" margin-ref"]'
+  );
+
+  // Filter all the possibly conflicting elements into ones
+  // the do conflict on the left or ride side
+  const arrConflictingEls = Array.from(conflictingEls);
+  const leftSideConflictEls = arrConflictingEls.filter((el) => {
+    if (el.tagName === "ASIDE") {
+      return false;
+    }
+    return Array.from(el.classList).find((className) => {
+      return (
+        className !== "column-body" &&
+        className.startsWith("column-") &&
+        !className.endsWith("right") &&
+        !className.endsWith("container") &&
+        className !== "column-margin"
+      );
+    });
+  });
+  const rightSideConflictEls = arrConflictingEls.filter((el) => {
+    if (el.tagName === "ASIDE") {
+      return true;
+    }
+
+    const hasMarginCaption = Array.from(el.classList).find((className) => {
+      return className == "margin-caption";
+    });
+    if (hasMarginCaption) {
+      return true;
+    }
+
+    return Array.from(el.classList).find((className) => {
+      return (
+        className !== "column-body" &&
+        !className.endsWith("container") &&
+        className.startsWith("column-") &&
+        !className.endsWith("left")
+      );
+    });
+  });
+
+  const kOverlapPaddingSize = 10;
+  function toRegions(els) {
+    return els.map((el) => {
+      const boundRect = el.getBoundingClientRect();
+      const top =
+        boundRect.top +
+        document.documentElement.scrollTop -
+        kOverlapPaddingSize;
+      return {
+        top,
+        bottom: top + el.scrollHeight + 2 * kOverlapPaddingSize,
+      };
+    });
+  }
+
+  let hasObserved = false;
+  const visibleItemObserver = (els) => {
+    let visibleElements = [...els];
+    const intersectionObserver = new IntersectionObserver(
+      (entries, _observer) => {
+        entries.forEach((entry) => {
+          if (entry.isIntersecting) {
+            if (visibleElements.indexOf(entry.target) === -1) {
+              visibleElements.push(entry.target);
+            }
+          } else {
+            visibleElements = visibleElements.filter((visibleEntry) => {
+              return visibleEntry !== entry;
+            });
+          }
+        });
+
+        if (!hasObserved) {
+          hideOverlappedSidebars();
+        }
+        hasObserved = true;
+      },
+      {}
+    );
+    els.forEach((el) => {
+      intersectionObserver.observe(el);
+    });
+
+    return {
+      getVisibleEntries: () => {
+        return visibleElements;
+      },
+    };
+  };
+
+  const rightElementObserver = visibleItemObserver(rightSideConflictEls);
+  const leftElementObserver = visibleItemObserver(leftSideConflictEls);
+
+  const hideOverlappedSidebars = () => {
+    marginScrollVisibility(toRegions(rightElementObserver.getVisibleEntries()));
+    sidebarScrollVisiblity(toRegions(leftElementObserver.getVisibleEntries()));
+    if (tocLeftScrollVisibility) {
+      tocLeftScrollVisibility(
+        toRegions(leftElementObserver.getVisibleEntries())
+      );
+    }
+  };
+
+  window.quartoToggleReader = () => {
+    // Applies a slow class (or removes it)
+    // to update the transition speed
+    const slowTransition = (slow) => {
+      const manageTransition = (id, slow) => {
+        const el = document.getElementById(id);
+        if (el) {
+          if (slow) {
+            el.classList.add("slow");
+          } else {
+            el.classList.remove("slow");
+          }
+        }
+      };
+
+      manageTransition("TOC", slow);
+      manageTransition("quarto-sidebar", slow);
+    };
+    const readerMode = !isReaderMode();
+    setReaderModeValue(readerMode);
+
+    // If we're entering reader mode, slow the transition
+    if (readerMode) {
+      slowTransition(readerMode);
+    }
+    highlightReaderToggle(readerMode);
+    hideOverlappedSidebars();
+
+    // If we're exiting reader mode, restore the non-slow transition
+    if (!readerMode) {
+      slowTransition(!readerMode);
+    }
+  };
+
+  const highlightReaderToggle = (readerMode) => {
+    const els = document.querySelectorAll(".quarto-reader-toggle");
+    if (els) {
+      els.forEach((el) => {
+        if (readerMode) {
+          el.classList.add("reader");
+        } else {
+          el.classList.remove("reader");
+        }
+      });
+    }
+  };
+
+  const setReaderModeValue = (val) => {
+    if (window.location.protocol !== "file:") {
+      window.localStorage.setItem("quarto-reader-mode", val);
+    } else {
+      localReaderMode = val;
+    }
+  };
+
+  const isReaderMode = () => {
+    if (window.location.protocol !== "file:") {
+      return window.localStorage.getItem("quarto-reader-mode") === "true";
+    } else {
+      return localReaderMode;
+    }
+  };
+  let localReaderMode = null;
+
+  const tocOpenDepthStr = tocEl?.getAttribute("data-toc-expanded");
+  const tocOpenDepth = tocOpenDepthStr ? Number(tocOpenDepthStr) : 1;
+
+  // Walk the TOC and collapse/expand nodes
+  // Nodes are expanded if:
+  // - they are top level
+  // - they have children that are 'active' links
+  // - they are directly below an link that is 'active'
+  const walk = (el, depth) => {
+    // Tick depth when we enter a UL
+    if (el.tagName === "UL") {
+      depth = depth + 1;
+    }
+
+    // It this is active link
+    let isActiveNode = false;
+    if (el.tagName === "A" && el.classList.contains("active")) {
+      isActiveNode = true;
+    }
+
+    // See if there is an active child to this element
+    let hasActiveChild = false;
+    for (child of el.children) {
+      hasActiveChild = walk(child, depth) || hasActiveChild;
+    }
+
+    // Process the collapse state if this is an UL
+    if (el.tagName === "UL") {
+      if (tocOpenDepth === -1 && depth > 1) {
+        // toc-expand: false
+        el.classList.add("collapse");
+      } else if (
+        depth <= tocOpenDepth ||
+        hasActiveChild ||
+        prevSiblingIsActiveLink(el)
+      ) {
+        el.classList.remove("collapse");
+      } else {
+        el.classList.add("collapse");
+      }
+
+      // untick depth when we leave a UL
+      depth = depth - 1;
+    }
+    return hasActiveChild || isActiveNode;
+  };
+
+  // walk the TOC and expand / collapse any items that should be shown
+  if (tocEl) {
+    updateActiveLink();
+    walk(tocEl, 0);
+  }
+
+  // Throttle the scroll event and walk peridiocally
+  window.document.addEventListener(
+    "scroll",
+    throttle(() => {
+      if (tocEl) {
+        updateActiveLink();
+        walk(tocEl, 0);
+      }
+      if (!isReaderMode()) {
+        hideOverlappedSidebars();
+      }
+    }, 5)
+  );
+  window.addEventListener(
+    "resize",
+    throttle(() => {
+      if (tocEl) {
+        updateActiveLink();
+        walk(tocEl, 0);
+      }
+      if (!isReaderMode()) {
+        hideOverlappedSidebars();
+      }
+    }, 10)
+  );
+  hideOverlappedSidebars();
+  highlightReaderToggle(isReaderMode());
+});
+
+// grouped tabsets
+window.addEventListener("pageshow", (_event) => {
+  function getTabSettings() {
+    const data = localStorage.getItem("quarto-persistent-tabsets-data");
+    if (!data) {
+      localStorage.setItem("quarto-persistent-tabsets-data", "{}");
+      return {};
+    }
+    if (data) {
+      return JSON.parse(data);
+    }
+  }
+
+  function setTabSettings(data) {
+    localStorage.setItem(
+      "quarto-persistent-tabsets-data",
+      JSON.stringify(data)
+    );
+  }
+
+  function setTabState(groupName, groupValue) {
+    const data = getTabSettings();
+    data[groupName] = groupValue;
+    setTabSettings(data);
+  }
+
+  function toggleTab(tab, active) {
+    const tabPanelId = tab.getAttribute("aria-controls");
+    const tabPanel = document.getElementById(tabPanelId);
+    if (active) {
+      tab.classList.add("active");
+      tabPanel.classList.add("active");
+    } else {
+      tab.classList.remove("active");
+      tabPanel.classList.remove("active");
+    }
+  }
+
+  function toggleAll(selectedGroup, selectorsToSync) {
+    for (const [thisGroup, tabs] of Object.entries(selectorsToSync)) {
+      const active = selectedGroup === thisGroup;
+      for (const tab of tabs) {
+        toggleTab(tab, active);
+      }
+    }
+  }
+
+  function findSelectorsToSyncByLanguage() {
+    const result = {};
+    const tabs = Array.from(
+      document.querySelectorAll(`div[data-group] a[id^='tabset-']`)
+    );
+    for (const item of tabs) {
+      const div = item.parentElement.parentElement.parentElement;
+      const group = div.getAttribute("data-group");
+      if (!result[group]) {
+        result[group] = {};
+      }
+      const selectorsToSync = result[group];
+      const value = item.innerHTML;
+      if (!selectorsToSync[value]) {
+        selectorsToSync[value] = [];
+      }
+      selectorsToSync[value].push(item);
+    }
+    return result;
+  }
+
+  function setupSelectorSync() {
+    const selectorsToSync = findSelectorsToSyncByLanguage();
+    Object.entries(selectorsToSync).forEach(([group, tabSetsByValue]) => {
+      Object.entries(tabSetsByValue).forEach(([value, items]) => {
+        items.forEach((item) => {
+          item.addEventListener("click", (_event) => {
+            setTabState(group, value);
+            toggleAll(value, selectorsToSync[group]);
+          });
+        });
+      });
+    });
+    return selectorsToSync;
+  }
+
+  const selectorsToSync = setupSelectorSync();
+  for (const [group, selectedName] of Object.entries(getTabSettings())) {
+    const selectors = selectorsToSync[group];
+    // it's possible that stale state gives us empty selections, so we explicitly check here.
+    if (selectors) {
+      toggleAll(selectedName, selectors);
+    }
+  }
+});
+
+function throttle(func, wait) {
+  let waiting = false;
+  return function () {
+    if (!waiting) {
+      func.apply(this, arguments);
+      waiting = true;
+      setTimeout(function () {
+        waiting = false;
+      }, wait);
+    }
+  };
+}
+
+function nexttick(func) {
+  return setTimeout(func, 0);
+}
diff --git a/docs/vignettes/Time_Series_files/libs/quarto-html/tippy.css b/docs/vignettes/Time_Series_files/libs/quarto-html/tippy.css
new file mode 100644
index 0000000..e6ae635
--- /dev/null
+++ b/docs/vignettes/Time_Series_files/libs/quarto-html/tippy.css
@@ -0,0 +1 @@
+.tippy-box[data-animation=fade][data-state=hidden]{opacity:0}[data-tippy-root]{max-width:calc(100vw - 10px)}.tippy-box{position:relative;background-color:#333;color:#fff;border-radius:4px;font-size:14px;line-height:1.4;white-space:normal;outline:0;transition-property:transform,visibility,opacity}.tippy-box[data-placement^=top]>.tippy-arrow{bottom:0}.tippy-box[data-placement^=top]>.tippy-arrow:before{bottom:-7px;left:0;border-width:8px 8px 0;border-top-color:initial;transform-origin:center top}.tippy-box[data-placement^=bottom]>.tippy-arrow{top:0}.tippy-box[data-placement^=bottom]>.tippy-arrow:before{top:-7px;left:0;border-width:0 8px 8px;border-bottom-color:initial;transform-origin:center bottom}.tippy-box[data-placement^=left]>.tippy-arrow{right:0}.tippy-box[data-placement^=left]>.tippy-arrow:before{border-width:8px 0 8px 8px;border-left-color:initial;right:-7px;transform-origin:center left}.tippy-box[data-placement^=right]>.tippy-arrow{left:0}.tippy-box[data-placement^=right]>.tippy-arrow:before{left:-7px;border-width:8px 8px 8px 0;border-right-color:initial;transform-origin:center right}.tippy-box[data-inertia][data-state=visible]{transition-timing-function:cubic-bezier(.54,1.5,.38,1.11)}.tippy-arrow{width:16px;height:16px;color:#333}.tippy-arrow:before{content:"";position:absolute;border-color:transparent;border-style:solid}.tippy-content{position:relative;padding:5px 9px;z-index:1}
\ No newline at end of file
diff --git a/docs/vignettes/Time_Series_files/libs/quarto-html/tippy.umd.min.js b/docs/vignettes/Time_Series_files/libs/quarto-html/tippy.umd.min.js
new file mode 100644
index 0000000..ca292be
--- /dev/null
+++ b/docs/vignettes/Time_Series_files/libs/quarto-html/tippy.umd.min.js
@@ -0,0 +1,2 @@
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+
diff --git a/vignettes/Package_Introduction.qmd b/vignettes/Package_Introduction.qmd
index 64f9380..5d5e3cd 100755
--- a/vignettes/Package_Introduction.qmd
+++ b/vignettes/Package_Introduction.qmd
@@ -3,7 +3,6 @@ title: "Introduction to Idealstan"
 author: "Robert Kubinec"
 date: last-modified
 format: html
-cache: true
 vignette: >
   %\VignetteIndexEntry{Time-Varying Ideal Points}
   %\VignetteEngine{R.rsp::asis}
@@ -37,7 +36,7 @@ The approach to handling missing data in this package is to model cases where mi
 The package includes the following models:
 
 | Model ID | Model Type | Response Type | Missing Data Adjustment |
-|-----------------|-----------------------|-----------------|-----------------|
+|-----------------|---------------------|-----------------|-----------------|
 | 1 | IRT 2-PL | Binary | No |
 | 2 | IRT 2-PL | Binary | Yes |
 | 3 | IRT rating scale | Ordinal | No |
@@ -88,6 +87,7 @@ To begin with, we can simulate data from an ordinal ideal-point model in which t
 The function `id_sim_gen()` allows you to simulate data from any of the sixteen models currently implemented in `idealstan` (see previous list). To include missing data, specify the `inflate` option as `TRUE`. For example, here we sample data from an ordinal graded response model:
 
 ```{r sim_data}
+#| cache: false
 
 ord_ideal_sim <- id_sim_gen(model='ordinal_grm',inflate = T)
 
@@ -157,6 +157,8 @@ To demonstrate how the package functions empirically, I include in the package a
 We can first take a look at the raw data:
 
 ```{r check_data}
+#| cache: false
+
 
 data('senate114')
 
@@ -243,6 +245,9 @@ The wide high-posterior density (HPD) interval of the absence midpoint ruglines
 We can obtain summary estimates of all the ideal points and item/bill discrimination/difficulty parameters using the summary function that provides the median value of the parameters in addition to a specified posterior density interval (i.e., 5%-95%). For example, we can extract summaries for the ideal points:
 
 ```{r ideal_pts_sum}
+#| cache: false
+
+
 ideal_pts_sum <- summary(sen_est,pars='ideal_pts')
 tt(head(ideal_pts_sum))
 ```
@@ -266,8 +271,9 @@ stan_trace(sen_est,par='L_full[1]')
 Finally we can also extract all of the posterior iterations to do additional calculations that average over posterior uncertainty by changing the `aggregate` option in `summary`. In the following code, I access the individual posterior iterations for the item/bill parameters, including difficulty (average probability of voting yes), discrimination (how strongly the item/bill loads on either end of the ideal point scale) and the midpoints (position where someone with that ideal point would be indifferent to voting yes/no).
 
 ```{r ideal_pts_ind}
+#| cache: false
 item_all <- summary(sen_est,pars='items', aggregate=F)
-knitr::kable(head(item_all))
+tt(head(item_all))
 ```
 
 ## Hierarchical Covariates
@@ -358,6 +364,8 @@ Because these covariates are on the ideal point scale, the meaning of the scale
 We can also extract the covariate summary values using the `summary` function:
 
 ```{r cov_values}
+#| cache: false
+
 cov_sum <- summary(sen_est_cov,pars='person_cov')
 tt(cov_sum)
 ```
diff --git a/vignettes/Time_Series.qmd b/vignettes/Time_Series.qmd
index 382ef5c..d0eea4c 100755
--- a/vignettes/Time_Series.qmd
+++ b/vignettes/Time_Series.qmd
@@ -2,7 +2,6 @@
 title: "Time-Varying Ideal Points"
 author: "Robert Kubinec"
 date: last-modified
-cache: true
 format: html
 vignette: >
   %\VignetteIndexEntry{Time-Varying Ideal Points}


         
         
               

                 

                   party_codeR    14.411400015.529235013.235560-15.5384000-14.451030-16.697360
                   legis_x
                 

                 

                   party_codeI    -0.0402673 6.0862770-6.466765 -0.6862375  5.981570 -6.834136
                   legis_x
                 

                 

                   age            -1.6332200-0.8166661-2.446573  2.3011950  3.067987  1.463249
                   legis_x
                 

                 

                   party_codeR:age 2.4787250 3.4572140 1.428219 -3.2372250 -2.184633 -4.234465
                   legis_x
                 

                 

                   party_codeI:age-1.7233150 4.4371645-7.166542  1.1277700  6.660751 -5.019880
                   legis_x
                 

         
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 time_var_free[100]0.68191000.68191000.68191000.67453500.67453500.6745350
 100
 Pettyjohn, Brian Guy 137
 R
 

 

 time_var_free[101]0.05773490.05773490.05773490.05367050.05367050.0536705
 101
 Plant, Al Sr. 76
 D
 

 

 time_var_free[102]0.20795700.20795700.20795700.20839900.20839900.2083990
 102
 Plant, Hazel 77
 D
 

 

 time_var_free[103]0.19062200.19062200.19062200.17203900.17203900.1720390
 103
 Poore, Nicole 138
 D
 

 

 time_var_free[104]0.38057700.38057700.38057700.38259700.38259700.3825970
 104
 Postles, Charles S. 78
 R
 

 

 time_var_free[105]0.30664500.30664500.30664500.31293200.31293200.3129320
 105
 Potter, Charles Jr. 79
 DNA
 NA
 NA0.4336860.4336860.4336861.5904901.5904901.590490
 L_tp1[1,100]
 

 

 Plant, Al Sr. 76
 D
 1995-01-01-6.352500-6.352500-6.352500-6.750600-6.750600-6.750600
 L_tp1[1,101]
 

 

 NA
 NA
 NA-5.640150-5.640150-5.640150-5.226830-5.226830-5.226830
 L_tp1[1,102]
 

 

 NA
 NA
 NA-0.123376-0.123376-0.123376-0.341960-0.341960-0.341960
 L_tp1[1,103]
 

 

 NA
 NA
 NA-0.453890-0.453890-0.453890-0.133957-0.133957-0.133957
 L_tp1[1,104]
 

 

 NA
 NA
 NA-0.518331-0.518331-0.518331-0.376860-0.376860-0.376860
 L_tp1[1,105]
 

 
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