Stefan P. Thoma 3/10/2020
Install / load packages needed:
knitr::opts_chunk$set(echo = TRUE)
if (!require("pacman")) install.packages("pacman")## Loading required package: pacman
p_load(tidyverse, lme4, lmerTest, mvoutlier, nlme, multcomp, lsmeans, xtable, jtools, tikzDevice, gmodels, parallel, performance, optimx, tidylog)
#pacman::p_load_gh("jaredhuling/jcolors")
#jcolors::jcolors("default")
#ggplot <- function(...) ggplot2::ggplot(...) + scale_color_brewer(palette=jcolors::jcolors()) + scale_fill_brewer(palette=jcolors::jcolors()) + #ggplot2::scale_colour_brewer(palette=jcolors::jcolors()) + ggplot2::scale_color_discrete(palette=jcolors::jcolors()) #+ ggplot2::scale_fill_discrete(palette=jcolors::jcolors())sessionInfo()## R version 4.2.1 (2022-06-23)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Big Sur ... 10.16
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] parallel stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] tidylog_1.0.2 optimx_2022-4.30 performance_0.9.2
## [4] gmodels_2.18.1.1 tikzDevice_0.12.3.1 jtools_2.2.0
## [7] xtable_1.8-4 lsmeans_2.30-0 emmeans_1.8.0
## [10] multcomp_1.4-20 TH.data_1.1-1 MASS_7.3-57
## [13] survival_3.3-1 mvtnorm_1.1-3 nlme_3.1-157
## [16] mvoutlier_2.1.1 sgeostat_1.0-27 lmerTest_3.1-3
## [19] lme4_1.1-30 Matrix_1.4-1 forcats_0.5.2
## [22] stringr_1.4.1 dplyr_1.0.10 purrr_0.3.4
## [25] readr_2.1.2 tidyr_1.2.1 tibble_3.1.8
## [28] ggplot2_3.3.6 tidyverse_1.3.2 pacman_0.5.1
##
## loaded via a namespace (and not attached):
## [1] fs_1.5.2 lubridate_1.8.0 insight_0.18.2
## [4] httr_1.4.4 numDeriv_2016.8-1.1 tools_4.2.1
## [7] backports_1.4.1 utf8_1.2.2 R6_2.5.1
## [10] DBI_1.1.3 colorspace_2.0-3 withr_2.5.0
## [13] tidyselect_1.2.0 compiler_4.2.1 cli_3.4.1
## [16] rvest_1.0.3 xml2_1.3.3 sandwich_3.0-2
## [19] scales_1.2.1 DEoptimR_1.0-11 robustbase_0.95-0
## [22] digest_0.6.29 minqa_1.2.4 rmarkdown_2.16
## [25] pkgconfig_2.0.3 htmltools_0.5.3 dbplyr_2.2.1
## [28] fastmap_1.1.0 rlang_1.0.6 readxl_1.4.1
## [31] rstudioapi_0.14 generics_0.1.3 zoo_1.8-10
## [34] jsonlite_1.8.1 gtools_3.9.3 googlesheets4_1.0.1
## [37] magrittr_2.0.3 Rcpp_1.0.9 munsell_0.5.0
## [40] fansi_1.0.3 lifecycle_1.0.3 stringi_1.7.8
## [43] yaml_2.3.5 grid_4.2.1 gdata_2.18.0.1
## [46] crayon_1.5.2 lattice_0.20-45 haven_2.5.1
## [49] splines_4.2.1 pander_0.6.5 hms_1.1.2
## [52] knitr_1.40 pillar_1.8.1 boot_1.3-28
## [55] estimability_1.4.1 clisymbols_1.2.0 codetools_0.2-18
## [58] reprex_2.0.2 glue_1.6.2 evaluate_0.16
## [61] modelr_0.1.9 vctrs_0.4.2 nloptr_2.0.3
## [64] tzdb_0.3.0 cellranger_1.1.0 gtable_0.3.1
## [67] assertthat_0.2.1 xfun_0.33 broom_1.0.1
## [70] coda_0.19-4 filehash_2.4-3 googledrive_2.0.0
## [73] gargle_1.2.0 ellipsis_0.3.2
data <- read_csv("data/cleanData.csv") ## Rows: 284 Columns: 131
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (9): id, sex, condition, Frage1, Frage2, Frage3, Leiter, Anmerkungen,...
## dbl (121): time, iat, ccs1, ccs2, ccs3, ccs4, ccs5, ccs6, ccs7, ccs8, ccs9,...
## dttm (1): StartDate
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
#data <- data %>% dplyr::select(
# id, time, iat, ccs, nr, nep, ipq, sod, ses, age, edu, sex, pol, vr_exp, vr_eval1, vr_eval2, vr_eval3,
# vr_eval4, vr_eval5, span, seen, condition, starts_with("Frage"), hr_mean, Leiter, Anmerkungen, Zeit
#)
head(data)## # A tibble: 6 × 131
## id time iat StartDate ccs1 ccs2 ccs3 ccs4 ccs5 ccs6
## <chr> <dbl> <dbl> <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 28287312 1 0.179 NA 1 1 2 1 1 1
## 2 28287312 2 0.409 NA 1 1 1 1 1 1
## 3 77995467 1 -0.496 NA 1 1 1 1 1 1
## 4 77995467 2 -0.362 NA 1 1 1 1 1 1
## 5 43795961 1 0.517 NA 2 1 1 1 2 1
## 6 43795961 2 0.634 NA 2 1 1 1 2 1
## # … with 121 more variables: ccs7 <dbl>, ccs8 <dbl>, ccs9 <dbl>, ccs10 <dbl>,
## # ccs11 <dbl>, ccs12 <dbl>, nr1 <dbl>, nr2 <dbl>, nr3 <dbl>, nr4 <dbl>,
## # nr5 <dbl>, nr6 <dbl>, nr7 <dbl>, nr8 <dbl>, nr9 <dbl>, nr10 <dbl>,
## # nr11 <dbl>, nr12 <dbl>, nr13 <dbl>, nr14 <dbl>, nr15 <dbl>, nr16 <dbl>,
## # nr17 <dbl>, nr18 <dbl>, nr19 <dbl>, nr20 <dbl>, nr21 <dbl>, nep1 <dbl>,
## # nep2 <dbl>, nep3 <dbl>, nep4 <dbl>, nep5 <dbl>, nep6 <dbl>, nep7 <dbl>,
## # nep8 <dbl>, nep9 <dbl>, nep10 <dbl>, nep11 <dbl>, nep12 <dbl>, …
# factor for vr or not
data <- data %>% group_by(id) %>%
mutate(
vr = ifelse(condition %in% c("a", "b", "c"), TRUE, FALSE),
type = factor(ifelse(vr, "vr", "control")),
condition = factor(condition, levels = c("b", "a", "c", "video", "text.bild", "text"))
)## group_by: one grouping variable (id)
## mutate (grouped): converted 'condition' from character to factor (0 new NA)
## new variable 'vr' (logical) with 2 unique values and 0% NA
## new variable 'type' (factor) with 2 unique values and 0% NA
Keep in mind the conditions coding:
a == abstract
b == realistic
c == realistic but badly so
Does IAT correlate to the other measures?
cor(data %>% ungroup() %>% dplyr::select(iat, nep, ccs, nr), use = "pairwise.complete.obs")## ungroup: no grouping variables
## iat nep ccs nr
## iat 1.00000000 0.1390394 -0.05361938 0.1366695
## nep 0.13903938 1.0000000 -0.37813922 0.3584078
## ccs -0.05361938 -0.3781392 1.00000000 -0.2009210
## nr 0.13666952 0.3584078 -0.20092101 1.0000000
cor.test.f <- Vectorize(FUN = function(var){
cor.test(data$iat, data[[var]], arg = "two.sided")
})
cor.test.f(c("nep", "ccs", "nr"))## nep
## statistic 2.35777
## parameter 282
## p.value 0.01906812
## estimate 0.1390394
## null.value 0
## alternative "two.sided"
## method "Pearson's product-moment correlation"
## data.name "data$iat and data[[var]]"
## conf.int numeric,2
## ccs
## statistic -0.9017197
## parameter 282
## p.value 0.3679753
## estimate -0.05361938
## null.value 0
## alternative "two.sided"
## method "Pearson's product-moment correlation"
## data.name "data$iat and data[[var]]"
## conf.int numeric,2
## nr
## statistic 2.316811
## parameter 282
## p.value 0.0212306
## estimate 0.1366695
## null.value 0
## alternative "two.sided"
## method "Pearson's product-moment correlation"
## data.name "data$iat and data[[var]]"
## conf.int numeric,2
The IAT scores correlated significantly with the nr scores (r = 0.137, p = 0.021) and with the nep scores (r = 0.139, p = 0.019) but not significantly with ccs scores (r = -0.054, p = .368). The signs of the correlations were as expected.
vars <- names(data)
ccs.vars <- vars[startsWith(vars, "ccs")]
nr.vars <- vars[startsWith(vars, "nr")]
nep.vars <- vars[startsWith(vars, "nep")]
ipq.vars <- vars[startsWith(vars, "ipq")]
sod.vars <- vars[startsWith(vars, "sod")]
vars.list1 <- list(ccs.vars, nr.vars, nep.vars)
vars.list2 <- list(ipq.vars, sod.vars)
#remove overall score (shortest name)
# this is a bit more robust compared to simply removing the last item
remove_overall <- function(char.vec){
nm <- char.vec[which.min(nchar(char.vec))]
char.vec <- char.vec[-which.min(nchar(char.vec))]
char.vec
}
vars.list1 <- lapply(vars.list1, remove_overall)
vars.list2 <- lapply(vars.list2, remove_overall)
reliable <- function(data, vars){
alph <- psych::alpha(data[vars], title = vars[1])
#omeg <- psych::omega(data[vars], plot = FALSE)
df <- data.frame(alpha = alph$total$raw_alpha, ci.low = alph$total$raw_alpha - 1.96 * alph$total$ase, ci.up = alph$total$raw_alpha + 1.96 * alph$total$ase)
df <- round(df, 3)
df$var = vars[1]
df
}
# measures which are measured twice
alpha.1 <- lapply(vars.list1, function(x) reliable(data = data, x))
# measures which are measured only once (sod and ipq)
alpha.2 <- lapply(vars.list2, function(x) reliable(data = data %>% filter(time == 1), x))## filter (grouped): removed 142 rows (50%), 142 rows remaining
## filter (grouped): removed 142 rows (50%), 142 rows remaining
alphas <- c(alpha.1, alpha.2)
(alpha.df <- do.call("rbind", alphas) %>%
dplyr::select(var, alpha, ci.low, ci.up))## var alpha ci.low ci.up
## 1 ccs1 0.845 0.819 0.871
## 2 nr1 0.840 0.813 0.866
## 3 nep1 0.686 0.632 0.739
## 4 ipq1 0.826 0.785 0.867
## 5 sod_1 0.805 0.759 0.852
cronbach alpha of nep is relatively small. What would mcdonalds omega look like for nep?
psych::omega(data[vars.list1[[3]]], nfactors = 1)## Loading required namespace: GPArotation
## Omega_h for 1 factor is not meaningful, just omega_t
## Warning in schmid(m, nfactors, fm, digits, rotate = rotate, n.obs = n.obs, :
## Omega_h and Omega_asymptotic are not meaningful with one factor
## Omega
## Call: omegah(m = m, nfactors = nfactors, fm = fm, key = key, flip = flip,
## digits = digits, title = title, sl = sl, labels = labels,
## plot = plot, n.obs = n.obs, rotate = rotate, Phi = Phi, option = option,
## covar = covar)
## Alpha: 0.7
## G.6: 0.73
## Omega Hierarchical: 0.7
## Omega H asymptotic: 0.99
## Omega Total 0.71
##
## Schmid Leiman Factor loadings greater than 0.2
## g F1* h2 u2 p2
## nep1 0.31 0.10 0.90 1
## nep2 0.38 0.15 0.85 1
## nep3 0.59 0.35 0.65 1
## nep4 0.44 0.20 0.80 1
## nep5 0.55 0.30 0.70 1
## nep6 0.03 0.97 1
## nep7 0.41 0.17 0.83 1
## nep8 0.21 0.04 0.96 1
## nep9 0.01 0.99 1
## nep10 0.46 0.21 0.79 1
## nep11 0.27 0.07 0.93 1
## nep12 0.48 0.23 0.77 1
## nep13 0.29 0.08 0.92 1
## nep14 0.32 0.10 0.90 1
## nep15 0.56 0.31 0.69 1
##
## With eigenvalues of:
## g F1*
## 2.4 0.0
##
## general/max 1.878568e+16 max/min = 1
## mean percent general = 1 with sd = 0 and cv of 0
## Explained Common Variance of the general factor = 1
##
## The degrees of freedom are 90 and the fit is 0.94
## The number of observations was 284 with Chi Square = 261.23 with prob < 1.3e-18
## The root mean square of the residuals is 0.08
## The df corrected root mean square of the residuals is 0.09
## RMSEA index = 0.082 and the 10 % confidence intervals are 0.071 0.094
## BIC = -247.18
##
## Compare this with the adequacy of just a general factor and no group factors
## The degrees of freedom for just the general factor are 90 and the fit is 0.94
## The number of observations was 284 with Chi Square = 261.23 with prob < 1.3e-18
## The root mean square of the residuals is 0.08
## The df corrected root mean square of the residuals is 0.09
##
## RMSEA index = 0.082 and the 10 % confidence intervals are 0.071 0.094
## BIC = -247.18
##
## Measures of factor score adequacy
## g F1*
## Correlation of scores with factors 0.87 0
## Multiple R square of scores with factors 0.75 0
## Minimum correlation of factor score estimates 0.51 -1
##
## Total, General and Subset omega for each subset
## g F1*
## Omega total for total scores and subscales 0.71 0.7
## Omega general for total scores and subscales 0.70 0.7
## Omega group for total scores and subscales 0.00 0.0
Omega Total 0.71 seems ok.
psych::principal(r = data[nep.vars[-length(nep.vars)]])## Principal Components Analysis
## Call: psych::principal(r = data[nep.vars[-length(nep.vars)]])
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 h2 u2 com
## nep1 0.38 0.146 0.85 1
## nep2 0.46 0.209 0.79 1
## nep3 0.65 0.418 0.58 1
## nep4 0.52 0.273 0.73 1
## nep5 0.60 0.365 0.63 1
## nep6 0.21 0.045 0.95 1
## nep7 0.48 0.230 0.77 1
## nep8 0.27 0.071 0.93 1
## nep9 0.11 0.012 0.99 1
## nep10 0.52 0.275 0.72 1
## nep11 0.34 0.114 0.89 1
## nep12 0.55 0.297 0.70 1
## nep13 0.36 0.128 0.87 1
## nep14 0.39 0.155 0.84 1
## nep15 0.62 0.384 0.62 1
##
## PC1
## SS loadings 3.13
## Proportion Var 0.21
##
## Mean item complexity = 1
## Test of the hypothesis that 1 component is sufficient.
##
## The root mean square of the residuals (RMSR) is 0.1
## with the empirical chi square 583.99 with prob < 2e-73
##
## Fit based upon off diagonal values = 0.68
For the following analysis we reduce the dataframe.
data <- data %>% dplyr::select(
id, time, vr, type, condition, iat, ccs, nr, nep, ipq, sod, ses, age, edu, sex, pol, vr_exp, vr_eval1, vr_eval2, vr_eval3, vr_eval4, vr_eval5, span, seen, starts_with("Frage"), hr_mean, Leiter, Anmerkungen, Zeit
)We try to find an acceptable model for each DV.
First, I would like to calculate a principal component of all dependent variables (dvs)
df_env <- data[c("iat", "ccs", "nr", "nep")]
psych::fa.parallel(df_env)
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1
prc_env <- princomp(df_env, cor = TRUE)
# Seems like one factor might just be enough. However, this may be more revealing when done
# on raw data
summary(prc_env)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 1.2980576 0.9835519 0.8829992 0.7536475
## Proportion of Variance 0.4212384 0.2418436 0.1949219 0.1419962
## Cumulative Proportion 0.4212384 0.6630819 0.8580038 1.0000000
data$env_pc <- prc_env$scores[,1]Unidimensionality could be assumed. The scores of the first principal
component were stored in data$env_pc. This vector can now be used as a
dependent variable in further exploratory analyses.
This plot is not very useful I guess. Too crowded.
This section is concerned only with the VR conditions a, b, c. Specifically with the variables vr_eval 1:5 and with the sod and presence scale IPQ.
Check for outliers on these scales:
#check.data <- data %>% dplyr::filter((vr == T & time == 1 ) & !is.na(ipq))
check.data <- data %>% dplyr::filter((time == 1 ) & !is.na(ipq))
#outlier.data <- data %>% ungroup() %>% dplyr::filter(vr == T & time == 1) %>% dplyr::select(starts_with("vr_eval"), sod, ipq) %>%
# drop_na()
#mvoutlier::chisq.plot(check.data %>% ungroup() %>% dplyr::select(starts_with("vr_eval"), sod, ipq))
# remove: 38 1 63
# which corresponds to the ids:
#remove.ids <- check.data$id[c(38, 1, 63)]
# "44466757" "32504483" "80688810"vars <-c("vr_eval1", "vr_eval2", "vr_eval3", "vr_eval4", "vr_eval5", "ipq", "sod")
desc_plot_data <- gather(data, specific, value, vars) %>%
# filter(!is.na(ipq)) %>%
arrange(id, specific) %>%
mutate(specific = ifelse(specific=="vr_eval1", "excitement",
ifelse(specific=="vr_eval2", "graphically pleasing",
ifelse(specific=="vr_eval3", "pleasant",
ifelse(specific=="vr_eval4", "realistic",
ifelse(specific=="vr_eval5", "enjoyment", specific))))),
VRE = ifelse(condition == "b", "Real+",
ifelse(condition=="c", "Real-",
ifelse(condition=="a", "Abstract", as.character(condition))))) %>%
dplyr::select(specific, value, id, VRE)## Warning: Using an external vector in selections was deprecated in tidyselect 1.1.0.
## ℹ Please use `all_of()` or `any_of()` instead.
## # Was:
## data %>% select(vars)
##
## # Now:
## data %>% select(all_of(vars))
##
## See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## gather: reorganized (ipq, sod, vr_eval1, vr_eval2, vr_eval3, …) into (specific, value) [was 284x32, now 1988x27]
## mutate: changed 1,420 values (71%) of 'specific' (0 new NA)
## new variable 'VRE' (character) with 6 unique values and 0% NA
(vr_eval_plot <- ggplot(data = desc_plot_data, aes(x = VRE, y = value, color = VRE)) +
facet_wrap( ~specific, nrow = 2)+
geom_violin(draw_quantiles = .5) + #, position = position_jitterdodge(dodge.width = 0.8, jitter.width = 0, jitter.height = 0))+
geom_point(alpha = .3, position = "jitter")+#, position = position_jitterdodge(dodge.width = 0, jitter.width = .2, jitter.height = .3)) +
ggthemes::theme_few() +
ylab("value") +
xlab("")+
# labs(title="")+
theme(axis.title.x=element_blank(),
axis.text.x=element_blank(),
axis.ticks.x=element_blank())+
scale_y_continuous(breaks = c(1,3,5,7)) +
theme(legend.position = "right") )## Warning: Removed 304 rows containing non-finite values (stat_ydensity).
## Warning: Removed 304 rows containing missing values (geom_point).
ipq and sod separately:
Vector containing name of all dv’s
dvs <- c("iat", "ccs", "nr", "nep", "env_pc")Mean dvs at time point 1.
data.dv1 <- data %>% filter(time==1) %>%
dplyr::mutate(condition = ifelse(condition =="b", "real+",
ifelse(condition == "c", "real-",
ifelse(condition == "a", "abstract", as.character(condition)))),
condition = as.factor(condition))## filter: removed 142 rows (50%), 142 rows remaining
(summar.cond <- data.dv1 %>% group_by(condition, type) %>%
summarise(mean_iat = mean(iat),
mean_ccs = mean(ccs),
mean_nr = mean(nr),
mean_nep = mean(nep)))## group_by: 2 grouping variables (condition, type)
## summarise: now 6 rows and 6 columns, one group variable remaining (condition)
## # A tibble: 6 × 6
## # Groups: condition [6]
## condition type mean_iat mean_ccs mean_nr mean_nep
## <fct> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 abstract vr -0.0430 1.5 3.63 3.79
## 2 real- vr 0.309 1.51 4.02 3.86
## 3 real+ vr 0.165 1.35 3.99 3.79
## 4 text control 0.355 1.47 3.77 3.83
## 5 text.bild control 0.233 1.42 3.83 3.87
## 6 video control 0.306 1.48 3.89 3.84
(summar.vr <- data.dv1 %>% group_by(type) %>%
summarise(mean_iat = mean(iat),
mean_ccs = mean(ccs),
mean_nr = mean(nr),
mean_nep = mean(nep)))## group_by: one grouping variable (type)
## summarise: now 2 rows and 5 columns, ungrouped
## # A tibble: 2 × 5
## type mean_iat mean_ccs mean_nr mean_nep
## <fct> <dbl> <dbl> <dbl> <dbl>
## 1 vr 0.144 1.45 3.88 3.81
## 2 control 0.299 1.46 3.83 3.85
contrasts(data.dv1$condition) <- contr.sum(n = 6)
contrasts(data.dv1$condition)## [,1] [,2] [,3] [,4] [,5]
## abstract 1 0 0 0 0
## real- 0 1 0 0 0
## real+ 0 0 1 0 0
## text 0 0 0 1 0
## text.bild 0 0 0 0 1
## video -1 -1 -1 -1 -1
lapply(dvs, function(x){
print(x)
summary(lm(get(x)~condition, data = data.dv1))
})## [1] "iat"
## [1] "ccs"
## [1] "nr"
## [1] "nep"
## [1] "env_pc"
## [[1]]
##
## Call:
## lm(formula = get(x) ~ condition, data = data.dv1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.10154 -0.28834 -0.00615 0.30680 0.94134
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.22074 0.03689 5.984 1.82e-08 ***
## condition1 -0.26378 0.08340 -3.163 0.00193 **
## condition2 0.08793 0.08340 1.054 0.29356
## condition3 -0.05547 0.08340 -0.665 0.50711
## condition4 0.13378 0.08067 1.658 0.09955 .
## condition5 0.01189 0.08199 0.145 0.88487
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4393 on 136 degrees of freedom
## Multiple R-squared: 0.08616, Adjusted R-squared: 0.05256
## F-statistic: 2.565 on 5 and 136 DF, p-value: 0.02985
##
##
## [[2]]
##
## Call:
## lm(formula = get(x) ~ condition, data = data.dv1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5109 -0.3359 -0.1458 0.1814 1.7500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.45522 0.04003 36.349 <2e-16 ***
## condition1 0.04478 0.09052 0.495 0.622
## condition2 0.05565 0.09052 0.615 0.540
## condition3 -0.10740 0.09052 -1.186 0.237
## condition4 0.01811 0.08756 0.207 0.836
## condition5 -0.03508 0.08899 -0.394 0.694
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4768 on 136 degrees of freedom
## Multiple R-squared: 0.01384, Adjusted R-squared: -0.02241
## F-statistic: 0.3819 on 5 and 136 DF, p-value: 0.8605
##
##
## [[3]]
##
## Call:
## lm(formula = get(x) ~ condition, data = data.dv1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.8610 -0.2856 0.0119 0.3534 0.9962
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.85568 0.04060 94.975 <2e-16 ***
## condition1 -0.22421 0.09179 -2.443 0.0159 *
## condition2 0.16917 0.09179 1.843 0.0675 .
## condition3 0.13811 0.09179 1.505 0.1347
## condition4 -0.08996 0.08879 -1.013 0.3127
## condition5 -0.03028 0.09024 -0.336 0.7377
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4835 on 136 degrees of freedom
## Multiple R-squared: 0.07317, Adjusted R-squared: 0.0391
## F-statistic: 2.147 on 5 and 136 DF, p-value: 0.06351
##
##
## [[4]]
##
## Call:
## lm(formula = get(x) ~ condition, data = data.dv1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3600 -0.2580 0.0058 0.2675 0.9478
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.82973 0.03525 108.653 <2e-16 ***
## condition1 -0.04422 0.07969 -0.555 0.580
## condition2 0.03404 0.07969 0.427 0.670
## condition3 -0.03842 0.07969 -0.482 0.630
## condition4 -0.00306 0.07709 -0.040 0.968
## condition5 0.04250 0.07835 0.542 0.588
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4198 on 136 degrees of freedom
## Multiple R-squared: 0.006267, Adjusted R-squared: -0.03027
## F-statistic: 0.1715 on 5 and 136 DF, p-value: 0.9728
##
##
## [[5]]
##
## Call:
## lm(formula = get(x) ~ condition, data = data.dv1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6228 -0.7179 0.1753 0.7888 2.5123
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.07852 0.10223 -0.768 0.4438
## condition1 -0.50214 0.23114 -2.172 0.0316 *
## condition2 0.21738 0.23114 0.940 0.3487
## condition3 0.16514 0.23114 0.714 0.4762
## condition4 -0.03430 0.22358 -0.153 0.8783
## condition5 0.07576 0.22724 0.333 0.7393
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.218 on 136 degrees of freedom
## Multiple R-squared: 0.03737, Adjusted R-squared: 0.001976
## F-statistic: 1.056 on 5 and 136 DF, p-value: 0.3878
So we will create two models for each dependent variables:
First, the model will have the formula:
dv ~ condition * time + (time | id)
This will be simplified to the following model if model fit is singular:
dv ~ condition * time + (1 | id)
This will estimate a random intercept for each participant. This model
will only take as input the vr conditions (a, b & c), or:
vr == TRUE.
The second model will have the formula:
dv ~ vr * time + (time | condition) + (1 | id)
Where a random slope for time is estimated per condition. Further, there is a random intercept per condition, and per id.
Should model fit be singular, we would simplify the model to:
dv ~ vr * time + (1 | condition) + (1 | id)
If still singular, we would simplify to:
dv ~ vr * time + (1 | id)
fit.lme <- function(form, dat){
lme4::lmer(formula = form, data = dat)
#lme4::lmer(formula = form, data = dat,
# control = lmerControl(optimizer = "optimx", optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) # alternative optimizer
}fit_models <- function(dv, dat){
# this function returns a function which fits a model based on a formula minus the predictors.
# This function can be used in the next function which implements the conditions for reducing model complexity if model fit is singular.
function(predictors){
form <- formula(paste(dv, predictors, sep = " ~ "))
print(form)
fit <- fit.lme(form = form, dat = dat)
}
}predictors.vr <- c("condition * time + (time | id)", "condition * time + (1 | id)")
predictors.all <- c("time*type + (time | condition) + (1 | id)", "time * type + (-1 + time | condition) + (1 | id)", "time * type + (1 | id)")
#predictors.all2 <- c("vr * time + (time | condition) + (1 | id)", "vr * time + (1 | condition) + (1 | id)", "vr * time + (1 | id)")
#predictors.all3 <- c("vr * time + (time | condition) + (1 | id)", "vr * time + (-1 + time | condition) + (1 | id)", "vr * time + (1 | id)")
# function to fit various models based on different inputs of predictors
fit_many <- function(pred.vector, dat, dv){
fit_model <- fit_models(dv, dat)
sing <- TRUE
i <- 1
while((sing) & i<=length(pred.vector)){
model <- try(fit_model(pred.vector[i]))
if(class(model)!="try-error"){
sing <- isSingular(model)
}
i <- i + 1
}
print(paste("is model singular: ", sing))
model
}# split data frame:
data.vr <- data %>% dplyr::filter(vr) Contrast: We want the effect of “time” to be the average effect over all
conditions. Therefore we set the contrast of the condition variable to
contr.sum in accordance with
https://stats.oarc.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/#DEVIATION.
This is sometimes called unweighted effect coding or
deviation coding.
data.vr$condition <-droplevels(data.vr$condition)
contrasts(data.vr$condition) <- contr.sum(3)
contrasts(data$type) <- contr.sum(2)vr.models <- lapply(dvs, FUN = function(dv) fit_many(pred.vector = predictors.vr, dat = data.vr, dv = dv))## iat ~ condition * time + (time | id)
## <environment: 0x7f9e4a81aef8>
## Error : number of observations (=138) <= number of random effects (=138) for term (time | id); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable
## iat ~ condition * time + (1 | id)
## <environment: 0x7f9ed99939a8>
## [1] "is model singular: FALSE"
## ccs ~ condition * time + (time | id)
## <environment: 0x7f9ed81927f0>
## Error : number of observations (=138) <= number of random effects (=138) for term (time | id); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable
## ccs ~ condition * time + (1 | id)
## <environment: 0x7f9e5b440c68>
## [1] "is model singular: FALSE"
## nr ~ condition * time + (time | id)
## <environment: 0x7f9ecf33d508>
## Error : number of observations (=138) <= number of random effects (=138) for term (time | id); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable
## nr ~ condition * time + (1 | id)
## <environment: 0x7f9ecf0cfd60>
## [1] "is model singular: FALSE"
## nep ~ condition * time + (time | id)
## <environment: 0x7f9ec99d9bf8>
## Error : number of observations (=138) <= number of random effects (=138) for term (time | id); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable
## nep ~ condition * time + (1 | id)
## <environment: 0x7f9ece8ce898>
## [1] "is model singular: FALSE"
## env_pc ~ condition * time + (time | id)
## <environment: 0x7f9ece1e7f20>
## Error : number of observations (=138) <= number of random effects (=138) for term (time | id); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable
## env_pc ~ condition * time + (1 | id)
## <environment: 0x7f9ebf7889b0>
## [1] "is model singular: FALSE"
all.models <- lapply(dvs, FUN = function(dv) fit_many(pred.vector = predictors.all, dat = data, dv = dv))## iat ~ time * type + (time | condition) + (1 | id)
## <environment: 0x7f9ec934a038>
## boundary (singular) fit: see help('isSingular')
## iat ~ time * type + (-1 + time | condition) + (1 | id)
## <environment: 0x7f9ec83cb668>
## [1] "is model singular: FALSE"
## ccs ~ time * type + (time | condition) + (1 | id)
## <environment: 0x7f9e5aad1a58>
## boundary (singular) fit: see help('isSingular')
## ccs ~ time * type + (-1 + time | condition) + (1 | id)
## <environment: 0x7f9e5b4cdf90>
## boundary (singular) fit: see help('isSingular')
## ccs ~ time * type + (1 | id)
## <environment: 0x7f9ebebdda10>
## [1] "is model singular: FALSE"
## nr ~ time * type + (time | condition) + (1 | id)
## <environment: 0x7f9ebea8dcc0>
## boundary (singular) fit: see help('isSingular')
## nr ~ time * type + (-1 + time | condition) + (1 | id)
## <environment: 0x7f9e5bc6b440>
## [1] "is model singular: FALSE"
## nep ~ time * type + (time | condition) + (1 | id)
## <environment: 0x7f9e89c281f8>
## boundary (singular) fit: see help('isSingular')
## nep ~ time * type + (-1 + time | condition) + (1 | id)
## <environment: 0x7f9e5f211f58>
## [1] "is model singular: FALSE"
## env_pc ~ time * type + (time | condition) + (1 | id)
## <environment: 0x7f9e89ac7d28>
## boundary (singular) fit: see help('isSingular')
## env_pc ~ time * type + (-1 + time | condition) + (1 | id)
## <environment: 0x7f9ebe27fff0>
## boundary (singular) fit: see help('isSingular')
## env_pc ~ time * type + (1 | id)
## <environment: 0x7f9eb9b30400>
## [1] "is model singular: FALSE"
presence.models <- lapply(dvs, FUN = function(dv) fit_many(pred.vector = "ipq * time + (1 | id)", dat = data.vr, dv = dv))## iat ~ ipq * time + (1 | id)
## <environment: 0x7f9e8941d040>
## [1] "is model singular: FALSE"
## ccs ~ ipq * time + (1 | id)
## <environment: 0x7f9eb8b9bde8>
## [1] "is model singular: FALSE"
## nr ~ ipq * time + (1 | id)
## <environment: 0x7f9e9f7b4a40>
## [1] "is model singular: FALSE"
## nep ~ ipq * time + (1 | id)
## <environment: 0x7f9e9e9c8cb8>
## [1] "is model singular: FALSE"
## env_pc ~ ipq * time + (1 | id)
## <environment: 0x7f9e9e076f60>
## [1] "is model singular: FALSE"
sod.models <- lapply(dvs, FUN = function(dv) fit_many(pred.vector = "sod * time + (1 | id)", dat = data.vr, dv = dv))## iat ~ sod * time + (1 | id)
## <environment: 0x7f9e9ccb4238>
## [1] "is model singular: FALSE"
## ccs ~ sod * time + (1 | id)
## <environment: 0x7f9e9c42ecd0>
## [1] "is model singular: FALSE"
## nr ~ sod * time + (1 | id)
## <environment: 0x7f9e9aa47b30>
## [1] "is model singular: FALSE"
## nep ~ sod * time + (1 | id)
## <environment: 0x7f9e98626288>
## [1] "is model singular: FALSE"
## env_pc ~ sod * time + (1 | id)
## <environment: 0x7f9e8f3b7e20>
## [1] "is model singular: FALSE"
I save model diagnostics as pdfs separately, for visibility reasons.
plot_diagn <- function(model){
filename <- paste( model@call$formula[2], sub("\\ .*", "", model@call$formula[3]), sep = "_")
png(filename = paste("analysisOutputs/diagnostics/", filename, ".png", sep = ""), # The directory you want to save the file in
#paper = "a3",
height = 5900/4,
width = 4200/4
)
print(performance::check_model(model) )
dev.off()
}lapply(vr.models, FUN = plot_diagn)## [[1]]
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lapply(all.models, FUN = plot_diagn)## [[1]]
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I focus model diagnostic on the vr models. They include all data. Residuals are slightly left skewed. However, this does not yet warrant a transformation of the dv in my opinion.
First some descriptives about ccs.
data %>% group_by(as.factor(time)) %>%
summarise(mean = mean(ccs),
range = range(ccs),
median = median(ccs))## group_by: one grouping variable (as.factor(time))
## summarise: now 4 rows and 4 columns, one group variable remaining (as.factor(time))
## # A tibble: 4 × 4
## # Groups: as.factor(time) [2]
## `as.factor(time)` mean range median
## <fct> <dbl> <dbl> <dbl>
## 1 1 1.46 1 1.33
## 2 1 1.46 3.25 1.33
## 3 2 1.44 1 1.29
## 4 2 1.44 3.83 1.29
Some thoughts: Homogeneity of variance appears implausible. Residual variance increases with larger fitted values.
Residuals are also not normally distributed. Random effects do not appear normal.
The reason for this unexpected behaviour may well be the floor-effect of the dv ccs. There was generally a very low ccs score for participants. This is due to the relatively extreme nature of climate change scepticism, especially in a relatively well educated sample.
Maybe a boxcox transformation may help:
#estimate lambda of the boxcox transformation
bc <- boxcox(ccs ~ vr * time, data = data)
lambda_ccs <- bc$x[which.max(bc$y)]
# transform data according to the transformation
data <- data %>%
mutate(ccs_bc = (ccs^lambda_ccs-1)/lambda_ccs)## mutate: new variable 'ccs_bc' (double) with 28 unique values and 0% NA
# refit the model
all.ccs2 <- fit_many(pred.vector = predictors.all, dat = data, dv = "ccs_bc")## ccs_bc ~ time * type + (time | condition) + (1 | id)
## <environment: 0x7f9e4cf22238>
## boundary (singular) fit: see help('isSingular')
## ccs_bc ~ time * type + (-1 + time | condition) + (1 | id)
## <environment: 0x7f9ed80c5e40>
## boundary (singular) fit: see help('isSingular')
## ccs_bc ~ time * type + (1 | id)
## <environment: 0x7f9ed9882e10>
## [1] "is model singular: FALSE"
performance::check_model(all.ccs2)
The situation has improved! All model assumptions appear plausible.
all.models[[2]] <- all.ccs2For within the VE:
And based on the transformed ccs:
data.vr <- data.vr %>%
mutate(ccs_bc = (ccs^lambda_ccs-1)/lambda_ccs)## mutate: new variable 'ccs_bc' (double) with 24 unique values and 0% NA
vr.ccs2 <- fit_many(pred.vector = predictors.vr, dat = data.vr, dv = "ccs_bc")## ccs_bc ~ condition * time + (time | id)
## <environment: 0x7f9e9f8c12a8>
## Error : number of observations (=138) <= number of random effects (=138) for term (time | id); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable
## ccs_bc ~ condition * time + (1 | id)
## <environment: 0x7f9e893f6978>
## [1] "is model singular: FALSE"
performance::check_model(vr.ccs2)
vr.models[[2]] <- vr.ccs2
Model assumptions are not too far off: Slight slope in the “fitted vs residuals”. Homogeneity assumption is appropriate. Residual distribution is slightly skewed with a heavy left tail. ID intercept distribution is not quite normal, but not far from it. Slightly skewed as well.
Overall assumptions seem acceptable and warrant no further action.
Overall assumptions seem acceptable and warrant no further action.
min(data$env_pc)## [1] -4.954711
data$env_pc2 <- data$env_pc + 6
#estimate lambda of the boxcox transformation
bc <- boxcox(env_pc2 ~ vr * time, data = data)
lambda_pc <- bc$x[which.max(bc$y)]
# transform data according to the transformation
data <- data %>%
mutate(env_pc_bc = (env_pc2^lambda_pc-1)/lambda_pc)## mutate: new variable 'env_pc_bc' (double) with 284 unique values and 0% NA
# refit the model
all.env_pc2 <- fit_many(pred.vector = predictors.all, dat = data, dv = "env_pc_bc")## env_pc_bc ~ time * type + (time | condition) + (1 | id)
## <environment: 0x7f9ec9eb9360>
## boundary (singular) fit: see help('isSingular')
## env_pc_bc ~ time * type + (-1 + time | condition) + (1 | id)
## <environment: 0x7f9e5f5279a8>
## boundary (singular) fit: see help('isSingular')
## env_pc_bc ~ time * type + (1 | id)
## <environment: 0x7f9ec9be8a68>
## [1] "is model singular: FALSE"
performance::check_model(all.env_pc2)
Transformation does not help much here. Lets not do it.
But let us save the final model diagnostics plots as well.
lapply(vr.models, FUN = plot_diagn)## [[1]]
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lapply(all.models, FUN = plot_diagn)## [[1]]
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lapply(all.models, FUN = lmerTest:::summary.lmerModLmerTest)## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## [[1]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: iat ~ time * type + (-1 + time | condition) + (1 | id)
## Data: dat
##
## REML criterion at convergence: 315.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.00917 -0.60925 0.02082 0.59421 2.05824
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.098991 0.31463
## condition time 0.002013 0.04486
## Residual 0.094707 0.30775
## Number of obs: 284, groups: id, 142; condition, 6
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.230413 0.063522 225.155717 3.627 0.000354 ***
## time -0.009332 0.040871 20.397083 -0.228 0.821660
## type1 -0.152101 0.063522 225.155717 -2.394 0.017465 *
## time:type1 0.074652 0.040871 20.397083 1.827 0.082445 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) time type1
## time -0.771
## type1 0.028 -0.022
## time:type1 -0.022 0.022 -0.771
##
## [[2]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ccs_bc ~ time * type + (1 | id)
## Data: dat
##
## REML criterion at convergence: -349
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.33016 -0.44377 -0.04596 0.56783 2.12335
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.018962 0.13770
## Residual 0.005645 0.07513
## Number of obs: 284, groups: id, 142
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.234121 0.018236 278.363626 12.838 <2e-16 ***
## time -0.011764 0.008920 140.000003 -1.319 0.189
## type1 -0.002096 0.018236 278.363626 -0.115 0.909
## time:type1 -0.002811 0.008920 140.000003 -0.315 0.753
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) time type1
## time -0.734
## type1 0.028 -0.021
## time:type1 -0.021 0.028 -0.734
##
## [[3]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: nr ~ time * type + (-1 + time | condition) + (1 | id)
## Data: dat
##
## REML criterion at convergence: 265.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.59554 -0.44842 0.02171 0.48568 1.76425
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.2263312 0.47574
## condition time 0.0003591 0.01895
## Residual 0.0400008 0.20000
## Number of obs: 284, groups: id, 142; condition, 6
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.81760 0.05482 268.09998 69.644 <2e-16 ***
## time 0.03769 0.02497 9.57301 1.509 0.164
## type1 -0.01084 0.05482 268.09998 -0.198 0.843
## time:type1 0.03891 0.02497 9.57301 1.558 0.152
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) time type1
## time -0.618
## type1 0.028 -0.017
## time:type1 -0.017 0.025 -0.618
##
## [[4]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: nep ~ time * type + (-1 + time | condition) + (1 | id)
## Data: dat
##
## REML criterion at convergence: 187.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.13567 -0.52383 -0.01767 0.49178 2.18200
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.1427876 0.37787
## condition time 0.0001482 0.01217
## Residual 0.0352898 0.18786
## Number of obs: 284, groups: id, 142; condition, 6
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.75582 0.04743 276.21351 79.181 < 2e-16 ***
## time 0.07381 0.02285 14.88848 3.230 0.00565 **
## type1 -0.03505 0.04743 276.21351 -0.739 0.46061
## time:type1 0.01894 0.02285 14.88848 0.829 0.42021
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) time type1
## time -0.688
## type1 0.028 -0.019
## time:type1 -0.019 0.027 -0.688
##
## [[5]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: env_pc ~ time * type + (1 | id)
## Data: dat
##
## REML criterion at convergence: 769
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.33852 -0.41115 0.01461 0.44995 1.90160
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 1.4722 1.2133
## Residual 0.2278 0.4773
## Number of obs: 284, groups: id, 142
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.23777 0.13566 267.65387 -1.753 0.08081 .
## time 0.15874 0.05667 140.00000 2.801 0.00581 **
## type1 -0.14234 0.13566 267.65387 -1.049 0.29502
## time:type1 0.10297 0.05667 140.00000 1.817 0.07134 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) time type1
## time -0.627
## type1 0.028 -0.018
## time:type1 -0.018 0.028 -0.627
Follow up tests:
# iat
contrast( emmeans(all.models[[1]], ~ time | type))## type = vr:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.0327 0.0292 23.0 -1.118 0.2753
## time2 effect 0.0327 0.0292 23.0 1.118 0.2753
##
## type = control:
## contrast estimate SE df t.ratio p.value
## time1 effect 0.0420 0.0286 21.2 1.470 0.1563
## time2 effect -0.0420 0.0286 21.2 -1.470 0.1563
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: fdr method for 2 tests
# ccs
contrast( emmeans(all.models[[2]], ~ time | type))## type = vr:
## contrast estimate SE df t.ratio p.value
## time1 effect 0.00729 0.00640 140 1.139 0.2565
## time2 effect -0.00729 0.00640 140 -1.139 0.2565
##
## type = control:
## contrast estimate SE df t.ratio p.value
## time1 effect 0.00448 0.00622 140 0.720 0.4728
## time2 effect -0.00448 0.00622 140 -0.720 0.4728
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: fdr method for 2 tests
# nr
contrast( emmeans(all.models[[3]], ~ time | type))## type = vr:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.038302 0.0179 10.66 -2.142 0.0562
## time2 effect 0.038302 0.0179 10.66 2.142 0.0562
##
## type = control:
## contrast estimate SE df t.ratio p.value
## time1 effect 0.000613 0.0174 9.67 0.035 0.9727
## time2 effect -0.000613 0.0174 9.67 -0.035 0.9727
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: fdr method for 2 tests
# nep
contrast( emmeans(all.models[[4]], ~ time | type))## type = vr:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.0464 0.0164 14.4 -2.833 0.0130
## time2 effect 0.0464 0.0164 14.4 2.833 0.0130
##
## type = control:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.0274 0.0159 13.0 -1.721 0.1090
## time2 effect 0.0274 0.0159 13.0 1.721 0.1090
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: fdr method for 2 tests
lapply(vr.models, FUN = lmerTest:::summary.lmerModLmerTest)## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## [[1]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: iat ~ condition * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 177.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.60384 -0.59622 -0.01456 0.55523 1.93986
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.1132 0.3365
## Residual 0.1068 0.3268
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.07831 0.09684 106.85910 0.809 0.421
## condition1 0.09886 0.13695 106.85910 0.722 0.472
## condition2 -0.22578 0.13695 106.85910 -1.649 0.102
## time 0.06532 0.05563 66.00000 1.174 0.245
## condition1:time -0.07723 0.07868 66.00000 -0.982 0.330
## condition2:time 0.03911 0.07868 66.00000 0.497 0.621
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 cndtn2 time cndt1:
## condition1 0.000
## condition2 0.000 -0.500
## time -0.862 0.000 0.000
## conditn1:tm 0.000 -0.862 0.431 0.000
## conditn2:tm 0.000 0.431 -0.862 0.000 -0.500
##
## [[2]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ccs_bc ~ condition * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: -149.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.88848 -0.39218 -0.03104 0.48900 1.99181
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.022653 0.15051
## Residual 0.004976 0.07054
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.232025 0.026247 131.560393 8.840 5.38e-15 ***
## condition1 -0.057282 0.037119 131.560393 -1.543 0.125
## condition2 0.014219 0.037119 131.560393 0.383 0.702
## time -0.014575 0.012010 66.000002 -1.214 0.229
## condition1:time 0.015010 0.016985 66.000001 0.884 0.380
## condition2:time 0.006983 0.016985 66.000001 0.411 0.682
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 cndtn2 time cndt1:
## condition1 0.000
## condition2 0.000 -0.500
## time -0.686 0.000 0.000
## conditn1:tm 0.000 -0.686 0.343 0.000
## conditn2:tm 0.000 0.343 -0.686 0.000 -0.500
##
## [[3]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: nr ~ condition * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 102.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.74225 -0.50265 -0.03626 0.54439 1.71416
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.11846 0.3442
## Residual 0.04125 0.2031
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.80676 0.06860 129.34427 55.494 < 2e-16 ***
## condition1 0.09593 0.09701 129.34427 0.989 0.32460
## condition2 -0.28916 0.09701 129.34427 -2.981 0.00344 **
## time 0.07660 0.03458 66.00000 2.215 0.03018 *
## condition1:time 0.01449 0.04890 66.00000 0.296 0.76787
## condition2:time 0.03727 0.04890 66.00000 0.762 0.44870
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 cndtn2 time cndt1:
## condition1 0.000
## condition2 0.000 -0.500
## time -0.756 0.000 0.000
## conditn1:tm 0.000 -0.756 0.378 0.000
## conditn2:tm 0.000 0.378 -0.756 0.000 -0.500
##
## [[4]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: nep ~ condition * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 98.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.32935 -0.59590 -0.04369 0.49713 1.85313
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.13842 0.3721
## Residual 0.03437 0.1854
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.72077 0.06706 131.99874 55.488 < 2e-16 ***
## condition1 -0.04541 0.09483 131.99874 -0.479 0.63283
## condition2 -0.05990 0.09483 131.99874 -0.632 0.52869
## time 0.09275 0.03156 66.00000 2.939 0.00454 **
## condition1:time 0.02319 0.04463 66.00000 0.520 0.60514
## condition2:time 0.03188 0.04463 66.00000 0.714 0.47754
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 cndtn2 time cndt1:
## condition1 0.000
## condition2 0.000 -0.500
## time -0.706 0.000 0.000
## conditn1:tm 0.000 -0.706 0.353 0.000
## conditn2:tm 0.000 0.353 -0.706 0.000 -0.500
##
## [[5]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: env_pc ~ condition * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 372.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.61435 -0.42168 0.01546 0.43108 1.86555
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 1.2457 1.1161
## Residual 0.2474 0.4974
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.380108 0.189692 130.611470 -2.004 0.04716 *
## condition1 0.214738 0.268266 130.611470 0.800 0.42489
## condition2 -0.532468 0.268266 130.611470 -1.985 0.04926 *
## time 0.261713 0.084687 66.000001 3.090 0.00293 **
## condition1:time -0.009723 0.119765 66.000001 -0.081 0.93554
## condition2:time 0.070200 0.119765 66.000001 0.586 0.55978
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 cndtn2 time cndt1:
## condition1 0.000
## condition2 0.000 -0.500
## time -0.670 0.000 0.000
## conditn1:tm 0.000 -0.670 0.335 0.000
## conditn2:tm 0.000 0.335 -0.670 0.000 -0.500
contrast analysis:
# iat
contrast( emmeans(vr.models[[1]], ~ time | condition))## condition = b:
## contrast estimate SE df t.ratio p.value
## time1 effect 0.00595 0.0482 66 0.124 0.9020
## time2 effect -0.00595 0.0482 66 -0.124 0.9020
##
## condition = a:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.05221 0.0482 66 -1.084 0.2824
## time2 effect 0.05221 0.0482 66 1.084 0.2824
##
## condition = c:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.05172 0.0482 66 -1.073 0.2870
## time2 effect 0.05172 0.0482 66 1.073 0.2870
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: fdr method for 2 tests
# ccs
contrast( emmeans(vr.models[[2]], ~ time | condition))## condition = b:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.000218 0.0104 66 -0.021 0.9834
## time2 effect 0.000218 0.0104 66 0.021 0.9834
##
## condition = a:
## contrast estimate SE df t.ratio p.value
## time1 effect 0.003796 0.0104 66 0.365 0.7163
## time2 effect -0.003796 0.0104 66 -0.365 0.7163
##
## condition = c:
## contrast estimate SE df t.ratio p.value
## time1 effect 0.018284 0.0104 66 1.758 0.0834
## time2 effect -0.018284 0.0104 66 -1.758 0.0834
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: fdr method for 2 tests
# nr
contrast( emmeans(vr.models[[3]], ~ time | condition))## condition = b:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.0455 0.0299 66 -1.521 0.1330
## time2 effect 0.0455 0.0299 66 1.521 0.1330
##
## condition = a:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.0569 0.0299 66 -1.901 0.0616
## time2 effect 0.0569 0.0299 66 1.901 0.0616
##
## condition = c:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.0124 0.0299 66 -0.415 0.6796
## time2 effect 0.0124 0.0299 66 0.415 0.6796
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: fdr method for 2 tests
# nep
contrast( emmeans(vr.models[[4]], ~ time | condition))## condition = b:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.0580 0.0273 66 -2.121 0.0377
## time2 effect 0.0580 0.0273 66 2.121 0.0377
##
## condition = a:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.0623 0.0273 66 -2.280 0.0258
## time2 effect 0.0623 0.0273 66 2.280 0.0258
##
## condition = c:
## contrast estimate SE df t.ratio p.value
## time1 effect -0.0188 0.0273 66 -0.689 0.4931
## time2 effect 0.0188 0.0273 66 0.689 0.4931
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: fdr method for 2 tests
For the three VE conditions we need ot test the predictor condition
with model comparisons.
compare.models <- function(model){
model0 <- update(model, .~. - time:condition)
anova(model0, model)
}
lapply(vr.models, compare.models)## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## refitting model(s) with ML (instead of REML)
## [[1]]
## Data: dat
## Models:
## model0: iat ~ condition + time + (1 | id)
## model: iat ~ condition * time + (1 | id)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## model0 6 168.31 185.87 -78.155 156.31
## model 8 171.31 194.73 -77.655 155.31 1.0001 2 0.6065
##
## [[2]]
## Data: dat
## Models:
## model0: ccs_bc ~ condition + time + (1 | id)
## model: ccs_bc ~ condition * time + (1 | id)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## model0 6 -172.93 -155.37 92.464 -184.93
## model 8 -170.74 -147.32 93.368 -186.74 1.8068 2 0.4052
##
## [[3]]
## Data: dat
## Models:
## model0: nr ~ condition + time + (1 | id)
## model: nr ~ condition * time + (1 | id)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## model0 6 90.456 108.02 -39.228 78.456
## model 8 93.220 116.64 -38.610 77.220 1.2358 2 0.5391
##
## [[4]]
## Data: dat
## Models:
## model0: nep ~ condition + time + (1 | id)
## model: nep ~ condition * time + (1 | id)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## model0 6 85.962 103.53 -36.981 73.962
## model 8 88.376 111.79 -36.188 72.376 1.5864 2 0.4524
##
## [[5]]
## Data: dat
## Models:
## model0: env_pc ~ condition + time + (1 | id)
## model: env_pc ~ condition * time + (1 | id)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## model0 6 371.07 388.63 -179.53 359.07
## model 8 374.64 398.06 -179.32 358.64 0.4205 2 0.8104
The condition:time interaction did not significantly add to the explained variance.
lapply(presence.models, FUN = lmerTest:::summary.lmerModLmerTest)## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## [[1]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: iat ~ ipq * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 163.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.69457 -0.54823 -0.02948 0.53493 2.01632
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.1131 0.3363
## Residual 0.1080 0.3286
## Number of obs: 130, groups: id, 65
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.58774 0.66781 101.74722 -0.880 0.381
## ipq 0.14043 0.14134 101.74722 0.994 0.323
## time -0.09185 0.38404 63.00001 -0.239 0.812
## ipq:time 0.03446 0.08128 63.00001 0.424 0.673
##
## Correlation of Fixed Effects:
## (Intr) ipq time
## ipq -0.989
## time -0.863 0.853
## ipq:time 0.853 -0.863 -0.989
##
## [[2]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ccs ~ ipq * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 120.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.7904 -0.3820 -0.1145 0.3312 2.1549
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.22587 0.4753
## Residual 0.03731 0.1931
## Number of obs: 130, groups: id, 65
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.11894 0.53069 121.79391 3.993 0.000112 ***
## ipq -0.14045 0.11232 121.79391 -1.251 0.213506
## time -0.10019 0.22573 63.00000 -0.444 0.658668
## ipq:time 0.01788 0.04777 63.00000 0.374 0.709468
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ipq time
## ipq -0.989
## time -0.638 0.631
## ipq:time 0.631 -0.638 -0.989
##
## [[3]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: nr ~ ipq * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 104
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.95321 -0.55273 -0.02821 0.50567 1.89383
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.14358 0.3789
## Residual 0.04248 0.2061
## Number of obs: 130, groups: id, 65
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.63662 0.49306 125.31336 7.376 1.96e-11 ***
## ipq 0.03827 0.10435 125.31336 0.367 0.714
## time -0.08722 0.24088 63.00001 -0.362 0.718
## ipq:time 0.03467 0.05098 63.00001 0.680 0.499
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ipq time
## ipq -0.989
## time -0.733 0.725
## ipq:time 0.725 -0.733 -0.989
##
## [[4]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: nep ~ ipq * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 85.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.41089 -0.54793 -0.05323 0.49528 1.82764
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.13287 0.3645
## Residual 0.03485 0.1867
## Number of obs: 130, groups: id, 65
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.45098 0.45794 125.94330 7.536 8.3e-12 ***
## ipq 0.05561 0.09692 125.94330 0.574 0.567
## time 0.01510 0.21816 63.00000 0.069 0.945
## ipq:time 0.01762 0.04617 63.00000 0.382 0.704
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ipq time
## ipq -0.989
## time -0.715 0.706
## ipq:time 0.706 -0.715 -0.989
##
## [[5]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: env_pc ~ ipq * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 348.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.70780 -0.41684 -0.02183 0.43990 1.79021
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 1.210 1.100
## Residual 0.254 0.504
## Number of obs: 130, groups: id, 65
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -2.05376 1.30141 125.23350 -1.578 0.117
## ipq 0.35511 0.27543 125.23350 1.289 0.200
## time -0.01667 0.58900 62.99999 -0.028 0.978
## ipq:time 0.06329 0.12466 62.99999 0.508 0.613
##
## Correlation of Fixed Effects:
## (Intr) ipq time
## ipq -0.989
## time -0.679 0.671
## ipq:time 0.671 -0.679 -0.989
lapply(sod.models, FUN = lmerTest:::summary.lmerModLmerTest)## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## Coercing object to class 'lmerModLmerTest'
## [[1]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: iat ~ sod * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 176.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.80798 -0.56967 0.02637 0.60711 1.76928
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.1244 0.3528
## Residual 0.1045 0.3233
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.109157 0.481524 111.121118 0.227 0.821
## sod -0.006195 0.094734 111.121118 -0.065 0.948
## time -0.254809 0.273689 67.000002 -0.931 0.355
## sod:time 0.064295 0.053845 67.000002 1.194 0.237
##
## Correlation of Fixed Effects:
## (Intr) sod time
## sod -0.980
## time -0.853 0.835
## sod:time 0.835 -0.853 -0.980
##
## [[2]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ccs ~ sod * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 135.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.73181 -0.38435 -0.09369 0.32377 2.19186
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.22349 0.4727
## Residual 0.04139 0.2034
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.65984 0.39278 131.61473 4.226 4.42e-05 ***
## sod -0.04011 0.07727 131.61473 -0.519 0.605
## time 0.07598 0.17224 67.00001 0.441 0.661
## sod:time -0.01672 0.03389 67.00001 -0.493 0.623
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sod time
## sod -0.980
## time -0.658 0.644
## sod:time 0.644 -0.658 -0.980
##
## [[3]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: nr ~ sod * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 109.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.91062 -0.53432 -0.01933 0.52449 1.83663
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.14449 0.3801
## Residual 0.04107 0.2027
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.98028 0.35411 133.57257 11.240 <2e-16 ***
## sod -0.03485 0.06967 133.57257 -0.500 0.618
## time -0.03995 0.17159 67.00000 -0.233 0.817
## sod:time 0.02341 0.03376 67.00000 0.693 0.490
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sod time
## sod -0.980
## time -0.727 0.712
## sod:time 0.712 -0.727 -0.980
##
## [[4]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: nep ~ sod * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 91.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.46069 -0.58390 -0.04105 0.50130 1.89785
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.13382 0.3658
## Residual 0.03445 0.1856
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.33827 0.33121 133.97744 10.079 <2e-16 ***
## sod 0.07682 0.06516 133.97744 1.179 0.241
## time 0.18737 0.15714 67.00000 1.192 0.237
## sod:time -0.01900 0.03092 67.00000 -0.615 0.541
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sod time
## sod -0.980
## time -0.712 0.697
## sod:time 0.697 -0.712 -0.980
##
## [[5]]
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: env_pc ~ sod * time + (1 | id)
## Data: dat
##
## REML criterion at convergence: 371.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.76166 -0.43974 0.00888 0.44844 1.81302
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 1.2802 1.1315
## Residual 0.2437 0.4937
## Number of obs: 138, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.956276 0.946384 132.028220 -1.010 0.314
## sod 0.115718 0.186190 132.028220 0.622 0.535
## time -0.001958 0.417982 66.999999 -0.005 0.996
## sod:time 0.052956 0.082233 67.000000 0.644 0.522
##
## Correlation of Fixed Effects:
## (Intr) sod time
## sod -0.980
## time -0.662 0.649
## sod:time 0.649 -0.662 -0.980
lower <- round(cor(data[dvs[-5]]),2)
lower[upper.tri(lower)] <- ""
lower <- as.data.frame(lower)
rownames(lower) <- toupper(rownames(lower))
colnames(lower) <- toupper(colnames(lower))
print(xtable(lower, label = "tab:cortable",
caption = "Correlation table of the four environmental attitudes measures. Computed on the untranformed CCS scale."), file = "analysisOutputs/tables/correlationtable.tex")First, we define a couple of helping functions
#lmermods = all.models
# x <- lmermods[[1]]
make.x.table <- function(lmermods, save = TRUE, add = ""){
#lapply(lmermods, function(x) formula(x)[2])
dvs <- as.character(lapply(lmermods, function(x) as.character(formula(x)[2])))
iv <- sub("\\ .*", "", lmermods[[1]]@call$formula[3])
helpf <- function(x){
# get fixed effects table
fix.temp <- round(as.data.frame(lmerTest:::summary.lmerModLmerTest(x)$coefficients), 3)
# calculate and round confidence intervals
conf.temp <- as.data.frame(confint(x, method = "profile"))
conf.temp <- round(conf.temp, 3)
conf.temp$CI <- paste("[", conf.temp[,1], "; ", conf.temp[,2],"]", sep = "")
# put together
fix.temp$CI <- conf.temp$CI[!startsWith(rownames(conf.temp), ".")]
fix.temp["DV"] <- ""
#fix.temp[paste(dv, " ~", sep = "")][1,] <-paste(formula(x))[3]
fix.temp["DV"][1,] <- "deleteme"
fix.temp <- rownames_to_column(fix.temp, var = "Coef")
fix.temp <- fix.temp[, c(8, 1, 2, 7, 5, 4, 6)]
colnames(fix.temp)[7] <- "p value"
# return value
return(fix.temp)
}
# confidence intervals:
fixed.effects.list <- lapply(lmermods, FUN = helpf)
fixed.effects.df <- do.call("rbind", fixed.effects.list)
fixed.effects.df$DV[fixed.effects.df$DV=="deleteme"] <- dvs
#l.temp <- length(rownames(fixed.effects.df))
#cond <- toupper(strsplit(rownames(fixed.effects.df)[l.temp], split = " ")[[1]][5])
rownames(fixed.effects.df) <- NULL
tabl <- xtable(fixed.effects.df,
caption = paste(toupper(iv), "Models", add),
label = paste("tab:",add , iv, "-models", sep = ""))
if(save){
print.xtable(tabl, file = paste("analysisOutputs/tables/", add, iv, "-modeltable.tex", sep = ""),
include.rownames=FALSE,
hline.after = c(-1, c(which(fixed.effects.df[1]!="")-1), nrow(tabl))#,
#add.to.row = list(list(-1), c(paste("\\hspace{-3mm}", toupper(dv), "$\\sim$%")))
)
}else{
print.xtable(tabl, #file = paste("analysisOutputs/tables/", add, dv, "-by", cond, "-modeltable.tex", sep = ""),
include.rownames=FALSE,
hline.after = c(-1, c(which(fixed.effects.df[1]!="")-1), nrow(tabl))#,
#add.to.row = list(list(-1), c(paste("\\hspace{-3mm}", toupper(dv), "$\\sim$%")))
)}
# which(fixed.effects.df[2]!="")-1
# this saves directly into my .tex folder
}Then we create and save the tables:
make.x.table(all.models[-5], save = FALSE)## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Warning in nextpar(mat, cc, i, delta, lowcut, upcut): unexpected decrease in
## profile: using minstep
## Warning in FUN(X[[i]], ...): non-monotonic profile for .sig02
## Warning in confint.thpr(pp, level = level, zeta = zeta): bad spline fit
## for .sig02: falling back to linear interpolation
## % latex table generated in R 4.2.1 by xtable 1.8-4 package
## % Tue Nov 1 16:00:50 2022
## \begin{table}[ht]
## \centering
## \begin{tabular}{llrlrrr}
## \hline
## DV & Coef & Estimate & CI & t value & df & p value \\
## \hline
## iat & (Intercept) & 0.23 & [0.106; 0.355] & 3.63 & 225.16 & 0.00 \\
## & time & -0.01 & [-0.085; 0.066] & -0.23 & 20.40 & 0.82 \\
## & type1 & -0.15 & [-0.276; -0.028] & -2.39 & 225.16 & 0.02 \\
## & time:type1 & 0.07 & [-0.001; 0.15] & 1.83 & 20.40 & 0.08 \\
## \hline
## ccs\_bc & (Intercept) & 0.23 & [0.199; 0.27] & 12.84 & 278.36 & 0.00 \\
## & time & -0.01 & [-0.029; 0.006] & -1.32 & 140.00 & 0.19 \\
## & type1 & -0.00 & [-0.038; 0.034] & -0.12 & 278.36 & 0.91 \\
## & time:type1 & -0.00 & [-0.02; 0.015] & -0.32 & 140.00 & 0.75 \\
## \hline
## nr & (Intercept) & 3.82 & [3.71; 3.925] & 69.64 & 268.10 & 0.00 \\
## & time & 0.04 & [-0.009; 0.085] & 1.51 & 9.57 & 0.16 \\
## & type1 & -0.01 & [-0.118; 0.096] & -0.20 & 268.10 & 0.84 \\
## & time:type1 & 0.04 & [-0.008; 0.086] & 1.56 & 9.57 & 0.15 \\
## \hline
## nep & (Intercept) & 3.76 & [3.663; 3.849] & 79.18 & 276.21 & 0.00 \\
## & time & 0.07 & [0.03; 0.117] & 3.23 & 14.89 & 0.01 \\
## & type1 & -0.04 & [-0.128; 0.058] & -0.74 & 276.21 & 0.46 \\
## & time:type1 & 0.02 & [-0.025; 0.063] & 0.83 & 14.89 & 0.42 \\
## \hline
## \end{tabular}
## \caption{TIME Models }
## \label{tab:time-models}
## \end{table}
make.x.table(vr.models[-5], save = FALSE)## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## % latex table generated in R 4.2.1 by xtable 1.8-4 package
## % Tue Nov 1 16:00:52 2022
## \begin{table}[ht]
## \centering
## \begin{tabular}{llrlrrr}
## \hline
## DV & Coef & Estimate & CI & t value & df & p value \\
## \hline
## iat & (Intercept) & 0.08 & [-0.109; 0.266] & 0.81 & 106.86 & 0.42 \\
## & condition1 & 0.10 & [-0.166; 0.364] & 0.72 & 106.86 & 0.47 \\
## & condition2 & -0.23 & [-0.491; 0.039] & -1.65 & 106.86 & 0.10 \\
## & time & 0.07 & [-0.043; 0.173] & 1.17 & 66.00 & 0.24 \\
## & condition1:time & -0.08 & [-0.23; 0.076] & -0.98 & 66.00 & 0.33 \\
## & condition2:time & 0.04 & [-0.114; 0.192] & 0.50 & 66.00 & 0.62 \\
## \hline
## ccs\_bc & (Intercept) & 0.23 & [0.181; 0.283] & 8.84 & 131.56 & 0.00 \\
## & condition1 & -0.06 & [-0.129; 0.014] & -1.54 & 131.56 & 0.12 \\
## & condition2 & 0.01 & [-0.057; 0.086] & 0.38 & 131.56 & 0.70 \\
## & time & -0.01 & [-0.038; 0.009] & -1.21 & 66.00 & 0.23 \\
## & condition1:time & 0.01 & [-0.018; 0.048] & 0.88 & 66.00 & 0.38 \\
## & condition2:time & 0.01 & [-0.026; 0.04] & 0.41 & 66.00 & 0.68 \\
## \hline
## nr & (Intercept) & 3.81 & [3.674; 3.939] & 55.49 & 129.34 & 0.00 \\
## & condition1 & 0.10 & [-0.091; 0.283] & 0.99 & 129.34 & 0.33 \\
## & condition2 & -0.29 & [-0.476; -0.102] & -2.98 & 129.34 & 0.00 \\
## & time & 0.08 & [0.009; 0.144] & 2.21 & 66.00 & 0.03 \\
## & condition1:time & 0.01 & [-0.081; 0.11] & 0.30 & 66.00 & 0.77 \\
## & condition2:time & 0.04 & [-0.058; 0.132] & 0.76 & 66.00 & 0.45 \\
## \hline
## nep & (Intercept) & 3.72 & [3.591; 3.85] & 55.49 & 132.00 & 0.00 \\
## & condition1 & -0.04 & [-0.228; 0.138] & -0.48 & 132.00 & 0.63 \\
## & condition2 & -0.06 & [-0.243; 0.123] & -0.63 & 132.00 & 0.53 \\
## & time & 0.09 & [0.031; 0.154] & 2.94 & 66.00 & 0.01 \\
## & condition1:time & 0.02 & [-0.064; 0.11] & 0.52 & 66.00 & 0.60 \\
## & condition2:time & 0.03 & [-0.055; 0.119] & 0.71 & 66.00 & 0.48 \\
## \hline
## \end{tabular}
## \caption{CONDITION Models }
## \label{tab:condition-models}
## \end{table}
make.x.table(all.models[-5], save = TRUE)## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Warning in nextpar(mat, cc, i, delta, lowcut, upcut): unexpected decrease in
## profile: using minstep
## Warning in FUN(X[[i]], ...): non-monotonic profile for .sig02
## Warning in confint.thpr(pp, level = level, zeta = zeta): bad spline fit
## for .sig02: falling back to linear interpolation
make.x.table(vr.models[-5], save = TRUE)## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
## Coercing object to class 'lmerModLmerTest'
## Computing profile confidence intervals ...
I would like to get a table / data structure that gives me the mean values for each combination of relevant time and condition ### CI plot helping functions
ci.plot <- function(colorby = "condition"){
#colorby = "condition"
#df <- vr.res.md.comp.mean
pos <- ifelse(colorby=="condition", "dodge2", "identity")
function(df){
df$cond <- df[[colorby]]
if(colorby != "condition"){
df <- df %>% dplyr::filter(condition=="a"|condition=="text" )
}
ggplot(df, aes(x = time, y = ml.value, color = cond)) +
facet_wrap(~dv, scales = "free") +
geom_line(position = position_jitterdodge(dodge.width = 0.2, jitter.width = 0, jitter.height = 0)) +
geom_point(position = position_jitterdodge(dodge.width = 0.2, jitter.width = 0, jitter.height = 0)) +
geom_errorbar(aes(ymin = df$`2.5 %`, ymax = df$`97.5 %`), position = "dodge2", width = 0.2) +
ggthemes::theme_tufte() +
ylab("scale value") +
scale_x_discrete() +
xlim(c("before", "after"))
}
}
ci.plot.vr <- ci.plot("type")
ci.plot.condition <- ci.plot("condition")
#ci.plot.condition(vr.res.md.comp.mean)
#ci.plot.vr(vr.nonvr.mean)cond.mean.ci <- function(data.temp){
predict.fun <- function(my.lmm) {
# my.lmm <- md
#data.temp <- df.predicted.vr
predict(my.lmm, newdata = data.temp, re.form = NA) # This is predict.merMod
#data.temp$x <- x
#data.temp$y <- rep(x[data.temp$time==1]-x[data.temp$time==2], each = 2)
#y <- x
}
function(md){
data.temp$ml.value <- predict.fun(md)
# Make predictions in 100 bootstraps of the LMM. Use these to get confidence
# intervals.
dv <- as.character(formula(md))[2]
lmm.boots <- bootMer(md, predict.fun, nsim = 1000,
#parallel = "multicore",
ncpus = (detectCores(all.tests = FALSE, logical = TRUE)-1),
type = "semiparametric",
use.u = T)
data.temp <- cbind("dv" = dv, data.temp, confint(lmm.boots))
return(data.temp)
}
}df.predicted.all <- data.frame(
id = rep(as.factor(1:6), each = 2),
time = rep(1:2, times = 6),
condition = rep(levels(as.factor(data$condition)), each = 2),
vr = rep(c(TRUE, FALSE), each = 6),
type = rep(c("vr", "control"), each = 6)
)
df.predicted.vr <- df.predicted.all %>% filter(vr)## filter: removed 6 rows (50%), 6 rows remaining
Create function for each option:
cond.mean.ci.all <- cond.mean.ci(data = df.predicted.all)
cond.mean.ci.vr <- cond.mean.ci(data = df.predicted.vr)First comparing VE to control conditions
# Bootstrap CI's
vr.nonvr.mean.list <- lapply(all.models[1:4], cond.mean.ci.all)
vr.nonvr.mean <- do.call("rbind", vr.nonvr.mean.list)(vr.ci.plot <- ci.plot.vr(vr.nonvr.mean) +
guides(color=guide_legend(title="VR")))## Scale for 'x' is already present. Adding another scale for 'x', which will
## replace the existing scale.
## Warning: Use of `df$`2.5 %`` is discouraged. Use `2.5 %` instead.
## Warning: Use of `df$`97.5 %`` is discouraged. Use `97.5 %` instead.
Then for only between the VE conditions:
onlyvr.cond.mean.list <- lapply(vr.models[1:4], cond.mean.ci.vr)
onlyvr.cond.mean <- do.call("rbind", onlyvr.cond.mean.list)(cond.ci.plot <- ci.plot.condition(onlyvr.cond.mean))## Scale for 'x' is already present. Adding another scale for 'x', which will
## replace the existing scale.
## Warning: Use of `df$`2.5 %`` is discouraged. Use `2.5 %` instead.
## Warning: Use of `df$`97.5 %`` is discouraged. Use `97.5 %` instead.
reverse <- function(lambda){
function(x){
exp(log(lambda * x + 1) / lambda)
}
}
reverse_ccs <- reverse(lambda = lambda_ccs)which.ccs <- which(onlyvr.cond.mean$dv=="ccs_bc")
which.ccs2 <- which(vr.nonvr.mean$dv=="ccs_bc")
vr.nonvr.mean2 <- vr.nonvr.mean
vr.nonvr.mean2[which.ccs2,c("ml.value", "2.5 %","97.5 %")] <- reverse_ccs(vr.nonvr.mean[which.ccs2,c("ml.value", "2.5 %","97.5 %")] )
onlyvr.cond.mean2 <- onlyvr.cond.mean
onlyvr.cond.mean2[which.ccs,c("ml.value", "2.5 %","97.5 %")] <- reverse_ccs(onlyvr.cond.mean[which.ccs,c("ml.value", "2.5 %","97.5 %")] )
# change dv names:
onlyvr.cond.mean2$dv[onlyvr.cond.mean2$dv=="ccs_bc"] <- "ccs"
vr.nonvr.mean2$dv[vr.nonvr.mean2$dv=="ccs_bc"] <- "ccs"
onlyvr.cond.mean2$dv <- toupper(onlyvr.cond.mean2$dv)
vr.nonvr.mean2$dv <- toupper(vr.nonvr.mean2$dv)
# change condition names:
onlyvr.cond.mean2 <-tibble( onlyvr.cond.mean2 ) %>%
dplyr::mutate(condition = ifelse(condition =="b", "real+",
ifelse(condition == "c", "real-",
ifelse(condition == "a", "abstract", condition))))(cond.ci.plot2 <- ci.plot.condition(onlyvr.cond.mean2)+
guides(color=guide_legend(title="condition")))## Scale for 'x' is already present. Adding another scale for 'x', which will
## replace the existing scale.
## Warning: Use of `df$`2.5 %`` is discouraged. Use `2.5 %` instead.
## Warning: Use of `df$`97.5 %`` is discouraged. Use `97.5 %` instead.
(vr.ci.plot2 <- ci.plot.vr(vr.nonvr.mean2) +
guides(color=guide_legend(title="type")))## Scale for 'x' is already present. Adding another scale for 'x', which will
## replace the existing scale.
## Warning: Use of `df$`2.5 %`` is discouraged. Use `2.5 %` instead.
## Warning: Use of `df$`97.5 %`` is discouraged. Use `97.5 %` instead.
save plots
pdf(file = "analysisOutputs/plots/vr_ci_plot2.pdf", width = 7, height = 5)
vr.ci.plot2## Warning: Use of `df$`2.5 %`` is discouraged. Use `2.5 %` instead.
## Warning: Use of `df$`97.5 %`` is discouraged. Use `97.5 %` instead.
dev.off()## quartz_off_screen
## 2
pdf(file = "analysisOutputs/plots/cond_ci_plot2.pdf", width = 7, height = 5)
cond.ci.plot2## Warning: Use of `df$`2.5 %`` is discouraged. Use `2.5 %` instead.
## Warning: Use of `df$`97.5 %`` is discouraged. Use `97.5 %` instead.
dev.off()## quartz_off_screen
## 2
# save the plots
tikz(file = "analysisOutputs/plots/check.tex", width = 7, height = 5)
grid::grid.draw(shift_legend(vr_eval_plot))## Warning: Removed 304 rows containing non-finite values (stat_ydensity).
## Warning: Removed 304 rows containing missing values (geom_point).
dev.off()## quartz_off_screen
## 2
contrasts(data$vr) <- NULL
contrasts(data$condition) <- NULL
class(data$vr)## [1] "factor"
data.desc <- data %>% filter(vr == TRUE, time == 1) %>%
ungroup()## filter: removed 215 rows (76%), 69 rows remaining
## ungroup: no grouping variables
scls <- c("excitement", "graphically pleasing", "pleasant", "realistic", "enjoyment")
forms <- paste("vr_eval",1:5, " ~ condition", sep = "")
vr_evals <- list()
for(i in 1:5){
paste("vr_eval", i, " ~ condition", sep = "")
formul <- as.formula(paste("vr_eval", i, " ~ condition", sep = ""))
vr_evals[["lm"]][[paste("vr_eval", i, ": ", scls[i])]] <- lm.temp <- lm(data.desc, formula = formul)
vr_evals[["comparisons"]][[scls[i]]] <- anova(lm.temp)
}
vr_evals## $lm
## $lm$`vr_eval 1 : excitement`
##
## Call:
## lm(formula = formul, data = data.desc)
##
## Coefficients:
## (Intercept) conditiona conditionc
## 6.34783 -0.17391 0.08696
##
##
## $lm$`vr_eval 2 : graphically pleasing`
##
## Call:
## lm(formula = formul, data = data.desc)
##
## Coefficients:
## (Intercept) conditiona conditionc
## 5.9565 -1.0435 -0.6087
##
##
## $lm$`vr_eval 3 : pleasant`
##
## Call:
## lm(formula = formul, data = data.desc)
##
## Coefficients:
## (Intercept) conditiona conditionc
## 6.0000 -0.1739 0.1739
##
##
## $lm$`vr_eval 4 : realistic`
##
## Call:
## lm(formula = formul, data = data.desc)
##
## Coefficients:
## (Intercept) conditiona conditionc
## 5.4348 -1.0000 -0.3478
##
##
## $lm$`vr_eval 5 : enjoyment`
##
## Call:
## lm(formula = formul, data = data.desc)
##
## Coefficients:
## (Intercept) conditiona conditionc
## 6.30435 -0.08696 0.17391
##
##
##
## $comparisons
## $comparisons$excitement
## Analysis of Variance Table
##
## Response: vr_eval1
## Df Sum Sq Mean Sq F value Pr(>F)
## condition 2 0.812 0.4058 0.6667 0.5168
## Residuals 66 40.174 0.6087
##
## $comparisons$`graphically pleasing`
## Analysis of Variance Table
##
## Response: vr_eval2
## Df Sum Sq Mean Sq F value Pr(>F)
## condition 2 12.638 6.3188 3.208 0.04682 *
## Residuals 66 130.000 1.9697
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## $comparisons$pleasant
## Analysis of Variance Table
##
## Response: vr_eval3
## Df Sum Sq Mean Sq F value Pr(>F)
## condition 2 1.391 0.69565 0.4307 0.6519
## Residuals 66 106.609 1.61528
##
## $comparisons$realistic
## Analysis of Variance Table
##
## Response: vr_eval4
## Df Sum Sq Mean Sq F value Pr(>F)
## condition 2 11.855 5.9275 4.49 0.01485 *
## Residuals 66 87.130 1.3202
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## $comparisons$enjoyment
## Analysis of Variance Table
##
## Response: vr_eval5
## Df Sum Sq Mean Sq F value Pr(>F)
## condition 2 0.812 0.40580 0.552 0.5784
## Residuals 66 48.522 0.73518
summary(vr_evals$lm$`vr_eval 2 : graphically pleasing`)##
## Call:
## lm(formula = formul, data = data.desc)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3478 -0.9565 0.0870 1.0435 2.0870
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.9565 0.2926 20.354 <2e-16 ***
## conditiona -1.0435 0.4139 -2.521 0.0141 *
## conditionc -0.6087 0.4139 -1.471 0.1461
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.403 on 66 degrees of freedom
## Multiple R-squared: 0.0886, Adjusted R-squared: 0.06098
## F-statistic: 3.208 on 2 and 66 DF, p-value: 0.04682
summary(vr_evals$lm$`vr_eval 4 : realistic`)##
## Call:
## lm(formula = formul, data = data.desc)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0870 -0.4348 0.5652 0.5652 1.9130
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.4348 0.2396 22.685 < 2e-16 ***
## conditiona -1.0000 0.3388 -2.951 0.00438 **
## conditionc -0.3478 0.3388 -1.027 0.30836
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.149 on 66 degrees of freedom
## Multiple R-squared: 0.1198, Adjusted R-squared: 0.09309
## F-statistic: 4.49 on 2 and 66 DF, p-value: 0.01485
Here we see that only the realism was rated clearly differently between the conditions, although excitement and graphical pleasantness are borderline.
vars <- c("sod", "ipq")
forms <- paste(vars, " ~ condition", sep = "")
sod_ipq_list <- list()
for(i in 1:2){
formul <- as.formula(forms[i])
sod_ipq_list[["lm"]][[vars[i]]] <- lm.temp <- lm(data.desc, formula = formul)
sod_ipq_list[["comparisons"]][[scls[i]]] <- anova(lm.temp)
}
sod_ipq_list## $lm
## $lm$sod
##
## Call:
## lm(formula = formul, data = data.desc)
##
## Coefficients:
## (Intercept) conditiona conditionc
## 4.888889 0.280193 -0.009662
##
##
## $lm$ipq
##
## Call:
## lm(formula = formul, data = data.desc)
##
## Coefficients:
## (Intercept) conditiona conditionc
## 4.7112 -0.2554 0.1324
##
##
##
## $comparisons
## $comparisons$excitement
## Analysis of Variance Table
##
## Response: sod
## Df Sum Sq Mean Sq F value Pr(>F)
## condition 2 1.247 0.62337 0.5808 0.5623
## Residuals 66 70.834 1.07324
##
## $comparisons$`graphically pleasing`
## Analysis of Variance Table
##
## Response: ipq
## Df Sum Sq Mean Sq F value Pr(>F)
## condition 2 1.635 0.81748 1.632 0.2038
## Residuals 62 31.057 0.50092
Now comparing vr to non-vr
vars <- c("sod", "ipq")
forms <- paste(vars, " ~ vr", sep = "")
sod_ipq_vr_list <- list()
for(i in 1:2){
formul <- as.formula(forms[i])
sod_ipq_vr_list[["lm"]][[vars[i]]] <- lm.temp <- lm(data, formula = formul, subset = time == 1)
sod_ipq_vr_list[["comparisons"]][[scls[i]]] <- anova(lm.temp)
}
sod_ipq_vr_list## $lm
## $lm$sod
##
## Call:
## lm(formula = formul, data = data, subset = time == 1)
##
## Coefficients:
## (Intercept) vrTRUE
## 4.6250 0.3541
##
##
## $lm$ipq
##
## Call:
## lm(formula = formul, data = data, subset = time == 1)
##
## Coefficients:
## (Intercept) vrTRUE
## 3.586 1.085
##
##
##
## $comparisons
## $comparisons$excitement
## Analysis of Variance Table
##
## Response: sod
## Df Sum Sq Mean Sq F value Pr(>F)
## vr 1 2.232 2.2323 1.886 0.173
## Residuals 91 107.706 1.1836
##
## $comparisons$`graphically pleasing`
## Analysis of Variance Table
##
## Response: ipq
## Df Sum Sq Mean Sq F value Pr(>F)
## vr 1 20.639 20.639 37.323 2.739e-08 ***
## Residuals 87 48.110 0.553
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
data.desc.all <- subset(data, subset = time==1) %>%
ungroup()## ungroup: no grouping variables
scls <- c("excitement", "graphically pleasing", "pleasant", "realistic", "enjoyment")
forms <- paste("vr_eval",1:5, " ~ condition", sep = "")
vr_evals_all <- list("lm" = list(), "comparisons" = list())
for(i in 1:5){
#i <- 1
paste("vr_eval", i, " ~ condition", sep = "")
formul <- as.formula(paste("vr_eval", i, " ~ vr + (1|condition)", sep = ""))
vr_evals_all[["lm"]][[scls[i]]] <- mem.temp <- lmer(data.desc.all, formula = formul)
vr_evals_all[["comparisons"]][[scls[i]]] <- anova(mem.temp)
}## boundary (singular) fit: see help('isSingular')
summary(lm(data.desc.all, formula = ipq ~ vr))##
## Call:
## lm(formula = ipq ~ vr, data = data.desc.all)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.65774 -0.52857 -0.02857 0.54286 1.62798
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.5863 0.1518 23.626 < 2e-16 ***
## vrTRUE 1.0851 0.1776 6.109 2.74e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7436 on 87 degrees of freedom
## (53 observations deleted due to missingness)
## Multiple R-squared: 0.3002, Adjusted R-squared: 0.2922
## F-statistic: 37.32 on 1 and 87 DF, p-value: 2.739e-08
summary(lm(data.desc.all, formula = sod ~ vr))##
## Call:
## lm(formula = sod ~ vr, data = data.desc.all)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.73611 -0.53462 -0.09018 0.70833 2.37500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.6250 0.2221 20.827 <2e-16 ***
## vrTRUE 0.3541 0.2578 1.373 0.173
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.088 on 91 degrees of freedom
## (49 observations deleted due to missingness)
## Multiple R-squared: 0.0203, Adjusted R-squared: 0.009539
## F-statistic: 1.886 on 1 and 91 DF, p-value: 0.173
Looks like VR has an impact on enjoyment and on excitement. It seems to be a positive impact! VR also leads to larger presence, but not to larger suspension of disbelief than video.