Study 4: Extroversion Data Analysis
Model 3 Results
R. Noah Padgett
2022-01-17
Last updated: 2022-01-20
Checks: 4 2
Knit directory: Padgett-Dissertation/
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# Load packages & utility functions
source("code/load_packages.R")
source("code/load_utility_functions.R")
# environment options
options(scipen = 999, digits=3)Describing the Observed Data
# Load diffIRT package with data
library(diffIRT)
data("extraversion")
mydata <- na.omit(extraversion)
# separate data then recombine
d1 <- mydata %>%
as.data.frame() %>%
select(contains("X"))%>%
mutate(id = 1:n()) %>%
pivot_longer(
cols=contains("X"),
names_to = c("item"),
values_to = "Response"
) %>%
mutate(
item = ifelse(nchar(item)==4,substr(item, 3,3),substr(item, 3,4))
)
d2 <- mydata %>%
as.data.frame() %>%
select(contains("T"))%>%
mutate(id = 1:n()) %>%
pivot_longer(
cols=starts_with("T"),
names_to = c("item"),
values_to = "Time"
) %>%
mutate(
item = ifelse(nchar(item)==4,substr(item, 3,3),substr(item, 3,4))
)
dat <- left_join(d1, d2)Joining, by = c("id", "item")dat_sum <- dat %>%
select(item, Response, Time) %>%
group_by(item) %>%
summarize(
M1 = mean(Response, na.rm=T),
Mt = mean(Time, na.rm=T),
SDt = sd(Time, na.rm=T),
Mlogt = mean(log(Time), na.rm=T),
)
colnames(dat_sum) <-
c(
"Item",
"Proportion Endorsed",
"Mean Response Time",
"SD Response Time",
"Mean Log Response Time"
)
kable(dat_sum, format = "html", digits = 3) %>%
kable_styling(full_width = T)| Item | Proportion Endorsed | Mean Response Time | SD Response Time | Mean Log Response Time |
|---|---|---|---|---|
| 1 | 0.739 | 1.488 | 0.805 | 0.288 |
| 10 | 0.866 | 0.979 | 0.520 | -0.115 |
| 2 | 0.535 | 1.354 | 0.648 | 0.208 |
| 3 | 0.852 | 1.115 | 0.632 | 0.002 |
| 4 | 0.923 | 1.001 | 0.664 | -0.114 |
| 5 | 0.542 | 1.301 | 0.706 | 0.163 |
| 6 | 0.901 | 1.255 | 0.682 | 0.119 |
| 7 | 0.944 | 1.143 | 0.546 | 0.054 |
| 8 | 0.965 | 1.067 | 0.575 | -0.030 |
| 9 | 0.824 | 1.728 | 0.745 | 0.463 |
# covariance among items
kable(cov(mydata[,colnames(mydata) %like% "X"]), digits = 3) %>%
kable_styling(full_width = T)| X[1] | X[2] | X[3] | X[4] | X[5] | X[6] | X[7] | X[8] | X[9] | X[10] | |
|---|---|---|---|---|---|---|---|---|---|---|
| X[1] | 0.194 | -0.001 | 0.039 | 0.029 | 0.000 | 0.002 | 0.014 | 0.005 | 0.011 | 0.015 |
| X[2] | -0.001 | 0.251 | 0.023 | 0.006 | 0.077 | 0.011 | 0.002 | 0.012 | 0.031 | 0.030 |
| X[3] | 0.039 | 0.023 | 0.127 | 0.038 | 0.024 | 0.028 | 0.020 | 0.016 | 0.016 | 0.051 |
| X[4] | 0.029 | 0.006 | 0.038 | 0.072 | 0.014 | 0.006 | 0.017 | 0.019 | 0.029 | 0.025 |
| X[5] | 0.000 | 0.077 | 0.024 | 0.014 | 0.250 | 0.004 | 0.017 | 0.005 | 0.032 | 0.031 |
| X[6] | 0.002 | 0.011 | 0.028 | 0.006 | 0.004 | 0.090 | 0.009 | 0.011 | 0.004 | 0.015 |
| X[7] | 0.014 | 0.002 | 0.020 | 0.017 | 0.017 | 0.009 | 0.054 | 0.019 | 0.004 | 0.007 |
| X[8] | 0.005 | 0.012 | 0.016 | 0.019 | 0.005 | 0.011 | 0.019 | 0.034 | 0.008 | 0.009 |
| X[9] | 0.011 | 0.031 | 0.016 | 0.029 | 0.032 | 0.004 | 0.004 | 0.008 | 0.146 | 0.033 |
| X[10] | 0.015 | 0.030 | 0.051 | 0.025 | 0.031 | 0.015 | 0.007 | 0.009 | 0.033 | 0.117 |
# correlation matrix
psych::polychoric(mydata[,colnames(mydata) %like% "X"])Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was doneCall: psych::polychoric(x = mydata[, colnames(mydata) %like% "X"])
Polychoric correlations
X[1] X[2] X[3] X[4] X[5] X[6] X[7] X[8] X[9] X[10]
X[1] 1.00
X[2] -0.01 1.00
X[3] 0.45 0.24 1.00
X[4] 0.50 0.11 0.70 1.00
X[5] 0.00 0.46 0.26 0.23 1.00
X[6] 0.04 0.15 0.50 0.21 0.06 1.00
X[7] 0.32 0.05 0.52 0.58 0.36 0.32 1.00
X[8] 0.18 0.38 0.57 0.71 0.17 0.48 0.78 1.00
X[9] 0.12 0.29 0.24 0.55 0.31 0.08 0.13 0.31 1.00
X[10] 0.19 0.34 0.69 0.54 0.35 0.32 0.22 0.39 0.47 1.00
with tau of
1
X[1] -0.642
X[2] -0.088
X[3] -1.046
X[4] -1.422
X[5] -0.106
X[6] -1.290
X[7] -1.586
X[8] -1.809
X[9] -0.930
X[10] -1.109Model 3: IFA with RT only
Model details
cat(read_file(paste0(w.d, "/code/study_4/model_3.txt")))model {
### Model
for(p in 1:N){
for(i in 1:nit){
# data model
y[p,i] ~ dbern(omega[p,i,2])
# LRV
ystar[p,i] ~ dnorm(lambda[i]*eta[p], 1)
# Pr(nu = 2)
pi[p,i,2] = phi(ystar[p,i] - tau[i,1])
# Pr(nu = 1)
pi[p,i,1] = 1 - phi(ystar[p,i] - tau[i,1])
# MISCLASSIFICATION MODEL
for(c in 1:ncat){
# generate informative prior for misclassificaiton
# parameters based on RT
for(ct in 1:ncat){
alpha[p,i,ct,c] <- ifelse(c == ct,
ilogit(lrt[p,i]),
(1/(ncat-1))*(1-ilogit(lrt[p,i]))
)
}
# sample misclassification parameters using the informative priors
gamma[p,i,c,1:ncat] ~ ddirch(alpha[p,i,c,1:ncat])
# observed category prob (Pr(y=c))
omega[p,i, c] = gamma[p,i,c,1]*pi[p,i,1] +
gamma[p,i,c,2]*pi[p,i,2]
}
}
}
### Priors
# person parameters
for(p in 1:N){
eta[p] ~ dnorm(0, 1) # latent ability
}
for(i in 1:nit){
# Thresholds
tau[i, 1] ~ dnorm(0.0,0.1)
# loadings
lambda[i] ~ dnorm(0, .44)T(0,)
# LRV total variance
# total variance = residual variance + fact. Var.
theta[i] = 1 + pow(lambda[i],2)
# standardized loading
lambda.std[i] = lambda[i]/pow(theta[i],0.5)
}
# compute omega
lambda_sum[1] = lambda[1]
for(i in 2:nit){
#lambda_sum (sum factor loadings)
lambda_sum[i] = lambda_sum[i-1]+lambda[i]
}
reli.omega = (pow(lambda_sum[nit],2))/(pow(lambda_sum[nit],2)+nit)
}Model results
# Save parameters
jags.params <- c("tau", "lambda", "theta", "reli.omega", "lambda.std")
# initial-values
jags.inits <- function(){
list(
"tau"=matrix(c(-0.64, -0.09, -1.05, -1.42, -0.11, -1.29, -1.59, -1.81, -0.93, -1.11),
ncol=1, nrow=10),
"lambda"=rep(0.7,10),
"eta"=rnorm(142),
"ystar"=matrix(c(0.7*rep(rnorm(142),10)), ncol=10)
)
}
jags.data <- list(
y = mydata[,1:10],
lrt = mydata[,11:20],
N = nrow(mydata),
nit = 10,
ncat = 2
)
model.fit <- R2jags::jags(
model = paste0(w.d, "/code/study_4/model_3.txt"),
parameters.to.save = jags.params,
data = jags.data,
n.chains = 4,
n.burnin = 5000,
n.iter = 10000
)module glm loadedCompiling model graph
Resolving undeclared variables
Allocating nodes
Graph information:
Observed stochastic nodes: 1420
Unobserved stochastic nodes: 4422
Total graph size: 34704
Initializing modelprint(model.fit, width=1000)Inference for Bugs model at "C:/Users/noahp/Documents/GitHub/Padgett-Dissertation/code/study_4/model_3.txt", fit using jags,
4 chains, each with 10000 iterations (first 5000 discarded), n.thin = 5
n.sims = 4000 iterations saved
mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff
lambda[1] 1.650 0.910 0.248 0.986 1.514 2.192 3.845 1.03 290
lambda[2] 2.023 0.886 0.616 1.334 1.946 2.614 3.895 1.06 51
lambda[3] 1.984 0.750 0.559 1.462 1.955 2.493 3.446 1.04 260
lambda[4] 1.608 0.957 0.078 0.852 1.560 2.233 3.653 1.13 28
lambda[5] 1.413 0.701 0.333 0.905 1.310 1.814 3.122 1.05 66
lambda[6] 0.728 0.555 0.026 0.289 0.611 1.032 2.083 1.00 770
lambda[7] 0.829 0.629 0.034 0.332 0.714 1.179 2.307 1.02 130
lambda[8] 0.812 0.635 0.034 0.322 0.667 1.161 2.415 1.03 100
lambda[9] 1.481 0.764 0.224 0.930 1.415 1.930 3.266 1.10 42
lambda[10] 1.792 0.822 0.263 1.214 1.768 2.358 3.528 1.09 47
lambda.std[1] 0.774 0.188 0.241 0.702 0.834 0.910 0.968 1.06 160
lambda.std[2] 0.848 0.121 0.525 0.800 0.889 0.934 0.969 1.06 74
lambda.std[3] 0.853 0.122 0.488 0.825 0.890 0.928 0.960 1.08 200
lambda.std[4] 0.742 0.239 0.078 0.649 0.842 0.913 0.965 1.11 45
lambda.std[5] 0.752 0.166 0.316 0.671 0.795 0.876 0.952 1.06 94
lambda.std[6] 0.497 0.261 0.026 0.278 0.521 0.718 0.901 1.00 1500
lambda.std[7] 0.534 0.267 0.034 0.315 0.581 0.763 0.918 1.02 160
lambda.std[8] 0.525 0.266 0.034 0.307 0.555 0.758 0.924 1.03 130
lambda.std[9] 0.755 0.187 0.218 0.681 0.817 0.888 0.956 1.14 52
lambda.std[10] 0.810 0.173 0.254 0.772 0.870 0.921 0.962 1.13 65
reli.omega 0.950 0.016 0.911 0.941 0.953 0.962 0.974 1.19 18
tau[1,1] -1.951 0.870 -4.334 -2.317 -1.747 -1.365 -0.868 1.08 66
tau[2,1] 0.026 0.436 -0.863 -0.244 0.024 0.297 0.904 1.02 200
tau[3,1] -3.211 0.895 -5.196 -3.761 -3.114 -2.572 -1.774 1.01 590
tau[4,1] -3.983 1.287 -7.167 -4.710 -3.742 -3.036 -2.153 1.14 27
tau[5,1] -0.260 0.407 -1.122 -0.503 -0.242 0.000 0.499 1.05 60
tau[6,1] -4.846 1.665 -8.785 -5.794 -4.568 -3.580 -2.479 1.02 120
tau[7,1] -4.855 1.492 -8.325 -5.677 -4.592 -3.758 -2.702 1.02 140
tau[8,1] -5.305 1.611 -9.217 -6.168 -5.015 -4.147 -2.984 1.01 250
tau[9,1] -2.898 0.937 -5.136 -3.434 -2.741 -2.223 -1.508 1.04 69
tau[10,1] -3.448 1.053 -5.890 -4.027 -3.297 -2.677 -1.859 1.02 150
theta[1] 4.551 3.765 1.062 1.973 3.292 5.804 15.781 1.02 670
theta[2] 5.876 4.074 1.380 2.779 4.786 7.833 16.170 1.06 49
theta[3] 5.498 3.151 1.313 3.137 4.823 7.216 12.878 1.01 460
theta[4] 4.500 3.713 1.006 1.726 3.433 5.988 14.347 1.17 21
theta[5] 3.488 2.450 1.111 1.819 2.715 4.289 10.749 1.05 59
theta[6] 1.838 1.189 1.001 1.084 1.373 2.066 5.337 1.03 160
theta[7] 2.083 1.562 1.001 1.111 1.510 2.391 6.322 1.03 110
theta[8] 2.063 1.656 1.001 1.104 1.445 2.349 6.830 1.03 91
theta[9] 3.777 2.820 1.050 1.865 3.003 4.725 11.664 1.06 46
theta[10] 4.888 3.281 1.069 2.474 4.127 6.560 13.448 1.06 47
deviance 906.111 40.987 827.567 878.036 905.952 934.364 985.376 1.04 71
For each parameter, n.eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor (at convergence, Rhat=1).
DIC info (using the rule, pD = var(deviance)/2)
pD = 804.9 and DIC = 1711.1
DIC is an estimate of expected predictive error (lower deviance is better).Posterior Distribution Summary
jags.mcmc <- as.mcmc(model.fit)
a <- colnames(as.data.frame(jags.mcmc[[1]]))
fit.mcmc <- data.frame(as.matrix(jags.mcmc, chains = T, iters = T))
colnames(fit.mcmc) <- c("chain", "iter", a)
fit.mcmc.ggs <- ggmcmc::ggs(jags.mcmc) # for GRB plot
# save posterior draws for later
write.csv(x=fit.mcmc, file=paste0(getwd(),"/data/study_4/posterior_draws_m3.csv"))Categroy Thresholds (\(\tau\))
# tau
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "tau", prob = 0.8); ggsave("fig/study4_model3_tau_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "tau"); ggsave("fig/study4_model3_tau_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "tau"); ggsave("fig/study4_model3_tau_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "tau"); ggsave("fig/study4_model3_tau_grb.pdf")
Saving 7 x 5 in imageFactor Loadings (\(\lambda\))
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "lambda", prob = 0.8)
bayesplot::mcmc_acf(fit.mcmc, regex_pars = "lambda")
bayesplot::mcmc_trace(fit.mcmc, regex_pars = "lambda")
ggmcmc::ggs_grb(fit.mcmc.ggs, family = "lambda")
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "lambda.std", prob = 0.8); ggsave("fig/study4_model3_lambda_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "lambda.std"); ggsave("fig/study4_model3_lambda_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "lambda.std"); ggsave("fig/study4_model3_lambda_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "lambda.std"); ggsave("fig/study4_model3_lambda_grb.pdf")
Saving 7 x 5 in imageLatent Response Total Variance (\(\theta\))
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "theta", prob = 0.8); ggsave("fig/study4_model3_theta_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "theta"); ggsave("fig/study4_model3_theta_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "theta"); ggsave("fig/study4_model3_theta_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "theta"); ggsave("fig/study4_model3_theta_grb.pdf")
Saving 7 x 5 in imageFactor Reliability Omega (\(\omega\))
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "reli.omega", prob = 0.8); ggsave("fig/study4_model3_omega_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/study4_model3_omega_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/study4_model3_omega_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "reli.omega"); ggsave("fig/study4_model3_omega_grb.pdf")
Saving 7 x 5 in image# extract omega posterior for results comparison
extracted_omega <- data.frame(model_3 = fit.mcmc$reli.omega)
write.csv(x=extracted_omega, file=paste0(getwd(),"/data/study_4/extracted_omega_m3.csv"))Posterior Predictive Distributions
# Posterior Predictive Check
Niter <- 200
model.fit$model$recompile()Compiling model graph
Resolving undeclared variables
Allocating nodes
Graph information:
Observed stochastic nodes: 1420
Unobserved stochastic nodes: 4422
Total graph size: 34704
Initializing modelfit.extra <- rjags::jags.samples(model.fit$model, variable.names = "omega", n.iter = Niter)NOTE: Stopping adaptationN <- 142
nit <- 10
nchain<-4
C <- 2
n <- i <- iter <- ppc.row.i <- 1
y.prob.ppc <- array(dim=c(Niter*nchain, nit, C))
for(chain in 1:nchain){
for(iter in 1:Niter){
# initialize simulated y for this iteration
y <- matrix(nrow=N, ncol=nit)
# loop over item
for(i in 1:nit){
# simulated data for item i for each person
for(n in 1:N){
y[n,i] <- sample(1:C, 1, prob = fit.extra$omega[n, i, 1:C, iter, chain])
}
# computer proportion of each response category
for(c in 1:C){
y.prob.ppc[ppc.row.i,i,c] <- sum(y[,i]==c)/N
}
}
# update row of output
ppc.row.i = ppc.row.i + 1
}
}
yppcmat <- matrix(c(y.prob.ppc), ncol=1)
z <- expand.grid(1:(Niter*nchain), 1:nit, 1:C)
yppcmat <- data.frame( iter = z[,1], nit=z[,2], C=z[,3], yppc = yppcmat)
ymat <- model.fit$model$data()[["y"]]
y.prob <- matrix(ncol=C, nrow=nit)
for(i in 1:nit){
for(c in 1:C){
y.prob[i,c] <- sum(ymat[,i]==c-1)/N
}
}
yobsmat <- matrix(c(y.prob), ncol=1)
z <- expand.grid(1:nit, 1:C)
yobsmat <- data.frame(nit=z[,1], C=z[,2], yobs = yobsmat)
plot.ppc <- full_join(yppcmat, yobsmat)Joining, by = c("nit", "C")p <- plot.ppc %>%
mutate(C = as.factor(C),
item = nit) %>%
ggplot()+
geom_boxplot(aes(x=C,y=y.prob.ppc), outlier.colour = NA)+
geom_point(aes(x=C,y=yobs), color="red")+
lims(y=c(0, 1))+
labs(y="Posterior Predictive Category Proportion", x="Item Category")+
facet_wrap(.~nit, nrow=1)+
theme_bw()+
theme(
panel.grid = element_blank(),
strip.background = element_rect(fill="white")
)
p
ggsave(filename = "fig/study4_model3_ppc_y.pdf",plot=p,width = 6, height=3,units="in")
ggsave(filename = "fig/study4_model3_ppc_y.png",plot=p,width = 6, height=3,units="in")
ggsave(filename = "fig/study4_model3_ppc_y.eps",plot=p,width = 6, height=3,units="in")Manuscript Table and Figures
Table
# print to xtable
print(
xtable(
model.fit$BUGSoutput$summary,
caption = c("study4 Model 3 posterior distribution summary")
,align = "lrrrrrrrrr"
),
include.rownames=T,
booktabs=T
)% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Thu Jan 20 14:06:05 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrr}
\toprule
& mean & sd & 2.5\% & 25\% & 50\% & 75\% & 97.5\% & Rhat & n.eff \\
\midrule
deviance & 906.11 & 40.99 & 827.57 & 878.04 & 905.95 & 934.36 & 985.38 & 1.04 & 71.00 \\
lambda[1] & 1.65 & 0.91 & 0.25 & 0.99 & 1.51 & 2.19 & 3.84 & 1.03 & 290.00 \\
lambda[2] & 2.02 & 0.89 & 0.62 & 1.33 & 1.95 & 2.61 & 3.89 & 1.06 & 51.00 \\
lambda[3] & 1.98 & 0.75 & 0.56 & 1.46 & 1.96 & 2.49 & 3.45 & 1.04 & 260.00 \\
lambda[4] & 1.61 & 0.96 & 0.08 & 0.85 & 1.56 & 2.23 & 3.65 & 1.13 & 28.00 \\
lambda[5] & 1.41 & 0.70 & 0.33 & 0.91 & 1.31 & 1.81 & 3.12 & 1.05 & 66.00 \\
lambda[6] & 0.73 & 0.55 & 0.03 & 0.29 & 0.61 & 1.03 & 2.08 & 1.01 & 770.00 \\
lambda[7] & 0.83 & 0.63 & 0.03 & 0.33 & 0.71 & 1.18 & 2.31 & 1.02 & 130.00 \\
lambda[8] & 0.81 & 0.64 & 0.03 & 0.32 & 0.67 & 1.16 & 2.41 & 1.03 & 100.00 \\
lambda[9] & 1.48 & 0.76 & 0.22 & 0.93 & 1.42 & 1.93 & 3.27 & 1.10 & 42.00 \\
lambda[10] & 1.79 & 0.82 & 0.26 & 1.21 & 1.77 & 2.36 & 3.53 & 1.09 & 47.00 \\
lambda.std[1] & 0.77 & 0.19 & 0.24 & 0.70 & 0.83 & 0.91 & 0.97 & 1.06 & 160.00 \\
lambda.std[2] & 0.85 & 0.12 & 0.52 & 0.80 & 0.89 & 0.93 & 0.97 & 1.06 & 74.00 \\
lambda.std[3] & 0.85 & 0.12 & 0.49 & 0.83 & 0.89 & 0.93 & 0.96 & 1.09 & 200.00 \\
lambda.std[4] & 0.74 & 0.24 & 0.08 & 0.65 & 0.84 & 0.91 & 0.96 & 1.11 & 45.00 \\
lambda.std[5] & 0.75 & 0.17 & 0.32 & 0.67 & 0.79 & 0.88 & 0.95 & 1.06 & 94.00 \\
lambda.std[6] & 0.50 & 0.26 & 0.03 & 0.28 & 0.52 & 0.72 & 0.90 & 1.00 & 1500.00 \\
lambda.std[7] & 0.53 & 0.27 & 0.03 & 0.32 & 0.58 & 0.76 & 0.92 & 1.02 & 160.00 \\
lambda.std[8] & 0.53 & 0.27 & 0.03 & 0.31 & 0.55 & 0.76 & 0.92 & 1.03 & 130.00 \\
lambda.std[9] & 0.76 & 0.19 & 0.22 & 0.68 & 0.82 & 0.89 & 0.96 & 1.14 & 52.00 \\
lambda.std[10] & 0.81 & 0.17 & 0.25 & 0.77 & 0.87 & 0.92 & 0.96 & 1.13 & 65.00 \\
reli.omega & 0.95 & 0.02 & 0.91 & 0.94 & 0.95 & 0.96 & 0.97 & 1.19 & 18.00 \\
tau[1,1] & -1.95 & 0.87 & -4.33 & -2.32 & -1.75 & -1.36 & -0.87 & 1.08 & 66.00 \\
tau[2,1] & 0.03 & 0.44 & -0.86 & -0.24 & 0.02 & 0.30 & 0.90 & 1.02 & 200.00 \\
tau[3,1] & -3.21 & 0.90 & -5.20 & -3.76 & -3.11 & -2.57 & -1.77 & 1.01 & 590.00 \\
tau[4,1] & -3.98 & 1.29 & -7.17 & -4.71 & -3.74 & -3.04 & -2.15 & 1.14 & 27.00 \\
tau[5,1] & -0.26 & 0.41 & -1.12 & -0.50 & -0.24 & 0.00 & 0.50 & 1.05 & 60.00 \\
tau[6,1] & -4.85 & 1.67 & -8.79 & -5.79 & -4.57 & -3.58 & -2.48 & 1.02 & 120.00 \\
tau[7,1] & -4.85 & 1.49 & -8.32 & -5.68 & -4.59 & -3.76 & -2.70 & 1.02 & 140.00 \\
tau[8,1] & -5.30 & 1.61 & -9.22 & -6.17 & -5.01 & -4.15 & -2.98 & 1.01 & 250.00 \\
tau[9,1] & -2.90 & 0.94 & -5.14 & -3.43 & -2.74 & -2.22 & -1.51 & 1.04 & 69.00 \\
tau[10,1] & -3.45 & 1.05 & -5.89 & -4.03 & -3.30 & -2.68 & -1.86 & 1.02 & 150.00 \\
theta[1] & 4.55 & 3.76 & 1.06 & 1.97 & 3.29 & 5.80 & 15.78 & 1.02 & 670.00 \\
theta[2] & 5.88 & 4.07 & 1.38 & 2.78 & 4.79 & 7.83 & 16.17 & 1.06 & 49.00 \\
theta[3] & 5.50 & 3.15 & 1.31 & 3.14 & 4.82 & 7.22 & 12.88 & 1.01 & 460.00 \\
theta[4] & 4.50 & 3.71 & 1.01 & 1.73 & 3.43 & 5.99 & 14.35 & 1.17 & 21.00 \\
theta[5] & 3.49 & 2.45 & 1.11 & 1.82 & 2.72 & 4.29 & 10.75 & 1.05 & 59.00 \\
theta[6] & 1.84 & 1.19 & 1.00 & 1.08 & 1.37 & 2.07 & 5.34 & 1.03 & 160.00 \\
theta[7] & 2.08 & 1.56 & 1.00 & 1.11 & 1.51 & 2.39 & 6.32 & 1.03 & 110.00 \\
theta[8] & 2.06 & 1.66 & 1.00 & 1.10 & 1.45 & 2.35 & 6.83 & 1.03 & 91.00 \\
theta[9] & 3.78 & 2.82 & 1.05 & 1.87 & 3.00 & 4.72 & 11.66 & 1.06 & 46.00 \\
theta[10] & 4.89 & 3.28 & 1.07 & 2.47 & 4.13 & 6.56 & 13.45 & 1.06 & 47.00 \\
\bottomrule
\end{tabular}
\caption{study4 Model 3 posterior distribution summary}
\end{table}Figure
sessionInfo()R version 4.0.5 (2021-03-31)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 22000)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.1252
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] car_3.0-10 carData_3.0-4 mvtnorm_1.1-1
[4] LaplacesDemon_16.1.4 runjags_2.2.0-2 lme4_1.1-26
[7] Matrix_1.3-2 sirt_3.9-4 R2jags_0.6-1
[10] rjags_4-12 eRm_1.0-2 diffIRT_1.5
[13] statmod_1.4.35 xtable_1.8-4 kableExtra_1.3.4
[16] lavaan_0.6-7 polycor_0.7-10 bayesplot_1.8.0
[19] ggmcmc_1.5.1.1 coda_0.19-4 data.table_1.14.0
[22] patchwork_1.1.1 forcats_0.5.1 stringr_1.4.0
[25] dplyr_1.0.5 purrr_0.3.4 readr_1.4.0
[28] tidyr_1.1.3 tibble_3.1.0 ggplot2_3.3.5
[31] tidyverse_1.3.0 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] minqa_1.2.4 TAM_3.5-19 colorspace_2.0-0 rio_0.5.26
[5] ellipsis_0.3.1 ggridges_0.5.3 rprojroot_2.0.2 fs_1.5.0
[9] rstudioapi_0.13 farver_2.1.0 fansi_0.4.2 lubridate_1.7.10
[13] xml2_1.3.2 codetools_0.2-18 splines_4.0.5 mnormt_2.0.2
[17] knitr_1.31 jsonlite_1.7.2 nloptr_1.2.2.2 broom_0.7.5
[21] dbplyr_2.1.0 compiler_4.0.5 httr_1.4.2 backports_1.2.1
[25] assertthat_0.2.1 cli_2.3.1 later_1.1.0.1 htmltools_0.5.1.1
[29] tools_4.0.5 gtable_0.3.0 glue_1.4.2 reshape2_1.4.4
[33] Rcpp_1.0.7 cellranger_1.1.0 jquerylib_0.1.3 vctrs_0.3.6
[37] svglite_2.0.0 nlme_3.1-152 psych_2.0.12 xfun_0.21
[41] ps_1.6.0 openxlsx_4.2.3 rvest_1.0.0 lifecycle_1.0.0
[45] MASS_7.3-53.1 scales_1.1.1 ragg_1.1.1 hms_1.0.0
[49] promises_1.2.0.1 parallel_4.0.5 RColorBrewer_1.1-2 curl_4.3
[53] yaml_2.2.1 sass_0.3.1 reshape_0.8.8 stringi_1.5.3
[57] highr_0.8 zip_2.1.1 boot_1.3-27 rlang_0.4.10
[61] pkgconfig_2.0.3 systemfonts_1.0.1 evaluate_0.14 lattice_0.20-41
[65] labeling_0.4.2 tidyselect_1.1.0 GGally_2.1.1 plyr_1.8.6
[69] magrittr_2.0.1 R6_2.5.0 generics_0.1.0 DBI_1.1.1
[73] foreign_0.8-81 pillar_1.5.1 haven_2.3.1 withr_2.4.1
[77] abind_1.4-5 modelr_0.1.8 crayon_1.4.1 utf8_1.1.4
[81] tmvnsim_1.0-2 rmarkdown_2.7 grid_4.0.5 readxl_1.3.1
[85] CDM_7.5-15 pbivnorm_0.6.0 git2r_0.28.0 reprex_1.0.0
[89] digest_0.6.27 webshot_0.5.2 httpuv_1.5.5 textshaping_0.3.1
[93] stats4_4.0.5 munsell_0.5.0 viridisLite_0.3.0 bslib_0.2.4
[97] R2WinBUGS_2.1-21