Study 4: Extroversion Data Analysis
Model 2 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 2: IFA with RT
Model details
cat(read_file(paste0(w.d, "/code/study_4/model_2.txt")))model {
### Model
for(p in 1:N){
for(i in 1:nit){
# data model
y[p,i] ~ dbern(pi[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])
# log-RT model
dev[p,i]<-lambda[i]*(eta[p] - tau[i,1])
mu.lrt[p,i] <- icept[i] - speed[p] - rho * abs(dev[p,i])
lrt[p,i] ~ dnorm(mu.lrt[p,i], prec[i])
}
}
### Priors
# person parameters
for(p in 1:N){
eta[p] ~ dnorm(0, 1) # latent ability
speed[p]~dnorm(sigma.ts*eta[p],prec.s) # latent speed
}
sigma.ts ~ dnorm(0, 0.1)
prec.s ~ dgamma(.1,.1)
# transformations
sigma.t = pow(prec.s, -1) + pow(sigma.ts, 2) # speed variance
cor.ts = sigma.ts/(pow(sigma.t,0.5)) # LV correlation
for(i in 1:nit){
# lrt parameters
icept[i]~dnorm(0,.1)
prec[i]~dgamma(.1,.1)
# 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)
}
rho~dnorm(0,.1)I(0,)
# 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
This model is similar to the BL-IRT model for jointly modeling item responses and response times (Molenaar et al., 2015).
# Save parameters
jags.params <- c("tau",
"lambda","lambda.std",
"theta",
"icept",
"prec",
"prec.s",
"sigma.ts",
"rho",
"reli.omega")
# 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),
"speed"=rnorm(142),
"ystar"=matrix(c(0.7*rep(rnorm(142),10)), ncol=10),
"rho"=0.1,
"icept"=rep(0, 10),
"prec.s"=10,
"prec"=rep(4, 10),
"sigma.ts"=0.1
)
}
jags.data <- list(
y = mydata[,1:10],
lrt = mydata[,11:20],
N = nrow(mydata),
nit = 10
)
# Run model
# Model 2
model.fit <- R2jags::jags(
model = paste0(w.d, "/code/study_4/model_2.txt"),
parameters.to.save = jags.params,
inits = jags.inits,
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: 2840
Unobserved stochastic nodes: 1747
Total graph size: 18995
Initializing modelprint(model.fit, width=1000)Inference for Bugs model at "C:/Users/noahp/Documents/GitHub/Padgett-Dissertation/code/study_4/model_2.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
icept[1] 1.555 0.080 1.402 1.501 1.553 1.606 1.721 1.00 520
icept[2] 1.403 0.057 1.290 1.365 1.403 1.441 1.515 1.00 620
icept[3] 1.539 0.160 1.270 1.427 1.524 1.637 1.897 1.01 360
icept[4] 1.641 0.312 1.144 1.413 1.602 1.831 2.332 1.03 99
icept[5] 1.357 0.064 1.235 1.312 1.355 1.398 1.483 1.01 340
icept[6] 1.428 0.105 1.256 1.355 1.416 1.490 1.673 1.01 330
icept[7] 1.506 0.175 1.221 1.380 1.489 1.610 1.902 1.01 1200
icept[8] 1.571 0.242 1.196 1.394 1.534 1.718 2.120 1.02 160
icept[9] 1.864 0.089 1.708 1.805 1.860 1.920 2.051 1.00 830
icept[10] 1.452 0.166 1.161 1.335 1.446 1.556 1.807 1.02 130
lambda[1] 0.517 0.228 0.104 0.358 0.502 0.662 1.006 1.00 1100
lambda[2] 0.568 0.240 0.139 0.398 0.556 0.728 1.064 1.00 2200
lambda[3] 1.706 0.406 1.022 1.423 1.665 1.936 2.670 1.01 230
lambda[4] 1.739 0.485 0.876 1.415 1.703 2.023 2.855 1.02 150
lambda[5] 0.619 0.245 0.185 0.449 0.603 0.770 1.144 1.02 350
lambda[6] 0.742 0.287 0.233 0.549 0.722 0.916 1.353 1.00 3300
lambda[7] 1.120 0.335 0.507 0.895 1.099 1.328 1.845 1.01 230
lambda[8] 1.275 0.379 0.610 1.008 1.234 1.519 2.068 1.01 390
lambda[9] 0.779 0.255 0.294 0.611 0.771 0.948 1.313 1.01 540
lambda[10] 1.734 0.357 1.097 1.477 1.711 1.967 2.491 1.01 520
lambda.std[1] 0.439 0.155 0.103 0.337 0.449 0.552 0.709 1.00 1200
lambda.std[2] 0.471 0.155 0.137 0.370 0.486 0.588 0.729 1.00 2700
lambda.std[3] 0.849 0.057 0.715 0.818 0.857 0.888 0.936 1.01 270
lambda.std[4] 0.848 0.071 0.659 0.817 0.862 0.896 0.944 1.01 230
lambda.std[5] 0.503 0.148 0.182 0.410 0.516 0.610 0.753 1.02 440
lambda.std[6] 0.568 0.149 0.227 0.481 0.585 0.676 0.804 1.00 2800
lambda.std[7] 0.721 0.110 0.452 0.667 0.740 0.799 0.879 1.01 450
lambda.std[8] 0.762 0.098 0.521 0.710 0.777 0.835 0.900 1.02 330
lambda.std[9] 0.592 0.130 0.282 0.521 0.610 0.688 0.795 1.01 690
lambda.std[10] 0.856 0.049 0.739 0.828 0.863 0.891 0.928 1.01 650
prec[1] 1.772 0.219 1.385 1.616 1.764 1.912 2.226 1.00 4000
prec[2] 3.690 0.493 2.805 3.344 3.665 4.005 4.714 1.00 1000
prec[3] 4.164 0.555 3.169 3.776 4.135 4.519 5.311 1.00 2200
prec[4] 2.544 0.326 1.962 2.311 2.525 2.761 3.214 1.00 1700
prec[5] 2.858 0.373 2.185 2.601 2.842 3.100 3.642 1.00 3200
prec[6] 3.033 0.390 2.328 2.761 3.017 3.284 3.840 1.00 2500
prec[7] 5.000 0.681 3.766 4.522 4.969 5.434 6.426 1.00 3800
prec[8] 3.914 0.514 2.972 3.553 3.888 4.245 5.015 1.00 630
prec[9] 2.613 0.337 2.004 2.372 2.593 2.838 3.293 1.00 4000
prec[10] 6.814 1.014 5.037 6.098 6.748 7.450 9.010 1.00 4000
prec.s 9.691 1.605 6.931 8.580 9.560 10.654 13.271 1.00 760
reli.omega 0.918 0.018 0.877 0.908 0.920 0.931 0.949 1.01 200
rho 0.112 0.033 0.056 0.087 0.110 0.133 0.185 1.04 75
sigma.ts 0.003 0.056 -0.110 -0.034 0.004 0.042 0.111 1.02 120
tau[1,1] -0.948 0.174 -1.298 -1.064 -0.944 -0.827 -0.620 1.00 3700
tau[2,1] -0.095 0.156 -0.410 -0.198 -0.094 0.007 0.216 1.00 3200
tau[3,1] -2.238 0.399 -3.145 -2.463 -2.199 -1.962 -1.559 1.01 340
tau[4,1] -3.179 0.593 -4.580 -3.519 -3.115 -2.767 -2.185 1.03 160
tau[5,1] -0.185 0.162 -0.500 -0.295 -0.184 -0.075 0.126 1.00 1500
tau[6,1] -2.071 0.277 -2.642 -2.244 -2.055 -1.887 -1.587 1.00 3600
tau[7,1] -2.845 0.412 -3.771 -3.106 -2.812 -2.554 -2.129 1.02 150
tau[8,1] -3.484 0.559 -4.749 -3.815 -3.426 -3.088 -2.569 1.01 540
tau[9,1] -1.463 0.218 -1.913 -1.604 -1.452 -1.312 -1.063 1.00 660
tau[10,1] -2.448 0.372 -3.246 -2.689 -2.422 -2.178 -1.796 1.00 1100
theta[1] 1.320 0.267 1.011 1.128 1.252 1.439 2.012 1.00 1000
theta[2] 1.381 0.302 1.019 1.159 1.309 1.529 2.131 1.00 1100
theta[3] 4.075 1.505 2.044 3.025 3.773 4.747 8.128 1.01 230
theta[4] 4.260 1.862 1.768 3.001 3.899 5.093 9.149 1.03 130
theta[5] 1.443 0.340 1.034 1.202 1.363 1.593 2.308 1.02 210
theta[6] 1.633 0.488 1.054 1.301 1.521 1.840 2.832 1.00 4000
theta[7] 2.365 0.799 1.257 1.801 2.207 2.764 4.404 1.02 150
theta[8] 2.768 1.044 1.372 2.016 2.522 3.306 5.278 1.01 400
theta[9] 1.672 0.423 1.086 1.373 1.594 1.898 2.723 1.01 380
theta[10] 4.134 1.295 2.203 3.183 3.928 4.868 7.204 1.01 480
deviance 2998.634 35.415 2931.106 2974.014 2998.348 3022.400 3069.817 1.01 470
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 = 623.6 and DIC = 3622.2
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_m2.csv"))Categroy Thresholds (\(\tau\))
# tau
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "tau", prob = 0.8); ggsave("fig/study4_model2_tau_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "tau"); ggsave("fig/study4_model2_tau_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "tau"); ggsave("fig/study4_model2_tau_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "tau"); ggsave("fig/study4_model2_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_model2_lambda_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "lambda.std"); ggsave("fig/study4_model2_lambda_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "lambda.std"); ggsave("fig/study4_model2_lambda_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "lambda.std"); ggsave("fig/study4_model2_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_model2_theta_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "theta"); ggsave("fig/study4_model2_theta_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "theta"); ggsave("fig/study4_model2_theta_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "theta"); ggsave("fig/study4_model2_theta_grb.pdf")
Saving 7 x 5 in imageResponse Time Intercept (\(\beta_{lrt}\))
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "icept", prob = 0.8); ggsave("fig/study4_model2_icept_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "icept"); ggsave("fig/study4_model2_icept_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "icept"); ggsave("fig/study4_model2_icept_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "icept"); ggsave("fig/study4_model2_icept_grb.pdf")
Saving 7 x 5 in imageResponse Time Precision (\(\sigma_{lrt}\))
bayesplot::mcmc_areas(fit.mcmc,pars = paste0("prec[",1:5,"]"), prob = 0.8); ggsave("fig/study4_model2_prec_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, pars = paste0("prec[",1:5,"]")); ggsave("fig/study4_model2_prec_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, pars = paste0("prec[",1:5,"]")); ggsave("fig/study4_model2_prec_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "prec"); ggsave("fig/study4_model2_prec_grb.pdf")
Saving 7 x 5 in imageSpeed Factor Variance (\(\sigma_s\))
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "prec.s", prob = 0.8); ggsave("fig/study4_model2_precs_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "prec.s"); ggsave("fig/study4_model2_precs_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "prec.s"); ggsave("fig/study4_model2_precs_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "prec.s"); ggsave("fig/study4_model2_precs_grb.pdf")
Saving 7 x 5 in imageFactor Covariance (\(\sigma_{ts}\))
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "sigma.ts", prob = 0.8); ggsave("fig/study4_model2_sigmats_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "sigma.ts"); ggsave("fig/study4_model2_sigmats_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "sigma.ts"); ggsave("fig/study4_model2_sigmats_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "sigma.ts"); ggsave("fig/study4_model2_sigmats_grb.pdf")
Saving 7 x 5 in imagePID (\(\rho\))
bayesplot::mcmc_areas(fit.mcmc, regex_pars = "rho", prob = 0.8); ggsave("fig/study4_model2_rho_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "rho"); ggsave("fig/study4_model2_rho_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "rho"); ggsave("fig/study4_model2_rho_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "rho"); ggsave("fig/study4_model2_rho_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_model2_omega_dens.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_acf(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/study4_model2_omega_acf.pdf")
Saving 7 x 5 in imagebayesplot::mcmc_trace(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/study4_model2_omega_trace.pdf")
Saving 7 x 5 in imageggmcmc::ggs_grb(fit.mcmc.ggs, family = "reli.omega"); ggsave("fig/study4_model2_omega_grb.pdf")
Saving 7 x 5 in image# extract omega posterior for results comparison
extracted_omega <- data.frame(model_2 = fit.mcmc$reli.omega)
write.csv(x=extracted_omega, file=paste0(getwd(),"/data/study_4/extracted_omega_m2.csv"))Posterior Predictive Distributions
# Posterior Predictive Check
Niter <- 200
model.fit$model$recompile()Compiling model graph
Resolving undeclared variables
Allocating nodes
Graph information:
Observed stochastic nodes: 2840
Unobserved stochastic nodes: 1747
Total graph size: 18995
Initializing modelfit.extra <- rjags::jags.samples(model.fit$model, variable.names = "pi", 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$pi[n, i, 1:C, iter, chain])
}
# computer proportion of each response category
for(c in 1:C){
y.prob.ppc[ppc.row.i,i,c] <- sum(y[,i]==c)/N
}
}
# update row of output
ppc.row.i = ppc.row.i + 1
}
}
yppcmat <- matrix(c(y.prob.ppc), ncol=1)
z <- expand.grid(1:(Niter*nchain), 1:nit, 1:C)
yppcmat <- data.frame( iter = z[,1], nit=z[,2], C=z[,3], yppc = yppcmat)
ymat <- model.fit$model$data()[[4]]
y.prob <- matrix(ncol=C, nrow=nit)
for(i in 1:nit){
for(c in 1:C){
y.prob[i,c] <- sum(ymat[,i]==c-1)/N
}
}
yobsmat <- matrix(c(y.prob), ncol=1)
z <- expand.grid(1:nit, 1:C)
yobsmat <- data.frame(nit=z[,1], C=z[,2], yobs = yobsmat)
plot.ppc <- full_join(yppcmat, yobsmat)Joining, by = c("nit", "C")p <- plot.ppc %>%
mutate(C = as.factor(C),
item = nit) %>%
ggplot()+
geom_boxplot(aes(x=C,y=y.prob.ppc), outlier.colour = NA)+
geom_point(aes(x=C,y=yobs), color="red")+
lims(y=c(0, 1))+
labs(y="Posterior Predictive Category Proportion", x="Item Category")+
facet_wrap(.~nit, nrow=1)+
theme_bw()+
theme(
panel.grid = element_blank(),
strip.background = element_rect(fill="white")
)
p
ggsave(filename = "fig/study4_model2_ppc_y.pdf",plot=p,width = 6, height=3,units="in")
ggsave(filename = "fig/study4_model2_ppc_y.png",plot=p,width = 6, height=3,units="in")
ggsave(filename = "fig/study4_model2_ppc_y.eps",plot=p,width = 6, height=3,units="in")Manuscript Table and Figures
Table
# print to xtable
print(
xtable(
model.fit$BUGSoutput$summary,
caption = c("study4 Model 2 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 14:05:11 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrr}
\toprule
& mean & sd & 2.5\% & 25\% & 50\% & 75\% & 97.5\% & Rhat & n.eff \\
\midrule
deviance & 2998.63 & 35.42 & 2931.11 & 2974.01 & 2998.35 & 3022.40 & 3069.82 & 1.01 & 470.00 \\
icept[1] & 1.56 & 0.08 & 1.40 & 1.50 & 1.55 & 1.61 & 1.72 & 1.01 & 520.00 \\
icept[2] & 1.40 & 0.06 & 1.29 & 1.37 & 1.40 & 1.44 & 1.51 & 1.00 & 620.00 \\
icept[3] & 1.54 & 0.16 & 1.27 & 1.43 & 1.52 & 1.64 & 1.90 & 1.01 & 360.00 \\
icept[4] & 1.64 & 0.31 & 1.14 & 1.41 & 1.60 & 1.83 & 2.33 & 1.03 & 99.00 \\
icept[5] & 1.36 & 0.06 & 1.24 & 1.31 & 1.35 & 1.40 & 1.48 & 1.01 & 340.00 \\
icept[6] & 1.43 & 0.10 & 1.26 & 1.35 & 1.42 & 1.49 & 1.67 & 1.01 & 330.00 \\
icept[7] & 1.51 & 0.17 & 1.22 & 1.38 & 1.49 & 1.61 & 1.90 & 1.01 & 1200.00 \\
icept[8] & 1.57 & 0.24 & 1.20 & 1.39 & 1.53 & 1.72 & 2.12 & 1.02 & 160.00 \\
icept[9] & 1.86 & 0.09 & 1.71 & 1.80 & 1.86 & 1.92 & 2.05 & 1.00 & 830.00 \\
icept[10] & 1.45 & 0.17 & 1.16 & 1.33 & 1.45 & 1.56 & 1.81 & 1.02 & 130.00 \\
lambda[1] & 0.52 & 0.23 & 0.10 & 0.36 & 0.50 & 0.66 & 1.01 & 1.00 & 1100.00 \\
lambda[2] & 0.57 & 0.24 & 0.14 & 0.40 & 0.56 & 0.73 & 1.06 & 1.00 & 2200.00 \\
lambda[3] & 1.71 & 0.41 & 1.02 & 1.42 & 1.67 & 1.94 & 2.67 & 1.01 & 230.00 \\
lambda[4] & 1.74 & 0.49 & 0.88 & 1.41 & 1.70 & 2.02 & 2.85 & 1.02 & 150.00 \\
lambda[5] & 0.62 & 0.25 & 0.19 & 0.45 & 0.60 & 0.77 & 1.14 & 1.02 & 350.00 \\
lambda[6] & 0.74 & 0.29 & 0.23 & 0.55 & 0.72 & 0.92 & 1.35 & 1.00 & 3300.00 \\
lambda[7] & 1.12 & 0.33 & 0.51 & 0.90 & 1.10 & 1.33 & 1.85 & 1.01 & 230.00 \\
lambda[8] & 1.27 & 0.38 & 0.61 & 1.01 & 1.23 & 1.52 & 2.07 & 1.02 & 390.00 \\
lambda[9] & 0.78 & 0.26 & 0.29 & 0.61 & 0.77 & 0.95 & 1.31 & 1.01 & 540.00 \\
lambda[10] & 1.73 & 0.36 & 1.10 & 1.48 & 1.71 & 1.97 & 2.49 & 1.01 & 520.00 \\
lambda.std[1] & 0.44 & 0.15 & 0.10 & 0.34 & 0.45 & 0.55 & 0.71 & 1.00 & 1200.00 \\
lambda.std[2] & 0.47 & 0.15 & 0.14 & 0.37 & 0.49 & 0.59 & 0.73 & 1.00 & 2700.00 \\
lambda.std[3] & 0.85 & 0.06 & 0.71 & 0.82 & 0.86 & 0.89 & 0.94 & 1.01 & 270.00 \\
lambda.std[4] & 0.85 & 0.07 & 0.66 & 0.82 & 0.86 & 0.90 & 0.94 & 1.01 & 230.00 \\
lambda.std[5] & 0.50 & 0.15 & 0.18 & 0.41 & 0.52 & 0.61 & 0.75 & 1.02 & 440.00 \\
lambda.std[6] & 0.57 & 0.15 & 0.23 & 0.48 & 0.59 & 0.68 & 0.80 & 1.00 & 2800.00 \\
lambda.std[7] & 0.72 & 0.11 & 0.45 & 0.67 & 0.74 & 0.80 & 0.88 & 1.01 & 450.00 \\
lambda.std[8] & 0.76 & 0.10 & 0.52 & 0.71 & 0.78 & 0.84 & 0.90 & 1.02 & 330.00 \\
lambda.std[9] & 0.59 & 0.13 & 0.28 & 0.52 & 0.61 & 0.69 & 0.80 & 1.01 & 690.00 \\
lambda.std[10] & 0.86 & 0.05 & 0.74 & 0.83 & 0.86 & 0.89 & 0.93 & 1.01 & 650.00 \\
prec[1] & 1.77 & 0.22 & 1.39 & 1.62 & 1.76 & 1.91 & 2.23 & 1.00 & 4000.00 \\
prec[2] & 3.69 & 0.49 & 2.80 & 3.34 & 3.67 & 4.00 & 4.71 & 1.00 & 1000.00 \\
prec[3] & 4.16 & 0.56 & 3.17 & 3.78 & 4.13 & 4.52 & 5.31 & 1.00 & 2200.00 \\
prec[4] & 2.54 & 0.33 & 1.96 & 2.31 & 2.52 & 2.76 & 3.21 & 1.00 & 1700.00 \\
prec[5] & 2.86 & 0.37 & 2.18 & 2.60 & 2.84 & 3.10 & 3.64 & 1.00 & 3200.00 \\
prec[6] & 3.03 & 0.39 & 2.33 & 2.76 & 3.02 & 3.28 & 3.84 & 1.00 & 2500.00 \\
prec[7] & 5.00 & 0.68 & 3.77 & 4.52 & 4.97 & 5.43 & 6.43 & 1.00 & 3800.00 \\
prec[8] & 3.91 & 0.51 & 2.97 & 3.55 & 3.89 & 4.24 & 5.01 & 1.00 & 630.00 \\
prec[9] & 2.61 & 0.34 & 2.00 & 2.37 & 2.59 & 2.84 & 3.29 & 1.00 & 4000.00 \\
prec[10] & 6.81 & 1.01 & 5.04 & 6.10 & 6.75 & 7.45 & 9.01 & 1.00 & 4000.00 \\
prec.s & 9.69 & 1.61 & 6.93 & 8.58 & 9.56 & 10.65 & 13.27 & 1.00 & 760.00 \\
reli.omega & 0.92 & 0.02 & 0.88 & 0.91 & 0.92 & 0.93 & 0.95 & 1.01 & 200.00 \\
rho & 0.11 & 0.03 & 0.06 & 0.09 & 0.11 & 0.13 & 0.18 & 1.04 & 75.00 \\
sigma.ts & 0.00 & 0.06 & -0.11 & -0.03 & 0.00 & 0.04 & 0.11 & 1.02 & 120.00 \\
tau[1,1] & -0.95 & 0.17 & -1.30 & -1.06 & -0.94 & -0.83 & -0.62 & 1.00 & 3700.00 \\
tau[2,1] & -0.10 & 0.16 & -0.41 & -0.20 & -0.09 & 0.01 & 0.22 & 1.00 & 3200.00 \\
tau[3,1] & -2.24 & 0.40 & -3.15 & -2.46 & -2.20 & -1.96 & -1.56 & 1.01 & 340.00 \\
tau[4,1] & -3.18 & 0.59 & -4.58 & -3.52 & -3.11 & -2.77 & -2.19 & 1.03 & 160.00 \\
tau[5,1] & -0.18 & 0.16 & -0.50 & -0.29 & -0.18 & -0.07 & 0.13 & 1.00 & 1500.00 \\
tau[6,1] & -2.07 & 0.28 & -2.64 & -2.24 & -2.05 & -1.89 & -1.59 & 1.00 & 3600.00 \\
tau[7,1] & -2.85 & 0.41 & -3.77 & -3.11 & -2.81 & -2.55 & -2.13 & 1.02 & 150.00 \\
tau[8,1] & -3.48 & 0.56 & -4.75 & -3.82 & -3.43 & -3.09 & -2.57 & 1.01 & 540.00 \\
tau[9,1] & -1.46 & 0.22 & -1.91 & -1.60 & -1.45 & -1.31 & -1.06 & 1.00 & 660.00 \\
tau[10,1] & -2.45 & 0.37 & -3.25 & -2.69 & -2.42 & -2.18 & -1.80 & 1.01 & 1100.00 \\
theta[1] & 1.32 & 0.27 & 1.01 & 1.13 & 1.25 & 1.44 & 2.01 & 1.00 & 1000.00 \\
theta[2] & 1.38 & 0.30 & 1.02 & 1.16 & 1.31 & 1.53 & 2.13 & 1.00 & 1100.00 \\
theta[3] & 4.07 & 1.50 & 2.04 & 3.02 & 3.77 & 4.75 & 8.13 & 1.01 & 230.00 \\
theta[4] & 4.26 & 1.86 & 1.77 & 3.00 & 3.90 & 5.09 & 9.15 & 1.03 & 130.00 \\
theta[5] & 1.44 & 0.34 & 1.03 & 1.20 & 1.36 & 1.59 & 2.31 & 1.02 & 210.00 \\
theta[6] & 1.63 & 0.49 & 1.05 & 1.30 & 1.52 & 1.84 & 2.83 & 1.00 & 4000.00 \\
theta[7] & 2.37 & 0.80 & 1.26 & 1.80 & 2.21 & 2.76 & 4.40 & 1.02 & 150.00 \\
theta[8] & 2.77 & 1.04 & 1.37 & 2.02 & 2.52 & 3.31 & 5.28 & 1.01 & 400.00 \\
theta[9] & 1.67 & 0.42 & 1.09 & 1.37 & 1.59 & 1.90 & 2.72 & 1.01 & 380.00 \\
theta[10] & 4.13 & 1.29 & 2.20 & 3.18 & 3.93 & 4.87 & 7.20 & 1.01 & 480.00 \\
\bottomrule
\end{tabular}
\caption{study4 Model 2 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