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Package: SPT
Type: Package
Title: SPHERE Psychometrics Tools
Version: 1.0.0
Author: Corentin Choisy
Maintainer: Corentin Choisy <corentin.choisy@univ-nantes.fr>
Description: Various tools for psychometrics analyses
License: AGPLv3
URL: https://git.corentinchoisy.xyz/corentinchoisy/SPT
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.3.2
Imports:
vcrpart,
rjags

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# Generated by roxygen2: do not edit by hand
export(bpcm)
export(pcm)
export(res_ij)
export(residif)
import(rjags)
import(vcrpart)

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## File Name: bpcm.R
## File version: 1.0
#' Compute Bayesian Partial Credit Model (BPCM) for polytomous and dichotomous items
#'
#' This function computes a bayesian PCM, potentially accounting for DIF on specified items
#'
#' @param df data.frame containing the response data
#' @param grp vector containing the column where an optional group membership variable is stored in df
#' @param is.dif indicator vector containing 1 at the inded of each DIF item in df and 0 otherwise
#' @param is.unif indicator vector containing 1 at the inded of each uniform DIF item in df and 0 otherwise
#' @param prior prior function to be used
#' @param diag.plots boolean indicating whether the JAGS diagnosis plots should be displayed
#' @return A data.frame containing various model outputs
#' @import rjags
#' @export
bpcm <- function(df=NULL,grp=NULL,is.dif=NULL,is.unif=NULL,priors=NULL,param=list(),verbose=T,diag.plots=F) {
##### Detecting errors
if ( (sum(is.dif)!=0 | sum(is.unif)!=0) & any(is.null(grp))) {
stop('ERROR: no group variable provided, but is.dif or is.unif are not NULL')
}
if ( sum(is.dif)==0 & sum(is.unif)!=0) {
warning('WARNING: no DIF item specified, but is.unif is not NULL. Ignoring is.unif')
}
if ( sum(is.dif)!=0 ) {
if (length(is.dif)!=ncol(df)) {
stop('ERROR: is.dif must have one element per item in df')
}
if (length(is.unif)!=ncol(df)) {
stop('ERROR: is.unif must have one element per item in df')
}
if ( !("m.gamma"%in%names(priors)) ) {
stop('ERROR: DIF requested. Please provide mean of prior gamma distribution as priors$m.gamma')
}
if ( !("s.gamma"%in%names(priors)) ) {
stop('ERROR: DIF requested. Please provide SD of prior gamma distribution as priors$s.gamma')
}
}
if ( !any(is.null(grp)) ) {
if ( !("m.beta"%in%names(priors)) ) {
stop('ERROR: Group effect requested. Please provide mean of prior beta distribution as priors$m.beta')
}
if ( !("s.gamma"%in%names(priors)) ) {
stop('ERROR: Group effect requested. Please provide SD of prior beta distribution as priors$s.beta')
}
if (nrow(df)!=length(grp)) {
stop('ERROR: grp must be of length nrow(df)')
}
}
if ( !("m.delta"%in%names(priors)) ) {
stop('ERROR: Please provide mean of prior delta distribution as priors$m.delta')
}
if ( !("s.delta"%in%names(priors)) ) {
stop('ERROR: Please provide SD of prior delta distribution as priors$s.delta')
}
if (verbose) {
cat('\n')
cat("#################################################################################################\n")
cat("######################################### FITTING MODEL #########################################\n")
cat("#################################################################################################\n")
}
###############################################
############### NO GROUP EFFECT ###############
###############################################
if (is.null(grp)) {
nam <- colnames(df)
nam_o <- nam
Y <- matrix(unlist(df),nrow=nrow(df))+1
n <- nrow(Y)
p <- ncol(Y)
K <- apply(Y,2,max,na.rm=TRUE)
m.delta <- priors$m.delta
s.delta <- priors$s.delta
namlist <- c(sapply(1:p, function(x) paste0("delta[",x,',',paste0(1:K[p],"]"))))
if (sum(is.dif)!=0) {
namlist <- c(namlist,sapply(1:p, function(x) paste0("gamma[",x,',',paste0(1:K[p],"]"))),"beta")
} else {
if (!is.null(grp)) {
namlist <- c(namlist,"beta")
}
}
data <- list(Y=Y,n=n,p=p,K=K,m.delta=m.delta,s.delta=s.delta)
params <- c("delta")
if ("n.burn"%in%names(param)) {
n.burn <- param$n.burn
} else {
n.burn <- 4000
}
if ("n.thin"%in%names(param)) {
n.thin <- param$n.thin
} else {
n.thin <- 20
}
if ("n.chains"%in%names(param)) {
n.chains <- param$n.chains
} else {
n.chains <- 2
}
if ("n.sim"%in%names(param)) {
n.sim <- param$n.sim
} else {
n.sim <- 20000
}
if ("nb.cores"%in%names(param)) {
nb.cores <- param$nb.cores
} else {
nb.cores <- 6
}
cl <- parallel::makeForkCluster(nb.cores)
if (verbose) {
cat('Initializing Chains...')
}
dclone::parJagsModel(cl,name="mod.jags",data = data,inits = NULL,file = "/home/corentin/Documents/These/Recherche/SPT/src/bpcm",n.chains=n.chains)
if (verbose) {
cat('DONE \n')
cat('Applying burn-in iterations...')
}
dclone::parUpdate(cl,object="mod.jags",n.burn=n.burn)
if (verbose) {
cat('DONE \n')
cat('Running Markov Chains...')
}
mod.samples <- dclone::parCodaSamples(cl,model="mod.jags",variable.names=params,n.iter = n.sim,thin = n.thin)
if (verbose) {
cat('DONE \n')
}
parallel::stopCluster(cl)
if (diag.plots) {
cat("Displaying traceplots...")
traceplot(mod.samples)
readline(prompt="Use the arrows to navigate between traceplots. Press [enter] to continue")
cat("DONE\n")
cat("Displaying autocorrelation plots...")
autocorr.plot(mod.samples,ask=F)
readline(prompt="Use the arrows to navigate between autocorr plots. Press [enter] to continue")
cat("DONE\n ")
}
res <- mod.samples[[1]]
res <- as.data.frame(res)[,namlist]
namlist2 <- unlist(c(sapply(nam,function(x) paste0(x,"_",1:K[which(nam_o==x)]-1))))
if (sum(is.dif)!=0) {
namlist2 <- c(namlist2,unlist(c(sapply(nam,function(x) paste0(x,"_",1:K[which(nam_o==x)]-1,":grp")))),"beta")
} else {
if (!is.null(grp)) {
namlist2 <- c(namlist2,"beta")
}
}
colnames(res) <- namlist2
res <- res[,namlist2]
res <- res[,apply(res,2,function(x) all(x==0))==0]
xsi <- apply(res,2,function(x) c(mean(x),sd(x),quantile(x,0.05),quantile(x,0.95)) )
rownames(xsi) <- c("post.mean","post.sd","post.90.cred.low","post.90.cred.high")
xsi <- round(t(xsi),4)
if ("beta" %in% rownames(xsi)) {
beta <- xsi[rownames(xsi)=="beta",]
xsi <- xsi[rownames(xsi)!="beta",]
}
out <- list(mcmc.res=res,
dif.items=nam_o[which(is.dif==1)],
beta=beta,
thresholds=xsi)
#####################################################
############### GROUP EFFECT / NO DIF ###############
#####################################################
} else if (is.null(is.dif) | sum(is.dif)==0) {
nam <- colnames(df)
nam_o <- nam
Y <- matrix(unlist(df),nrow=nrow(df))+1
Z <- matrix(unlist(grp),nrow=length(grp))
n <- nrow(Y)
p <- ncol(Y)
K <- apply(Y,2,max,na.rm=TRUE)
m.delta <- priors$m.delta
s.delta <- priors$s.delta
m.beta <- priors$m.beta
s.beta <- priors$s.beta
namlist <- c(sapply(1:p, function(x) paste0("delta[",x,',',paste0(1:K[p],"]"))))
if (sum(is.dif)!=0) {
namlist <- c(namlist,sapply(1:p, function(x) paste0("gamma[",x,',',paste0(1:K[p],"]"))),"beta")
} else {
if (!is.null(grp)) {
namlist <- c(namlist,"beta")
}
}
data <- list(Y=Y,Z=Z,n=n,p=p,K=K,m.beta=m.beta,s.beta=s.beta,m.delta=m.delta,s.delta=s.delta)
params <- c("delta","beta")
if ("n.burn"%in%names(param)) {
n.burn <- param$n.burn
} else {
n.burn <- 4000
}
if ("n.thin"%in%names(param)) {
n.thin <- param$n.thin
} else {
n.thin <- 20
}
if ("n.chains"%in%names(param)) {
n.chains <- param$n.chains
} else {
n.chains <- 2
}
if ("n.sim"%in%names(param)) {
n.sim <- param$n.sim
} else {
n.sim <- 20000
}
if ("nb.cores"%in%names(param)) {
nb.cores <- param$nb.cores
} else {
nb.cores <- 6
}
cl <- parallel::makeForkCluster(nb.cores)
if (verbose) {
cat('Initializing Chains...')
}
dclone::parJagsModel(cl,name="mod.jags",data = data,inits = NULL,file = "/home/corentin/Documents/These/Recherche/SPT/src/bpcm_beta",n.chains=n.chains)
if (verbose) {
cat('DONE \n')
cat('Applying burn-in iterations...')
}
dclone::parUpdate(cl,object="mod.jags",n.burn=n.burn)
if (verbose) {
cat('DONE \n')
cat('Running Markov Chains...')
}
mod.samples <- dclone::parCodaSamples(cl,model="mod.jags",variable.names=params,n.iter = n.sim,thin = n.thin)
if (verbose) {
cat('DONE \n')
}
parallel::stopCluster(cl)
if (diag.plots) {
cat("Displaying traceplots...")
traceplot(mod.samples)
readline(prompt="Use the arrows to navigate between traceplots. Press [enter] to continue")
cat("DONE\n")
cat("Displaying autocorrelation plots...")
autocorr.plot(mod.samples,ask=F)
readline(prompt="Use the arrows to navigate between autocorr plots. Press [enter] to continue")
cat("DONE\n ")
}
res <- mod.samples[[1]]
res <- as.data.frame(res)[,namlist]
namlist2 <- unlist(c(sapply(nam,function(x) paste0(x,"_",1:K[which(nam_o==x)]-1))))
if (sum(is.dif)!=0) {
namlist2 <- c(namlist2,unlist(c(sapply(nam,function(x) paste0(x,"_",1:K[which(nam_o==x)]-1,":grp")))),"beta")
} else {
if (!is.null(grp)) {
namlist2 <- c(namlist2,"beta")
}
}
colnames(res) <- namlist2
res <- res[,namlist2]
res <- res[,apply(res,2,function(x) all(x==0))==0]
xsi <- apply(res,2,function(x) c(mean(x),sd(x),quantile(x,0.05),quantile(x,0.95)) )
rownames(xsi) <- c("post.mean","post.sd","post.90.cred.low","post.90.cred.high")
xsi <- round(t(xsi),4)
if ("beta" %in% rownames(xsi)) {
beta <- xsi[rownames(xsi)=="beta",]
xsi <- xsi[rownames(xsi)!="beta",]
}
out <- list(mcmc.res=res,
dif.items=nam_o[which(is.dif==1)],
beta=beta,
thresholds=xsi)
#####################################################
############### GROUP EFFECT / NO DIF ###############
#####################################################
} else {
nam <- colnames(df)
nam_o <- nam
Y <- matrix(unlist(df),nrow=nrow(df))+1
Z <- matrix(unlist(grp),nrow=length(grp))
n <- nrow(Y)
p <- ncol(Y)
pnodif <- p-sum(is.dif)
pnodif1 <- p-sum(is.dif)+1
pdif <- sum(is.dif)
pnounif <- pnodif+pdif-sum(is.unif)
pnounif1 <- pnodif+pdif-sum(is.unif)+1
K <- apply(Y,2,max,na.rm=TRUE)
m.delta <- priors$m.delta
s.delta <- priors$s.delta
m.beta <- priors$m.beta
s.beta <- priors$s.beta
m.gamma <- priors$m.gamma
s.gamma <- priors$s.gamma
namlist <- c(sapply(1:p, function(x) paste0("delta[",x,',',paste0(1:K[p],"]"))))
if (sum(is.dif)!=0) {
namlist <- c(namlist,sapply(1:p, function(x) paste0("gamma[",x,',',paste0(1:K[p],"]"))),"beta")
} else {
if (!is.null(grp)) {
namlist <- c(namlist,"beta")
}
}
Y <- Y[,c(which(is.dif+is.unif==0),which(is.dif+is.unif==1),which(is.dif+is.unif==2))]
nam <- nam[c(which(is.dif+is.unif==0),which(is.dif+is.unif==1),which(is.dif+is.unif==2))]
data <- list(Y=Y,Z=Z,n=n,p=p,pnounif=pnounif,pnounif1=pnounif1,pdif=pdif,pnodif1=pnodif1,pnodif=pnodif,K=K,m.beta=m.beta,s.beta=s.beta,m.gamma=m.gamma,s.gamma=s.gamma,m.delta=m.delta,s.delta=s.delta,difff=as.factor(is.dif),unif=as.factor(is.unif))
params <- c("delta","gamma","beta")
if ("n.burn"%in%names(param)) {
n.burn <- param$n.burn
} else {
n.burn <- 4000
}
if ("n.thin"%in%names(param)) {
n.thin <- param$n.thin
} else {
n.thin <- 20
}
if ("n.chains"%in%names(param)) {
n.chains <- param$n.chains
} else {
n.chains <- 2
}
if ("n.sim"%in%names(param)) {
n.sim <- param$n.sim
} else {
n.sim <- 20000
}
if ("nb.cores"%in%names(param)) {
nb.cores <- param$nb.cores
} else {
nb.cores <- 6
}
cl <- parallel::makeForkCluster(nb.cores)
if (verbose) {
cat('Initializing Chains...')
}
dclone::parJagsModel(cl,name="mod.jags",data = data,inits = NULL,file = "/home/corentin/Documents/These/Recherche/SPT/src/bpcm_dif",n.chains=n.chains)
if (verbose) {
cat('DONE \n')
cat('Applying burn-in iterations...')
}
dclone::parUpdate(cl,object="mod.jags",n.burn=n.burn)
if (verbose) {
cat('DONE \n')
cat('Running Markov Chains...')
}
mod.samples <- dclone::parCodaSamples(cl,model="mod.jags",variable.names=params,n.iter = n.sim,thin = n.thin)
if (verbose) {
cat('DONE \n')
}
parallel::stopCluster(cl)
if (diag.plots) {
cat("Displaying traceplots...")
traceplot(mod.samples)
readline(prompt="Use the arrows to navigate between traceplots. Press [enter] to continue")
cat("DONE\n")
cat("Displaying autocorrelation plots...")
autocorr.plot(mod.samples,ask=F)
readline(prompt="Use the arrows to navigate between autocorr plots. Press [enter] to continue")
cat("DONE\n ")
}
res <- mod.samples[[1]]
res <- as.data.frame(res)[,namlist]
namlist2 <- unlist(c(sapply(nam,function(x) paste0(x,"_",1:K[which(nam_o==x)]-1))))
if (sum(is.dif)!=0) {
namlist2 <- c(namlist2,unlist(c(sapply(nam,function(x) paste0(x,"_",1:K[which(nam_o==x)]-1,":grp")))),"beta")
} else {
if (!is.null(grp)) {
namlist2 <- c(namlist2,"beta")
}
}
colnames(res) <- namlist2
res <- res[,namlist2]
res <- res[,apply(res,2,function(x) all(x==0))==0]
xsi <- apply(res,2,function(x) c(mean(x),sd(x),quantile(x,0.05),quantile(x,0.95)) )
rownames(xsi) <- c("post.mean","post.sd","post.90.cred.low","post.90.cred.high")
xsi <- round(t(xsi),4)
if ("beta" %in% rownames(xsi)) {
beta <- xsi[rownames(xsi)=="beta",]
if (is.null(grp)) {
beta <- NA
}
xsi <- xsi[rownames(xsi)!="beta",]
}
out <- list(mcmc.res=res,
dif.items=nam_o[which(is.dif==1)],
beta=beta,
thresholds=xsi)
}
if (is.null(dim(out$beta))) {
out$beta <- NA
}
return(out)
}

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## File Name: pcm.R
## File version: 1.0
#' Compute Partial Credit Model (PCM) for polytomous and dichotomous items
#'
#' This function computes a frequentist PCM, potentially accounting for DIF on specified items
#'
#' @param df data.frame containing the data
#' @param items vector containing the names of columns where item responses are stored in df
#' @param grp string containing the name of the column where an optional group membership variable is stored in df
#' @param dif.items vector containing the list of indexes in "items" corresponding to dif items
#' @param type.dif vector containing DIF form for each item specified in dif.items. 1 is homogeneous DIF, 0 is heterogeneous DIF
#' @return A data.frame containing various model outputs
#' @import vcrpart
#' @export
pcm <- function(df=NULL,items=NULL,grp=NULL,dif.items=NULL,type.dif=NULL,verbose=T,fit="ucminf") {
##### Detecting errors
if (any(!(items %in% colnames(df)))) {
stop("ERROR: provided item name does not exist in df")
}
if (any(!(grp %in% colnames(df)))) {
stop("ERROR: provided group variable name does not exist in df")
}
if (any(!is.null(grp))) {
if (any(!(grp%in%colnames(df)))) {
stop("ERROR: group name does not exist in df")
}
}
if (!is.null(dif.items) & length(dif.items)!=length(type.dif)) {
stop('ERROR: type.dif is not the same length as dif.items')
}
if (!is.null(dif.items) & is.null(type.dif)) {
warning("WARNING: no type.dif provided, assuming non-homogeneous DIF on all items")
}
if (!("id"%in%colnames(df))) {
stop('ERROR: no column named id provided')
}
if ( any(apply(df[df[,grp]==0,items],2,max)<max(df[,items])) | any(apply(df[df[,grp]==1,items],2,max)<max(df[,items])) ) {
if (fit=="ucminf") {
fit <- "optim"
}
}
##### Analysis
restab.diftype <- NULL
se.beta <- NULL
beta.ci <- NULL
beta.p <- NULL
nbitems <- length(items)
items_o <- items
colnames(df)[which(colnames(df)%in%items_o)] <- paste0("item",1:nbitems)
items <- paste0("item",1:nbitems)
# If no group
if (is.null(grp)) {
if (verbose) {
cat('\n')
cat("#################################################################################################\n")
cat("######################################### FITTING MODEL #########################################\n")
cat("#################################################################################################\n")
}
grp <- NULL
# prepare data
df <- df[,c('id',items)]
print(df)
colnames(df)[2:(length(colnames(df)))] <- paste0("item",seq(1,length(colnames(df))-1))
df.long <- reshape(df,v.names=c("item"),direction="long",varying=c(items))
colnames(df.long) <- c("id","item","resp")
nbitems <- length(2:(length(colnames(df))))
maxmod <- max(df[,2:(length(colnames(df)))])
df.long$item <- factor(df.long$item,levels=seq(1,length(colnames(df))-1),ordered = F)
df.long$resp <- factor(df.long$resp,0:maxmod,ordered=T)
df.long$id <- factor(df.long$id)
# fit pcm
mod <- olmm(resp ~ 0 + ce(item) + re(0|id),data=df.long,family = adjacent(link = "logit"))
comod <- coef(mod)
# output results
restab <- t(sapply(1:nbitems,function(x) comod[seq(x,length(comod)-1,nbitems)]))
rownames(restab) <- paste0("item",1:nbitems)
colnames(restab) <- paste0("delta_",1:maxmod)
restab.dif <- NULL
beta <- NULL
}
# If group
else {
grp <- df[,grp]
df$grp <- grp
# If group and DIF
if (!is.null(dif.items)) {
if (verbose) {
cat('\n')
cat("#################################################################################################\n")
cat("######################################### FITTING MODEL #########################################\n")
cat("#################################################################################################\n")
}
# prepare data
df <- df[,c('id',items,"grp")]
colnames(df)[2:(length(colnames(df))-1)] <- paste0("item",seq(1,length(colnames(df))-2))
df.long <- reshape(df,v.names=c("item"),direction="long",varying=c(items))
colnames(df.long) <- c("id","grp","item","resp")
nbitems <- length(2:(length(colnames(df))-1))
maxmod <- max(df[,2:(length(colnames(df))-1)])
df.long$item <- factor(df.long$item,levels=seq(1,length(colnames(df))-2),ordered = F)
df.long$resp <- factor(df.long$resp,0:maxmod,ordered=T)
df.long$id <- factor(df.long$id)
# Create 1 dif column per dif item
for (i in 1:length(dif.items)) {
df.long[,paste0("dif",i)] <- ifelse(df.long$item==dif.items[i],1,0)
}
difvar <- sapply(1:length(dif.items),function(x) paste0("dif",x))
difvar.unif <- difvar[type.dif==1]
difvar.nonunif <- difvar[type.dif==0]
# fit pcm
formudif <- paste0("resp ~ 0 + ge(grp",ifelse(length(difvar.unif>0),"+",""),ifelse(length(difvar.unif>0),paste0(difvar.unif,":grp",collapse="+"),""),")+ce(item",ifelse(length(difvar.nonunif>0),"+",""),ifelse(length(difvar.nonunif)>0,paste0(difvar.nonunif,":grp",collapse="+"),""),")+re(0|id)")
formudif <- as.formula(formudif)
mod <- olmm(formudif,data=df.long,family = adjacent(link = "logit"),control=olmm_control(fit=fit))
comod <- coef(mod)
# output results
nbcoef <- nbitems+length(difvar.nonunif)
restab <- t(sapply(1:nbcoef,function(x) comod[seq(x,length(comod)-2-length(difvar.unif),nbitems+length(difvar.nonunif))]))
difcoef.unif <- NULL
if (length(difvar.unif)>0) {
difcoef.unif <- comod[(length(comod)-length(difvar.unif)):(length(comod)-1)]
if (length(difvar.unif)!=1) {
difcoef.unif <- as.matrix(difcoef.unif)
} else {
difcoef.unif <- t(as.matrix(difcoef.unif))
}
rname <- paste0("item",dif.items[type.dif==1])
rownames(difcoef.unif) <- paste0("dif.",items_o[which(items%in%rname)])
colnames(difcoef.unif) <- "gamma"
difcoef.unif <- as.data.frame(difcoef.unif)
for (k in 1:maxmod) {
difcoef.unif[,paste0("gamma_",k)] <- difcoef.unif[,"gamma"]
}
difcoef.unif <- as.matrix(difcoef.unif[,2:ncol(difcoef.unif)])
}
difcoef.nonunif <- NULL
if (length(difvar.nonunif)>0) {
difcoef.nonunif <- restab[nbitems+c(1:length(difvar.nonunif)),]
if (length(difvar.nonunif)==1) {
difcoef.nonunif <- t(as.matrix(difcoef.nonunif))
} else {
difcoef.nonunif <- as.matrix(difcoef.nonunif)
}
rname <- paste0("item",dif.items[type.dif==0])
rownames(difcoef.nonunif) <- paste0("dif.",items_o[which(items%in%rname)])
colnames(difcoef.nonunif) <- paste0("gamma_",1:maxmod)
}
restab <- restab[1:nbitems,]
rownames(restab) <- items_o
colnames(restab) <- paste0("delta_",1:maxmod)
restab.dif <- rbind(difcoef.nonunif,difcoef.unif)
restab.diftype <- matrix(ifelse(type.dif==1,"HOMOGENEOUS","NON-HOMOGENEOUS"))
restab.diftype <- noquote(restab.diftype)
rownames(restab.diftype) <- rownames(restab.dif)
colnames(restab.diftype) <- "dif.type"
beta <- comod["grp"]
se.beta <- (confint(mod)["grp",2]-beta)/1.96
beta.ci <- confint(mod)["grp",]
beta.p <- 2*pnorm(-abs(beta/se.beta))
beta <- as.numeric(beta)
se.beta <- as.numeric(se.beta)
beta.p <- as.numeric(beta.p)
beta <- -1*beta
beta.ci <- -1*c(beta.ci[2],beta.ci[1])
} else {
# If group no DIF
if (verbose) {
cat('\n')
cat("#################################################################################################\n")
cat("######################################### FITTING MODEL #########################################\n")
cat("#################################################################################################\n")
}
# prepare data
df <- df[,c('id',items,"grp")]
colnames(df)[2:(length(colnames(df))-1)] <- paste0("item",seq(1,length(colnames(df))-2))
df.long <- reshape(df,v.names=c("item"),direction="long",varying=c(items))
colnames(df.long) <- c("id","grp","item","resp")
nbitems <- length(2:(length(colnames(df))-1))
maxmod <- max(df[,2:(length(colnames(df))-1)])
df.long$item <- factor(df.long$item,levels=seq(1,length(colnames(df))-2),ordered = F)
df.long$resp <- factor(df.long$resp,0:maxmod,ordered=T)
df.long$id <- factor(df.long$id)
# fit pcm
mod <- olmm(resp ~ 0 + ge(grp) + ce(item) + re(0|id),data=df.long,family = adjacent(link = "logit"),control=olmm_control(fit=fit))
comod <- coef(mod)
# output results
restab <- t(sapply(1:nbitems,function(x) comod[seq(x,length(comod)-2,nbitems)]))
rownames(restab) <- items_o
colnames(restab) <- paste0("delta_",1:maxmod)
restab.dif <- NULL
beta <- comod[length(comod)-1]
se.beta <- (confint(mod)["grp",2]-beta)/1.96
beta.ci <- confint(mod)["grp",]
beta.p <- 2*pnorm(-abs(beta/se.beta))
beta <- as.numeric(beta)
se.beta <- as.numeric(se.beta)
beta.p <- as.numeric(beta.p)
beta <- -1*beta
beta.ci <- -1*c(beta.ci[2],beta.ci[1])
}
}
theta <- -1*ranef(mod,norm=F)+ifelse(grp==1,beta,0)
resid <- apply(matrix(1:nbitems,ncol=length(nbitems)),1, function(k) sapply(1:nrow(df), function(j) res_ij(theta[j],restab[k,],df[j,items[k]],beta=0)))
colnames(resid) <- items_o
##### Output
if (verbose) {
cat(paste0('Number of individuals: ',nrow(df),"\n"))
cat(paste0('Number of items: ',length(items),"\n"))
cat(paste0('Item Thresholds and DIF parameters: ',"\n"))
}
out <- list(
beta=beta,
beta.se=se.beta,
beta.ci=beta.ci,
beta.p=beta.p,
dif.items=dif.items,
dif.type=restab.diftype,
thresholds=restab,
dif.param=restab.dif,
theta=theta,
residuals=resid
)
return(out)
}

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## File Name: res_ij.R
## File version: 1.0
#' Compute rasch person-item residuals
#'
#' This function computes person-item residuals for rasch family adjacent-categories models
#' like the Rasch model or the PCM
#'
#' @param thetahat_i Person parameter estimate for person i
#' @param delta_hat_j Item threshold parameter estimates for item j
#' @param res Response of person i to item j
#' @param beta Estimated latent mean difference between groups, can be ignored
#' @return A single scalar equal to the residual for person i on item j
#' @import vcrpart
#' @export
res_ij <- function(thetahat_i,delta_hat_j,res,beta=0){
var=0
denomin=1
for (i in 1:length(delta_hat_j)) {
denomin=denomin+exp(i*(thetahat_i+beta)-sum(delta_hat_j[1:i]))
}
posterior=c(1)
for (i in 1:length(delta_hat_j)) {
posterior=c(posterior,exp(i*(thetahat_i+beta)-sum(delta_hat_j[1:i])))
}
posterior=posterior/denomin
for(i in 0:length(delta_hat_j)){
var=var+((i-sum(posterior*0:length(delta_hat_j)))**2)*posterior[i+1]
}
return((res-sum(posterior*0:length(delta_hat_j)))/sqrt(var))
}

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## File Name: residif.R
## File version: 1.0
#' RESIDIF procedure for DIF detection as per Andrich and Hagquist (2015)
#'
#' This function detects DIF on PCM items using ANOVA of person-item residuals
#'
#' @param df data.frame containing the data
#' @param items vector containing the names of columns where item responses are stored in df
#' @param grp vector containing the name of the column where an optional group membership variable is stored in df
#' @return A data.frame containing a column listing the detected DIF item and another listing detected DIF forms
#' @import vcrpart
#' @export
residif <- function(df=NULL,items=NULL,grp=NULL,verbose=T) {
if (any(!(items %in% colnames(df)))) {
stop("ERROR: provided item name does not exist in df")
}
if (any(!(grp %in% colnames(df)))) {
stop("ERROR: provided grp variable name does not exist in df")
}
if (any(is.null(grp))) {
stop("ERROR: no grp variable provided")
}
if (any(is.null(items))) {
stop("ERROR: no items provided")
}
maxcat <- max(df[,items])
nbitems <- length(items)
nbitems_o <- nbitems
if (verbose) {
cat('\n')
cat("#################################################################################################\n")
cat("##################################### COMPUTING INITIAL PCM #####################################\n")
cat("#################################################################################################\n")
}
startt <- Sys.time()
pcm_initial <- pcm(df = df,items = items,grp = grp,verbose=F)
dat <- df
dat$score <- rowSums(dat[,items])
nqt <- ifelse(length(unique(quantile(dat$score,seq(0,1,0.2))))==6,5,length(unique(quantile(dat$score,seq(0,1,0.2))))-1)
while (length(unique(quantile(dat$score,seq(0,1,1/nqt))))!=nqt+1) {
nqt <- nqt-1
}
dat$score_q5 <- cut(dat$score,unique(quantile(dat$score,seq(0,1,1/nqt))),labels=1:nqt,include.lowest=T)
res.anova <- rep(NA,nbitems)
pval <- rep(NA,nbitems)
fval <- rep(NA,nbitems)
for (i in 1:nbitems) {
dat[,paste0('res_',i)] <- pcm_initial$residuals[,i]
res.anova[i] <- summary(aov(dat[,paste0('res_',i)]~get(grp)*score_q5,data=dat))
pval[c(i,i+nbitems)] <- c(res.anova[[i]][1,"Pr(>F)"],res.anova[[i]][3,"Pr(>F)"])
fval[c(i,i+nbitems)] <- c(res.anova[[i]][1,'F value'],res.anova[[i]][3,"F value"])
}
if (verbose) {
cat('DONE\n')
cat('#################################################################################################\n')
}
res.items <- c()
res.uniform <- c()
resp <- df[,items]
k <- 1
while(any(pval<0.05/(nbitems_o*3))) {
k <- k+1
if (verbose) {
cat(paste("######################################## COMPUTING STEP",k,"#######################################\n"))
cat("#################################################################################################\n")
}
numitem <- ifelse(which.max(fval)%%(length(fval)/2)!=0,which.max(fval)%%(length(fval)/2),length(fval)/2)
res.item <- gsub("[a-z]", "",colnames(resp)[numitem])
res.items <- c(res.items,res.item)
res.uni <- res.anova[[numitem]][3,"Pr(>F)"]>0.05
res.uniform <- c(res.uniform,res.uni)
pcm_while <- pcm(df = df,items = items,grp = grp,dif.items = res.items,type.dif = res.uniform,verbose=F)
res.anova <- rep(NA,nbitems)
pval <- rep(NA,nbitems_o)
fval <- rep(NA,nbitems_o)
numitems <- 1:nbitems_o
numitems <- numitems[-which(numitems%in%res.items)]
for (i in numitems) {
dat[,paste0('res_',i)] <- pcm_while$residuals[,i]
res.anova[i] <- summary(aov(dat[,paste0('res_',i)]~dat[,grp]*score_q5,data=dat))
pval[c(i,i+nbitems)] <- c(res.anova[[i]][1,"Pr(>F)"],res.anova[[i]][3,"Pr(>F)"])
fval[c(i,i+nbitems)] <- c(res.anova[[i]][1,'F value'],res.anova[[i]][3,"F value"])
}
for (i in 1:nbitems_o) {
pval[i] <- ifelse(is.na(pval[i]),999,pval[i])
fval[i] <- ifelse(is.na(fval[i]),-999,fval[i])
}
if (verbose) {
cat('DONE\n')
if (any(pval<0.05/(nbitems_o*3))) {
cat('#################################################################################################\n')
}
}
}
endt <- Sys.time()
cat(paste(c('Algorithm ran for',round(endt-startt,4),"seconds\n")))
if (verbose) {
cat('#################################################################################################\n')
cat("###################################### DETECTED DIF ITEMS #######################################\n")
cat("#################################################################################################\n")
}
if (length(res.items>0)) {
results <- data.frame(dif.items=res.items,
uniform=ifelse(res.uniform==1,TRUE,FALSE))
return(results)
}
else {
if (verbose) {
cat("No DIF was detected\n")
}
return(NULL)
}
}

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Version: 1.0
RestoreWorkspace: Default
SaveWorkspace: Default
AlwaysSaveHistory: Default
EnableCodeIndexing: Yes
UseSpacesForTab: Yes
NumSpacesForTab: 2
Encoding: UTF-8
RnwWeave: Sweave
LaTeX: pdfLaTeX
AutoAppendNewline: Yes
StripTrailingWhitespace: Yes
BuildType: Package
PackageUseDevtools: Yes
PackageInstallArgs: --no-multiarch --with-keep.source

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/bpcm.R
\name{bpcm}
\alias{bpcm}
\title{Compute Bayesian Partial Credit Model (BPCM) for polytomous and dichotomous items}
\usage{
bpcm(
df = NULL,
grp = NULL,
is.dif = NULL,
is.unif = NULL,
priors = NULL,
param = list(),
verbose = T,
diag.plots = F
)
}
\arguments{
\item{df}{data.frame containing the response data}
\item{grp}{vector containing the column where an optional group membership variable is stored in df}
\item{is.dif}{indicator vector containing 1 at the inded of each DIF item in df and 0 otherwise}
\item{is.unif}{indicator vector containing 1 at the inded of each uniform DIF item in df and 0 otherwise}
\item{diag.plots}{boolean indicating whether the JAGS diagnosis plots should be displayed}
\item{prior}{prior function to be used}
}
\value{
A data.frame containing various model outputs
}
\description{
This function computes a bayesian PCM, potentially accounting for DIF on specified items
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/pcm.R
\name{pcm}
\alias{pcm}
\title{Compute Partial Credit Model (PCM) for polytomous and dichotomous items}
\usage{
pcm(
df = NULL,
items = NULL,
grp = NULL,
dif.items = NULL,
type.dif = NULL,
verbose = T,
fit = "ucminf"
)
}
\arguments{
\item{df}{data.frame containing the data}
\item{items}{vector containing the names of columns where item responses are stored in df}
\item{grp}{string containing the name of the column where an optional group membership variable is stored in df}
\item{dif.items}{vector containing the list of indexes in "items" corresponding to dif items}
\item{type.dif}{vector containing DIF form for each item specified in dif.items. 1 is homogeneous DIF, 0 is heterogeneous DIF}
}
\value{
A data.frame containing various model outputs
}
\description{
This function computes a frequentist PCM, potentially accounting for DIF on specified items
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/res_ij.R
\name{res_ij}
\alias{res_ij}
\title{Compute rasch person-item residuals}
\usage{
res_ij(thetahat_i, delta_hat_j, res, beta = 0)
}
\arguments{
\item{thetahat_i}{Person parameter estimate for person i}
\item{delta_hat_j}{Item threshold parameter estimates for item j}
\item{res}{Response of person i to item j}
\item{beta}{Estimated latent mean difference between groups, can be ignored}
}
\value{
A single scalar equal to the residual for person i on item j
}
\description{
This function computes person-item residuals for rasch family adjacent-categories models
like the Rasch model or the PCM
}

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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/residif.R
\name{residif}
\alias{residif}
\title{RESIDIF procedure for DIF detection as per Andrich and Hagquist (2015)}
\usage{
residif(df = NULL, items = NULL, grp = NULL, verbose = T)
}
\arguments{
\item{df}{data.frame containing the data}
\item{items}{vector containing the names of columns where item responses are stored in df}
\item{grp}{vector containing the name of the column where an optional group membership variable is stored in df}
}
\value{
A data.frame containing a column listing the detected DIF item and another listing detected DIF forms
}
\description{
This function detects DIF on PCM items using ANOVA of person-item residuals
}

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model {
for (i in 1:n) {
for (j in 1:p) {
Y[i,j] ~ dcat(prob[i,j,1:K[j]])
}
theta[i] ~ dnorm(0,1)
}
for (i in 1:n) {
for (j in 1:p) {
for (k in 1:K[j] ) {
eta[i,j,k] <- theta[i] - delta[j,k]
psum[i,j,k] <- sum(eta[i,j,1:k])
exp.psum[i,j,k] <- exp(psum[i,j,k])
prob[i,j,k] <- exp.psum[i,j,k] / sum(exp.psum[i,j,1:K[j]])
} } }
for (j in 1:p) {
delta[j,1] <- 0.0
for (k in 2:K[j]) {
delta[j,k] ~ dnorm(m.delta, pr.delta)
}
}
pr.delta <- pow(s.delta, -2)
}

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model {
for (i in 1:n) {
for (j in 1:p) {
Y[i,j] ~ dcat(prob[i,j,1:K[j]])
}
theta[i] ~ dnorm(0,1)
}
for (i in 1:n) {
for (j in 1:p) {
for (k in 1:K[j] ) {
eta[i,j,k] <- theta[i] + (beta * Z[i,1]) - delta[j,k]
psum[i,j,k] <- sum(eta[i,j,1:k])
exp.psum[i,j,k] <- exp(psum[i,j,k])
prob[i,j,k] <- exp.psum[i,j,k] / sum(exp.psum[i,j,1:K[j]])
} } }
for (j in 1:p) {
delta[j,1] <- 0.0
for (k in 2:K[j]) {
delta[j,k] ~ dnorm(m.delta, pr.delta)
}
}
beta ~ dnorm(m.beta,pr.beta)
pr.delta <- pow(s.delta, -2)
pr.beta <- pow(s.beta,-2)
}

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model {
for (i in 1:n) {
for (j in 1:p) {
Y[i,j] ~ dcat(prob[i,j,1:K[j]])
}
theta[i] ~ dnorm(0, 1)
}
for (i in 1:n) {
for (j in 1:p) {
for (k in 1:K[j] ) {
eta[i,j,k] <- theta[i] + (beta * Z[i,1]) - ( delta[j,k] + Z[i,1]*ifelse(k==1,0,gamma[j,k]) )
psum[i,j,k] <- sum(eta[i,j,1:k])
exp.psum[i,j,k] <- exp(psum[i,j,k])
prob[i,j,k] <- exp.psum[i,j,k] / sum(exp.psum[i,j,1:K[j]])
} } }
for (j in 1:pnodif) {
delta[j,1] <- 0.0
gamma[j,1] <- 0.0
for (k in 2:K[j]) {
delta[j,k] ~ dnorm(m.delta, pr.delta)
gamma[j,k] <- 0.0
}
}
for (j in pnodif1:pnounif) {
delta[j,1] <- 0.0
gamma[j,1] <- 0.0
for (k in 2:K[j]) {
delta[j,k] ~ dnorm(m.delta, pr.delta)
gamma[j,k] ~ dnorm(m.gamma,s.gamma)
}
}
for (j in pnounif1:p) {
delta[j,1] <- 0.0
gamma[j,1] <- 0.0
gamma[j,2] ~ dnorm(m.gamma,pr.gamma)
delta[j,2] ~ dnorm(m.delta, pr.delta)
for (k in 3:K[j]) {
delta[j,k] ~ dnorm(m.delta, pr.delta)
gamma[j,k] <- gamma[j,2]
}
}
beta ~ dnorm(m.beta,pr.beta)
pr.delta <- pow(s.delta, -2)
pr.beta <- pow(s.beta,-2)
pr.gamma <- pow(s.gamma,-2)
}