R/LR.2step.R
In miguel-sorrel/cdcatR: Cognitive Diagnostic Computerized Adaptive Testing
Defines functions
LR.2step
Documented in
LR.2step
#' Item-level model comparison using 2LR test
#'
#' This function evaluates whether the saturated G-DINA model can be replaced by reduced CDMs without significant loss in model data fit for each item using two-step likelihood ratio test (2LR). Sorrel, de la Torre, Abad, and Olea (2017) and Ma & de la Torre (2018) can be consulted for details. Conducting this type of analysis can facilitate the calibration of the item bank and have implications for the CAT accuracy and item usage (Sorrel, Abad, & Nájera, 2021).
#'
#' @param fit Calibrated item bank with the \code{GDINA::GDINA} (Ma & de la Torre, 2020) or \code{CDM::gdina} (Robitzsch et al., 2020) R packages functions
#' @param p.adjust.method Scalar character. Correction method for \emph{p}-values. Possible values include \code{"holm"}, \code{"hochberg"}, \code{"hommel"}, \code{"bonferroni"}, \code{"BH"}, \code{"BY"}, \code{"fdr"}, and \code{"none"}. See \code{p.adjust} function from the \code{stats} R package for additional details. Default is \code{holm}
#' @param alpha.level Scalar numeric. Alpha level for decision. Default is \code{0.05}
#'
#' @return \code{LR2.step} returns an object of class \code{LR2.step}
#' \describe{
#' \item{LR2}{Numeric matrix. LR2 statistics}
#' \item{pvalues}{Numeric matrix. \emph{p}-values associated with the 2LR statistics}
#' \item{adj.pvalues}{Numeric matrix. Adjusted \emph{p}-values associated with the 2LR statistics}
#' \item{df}{Numeric matrix. Degrees of freedom}
#' \item{models.adj.pvalues}{Character vector denoting the model selected for each item using the \emph{largestp} rule (Ma et al., 2016). All statistics whose \emph{p}-values are less than \code{alpha.level} are rejected. All statistics with \emph{p}-value larger than \code{alpha.level} define the set of candidate reduced models. The G-DINA model is retained if all statistics are rejected. Whenever the set includes more than one model, the model with the largest \emph{p}-value is selected as the best model for that item}
#' }
#'
#' @references
#'
#' Ma, W. & de la Torre, J. (2018). Category-level model selection for the sequential G-DINA model. \emph{Journal of Educational and Behavorial Statistic, 44}, 45-77.
#'
#' Ma, W. & de la Torre, J. (2020). GDINA: The generalized DINA model framework. R package version 2.7.9. Retrived from https://CRAN.R-project.org/package=GDINA
#'
#' Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection and attribute classification.
#' \emph{Applied Psychological Measurement, 40}, 200-217.
#'
#' Robitzsch, A., Kiefer, T., George, A. C., & Uenlue, A. (2020). CDM: Cognitive Diagnosis Modeling. R package version 7.5-15. https://CRAN.R-project.org/package=CDM
#'
#' Sorrel, M. A., de la Torre, J., Abad, F. J., & Olea, J. (2017). Two-step likelihood ratio test for item-level model comparison in cognitive diagnosis models. \emph{Methodology, 13}, 39-47.
#'
#' Sorrel, M. A., Abad, F. J., & Nájera, P. (2021). Improving accuracy and usage by correctly selecting: The effects of model selection in cognitive diagnosis computerized adaptive testing. \emph{Applied Psychological Measurement, 45}, 112-129.
#'
#' @import stats
#'
#' @examples
#'Q <- sim180DINA$simQ
#'dat <- sim180DINA$simdat
#'resGDINA <- GDINA::GDINA(dat = dat, Q = Q, model = "GDINA",verbose = FALSE)
#'#resCDM <- CDM::gdina(data = dat, q.matrix = Q, rule = "GDINA", progress = FALSE)
#'LR2.GDINA <- LR.2step(fit = resGDINA) # GDINA package
#'#LR2.CDM <- LR.2step(fit = resCDM) # CDM package
#'mean(LR2.GDINA$models.adj.pvalues[which(rowSums(Q) != 1)] ==
#' sim180DINA$specifications$item.bank$specifications$model[which(rowSums(Q) != 1)])
#'#mean(LR2.CDM$models.adj.pvalues[which(rowSums(Q) != 1)] ==
#'# sim180DINA$specifications$item.bank$specifications$model[which(rowSums(Q) != 1)])
#'
#' @export
#'
LR.2step <- function(fit, p.adjust.method = "holm", alpha.level = 0.05)
{
if(!inherits(fit, what = c("GDINA", "gdina"))){stop("fit must be an object of class 'GDINA' or 'gdina'")}
if(!(p.adjust.method %in% c("holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none"))){stop("p.adjust.method must be one of the following: 'holm', 'hochberg', 'hommel', 'bonferroni', 'BH', 'BY', 'fdr', 'none'")}
if(alpha.level > 1 | alpha.level < 0){stop("alpha.level must be a value between 0 and 1.")}
make.Lik.DINA.k <- function(vP){
p <- rep(vP[1], classes - 1)
p[classes] <- vP[1] + vP[2]
logp <- log(p)
logq <- log(1 - p)
L <- sum(RNjjob[1,] * logp) + sum(RNjjob[3,] * logq)
return(-L)
}
make.Lik.DINO.k <- function(vP){
p <- rep(vP[1] + vP[2], classes)
p[1] <- vP[1]
logp <- log(p)
logq <- log(1 - p)
L <- sum(RNjjob[1,] * logp) + sum(RNjjob[3,] * logq)
return(-L)
}
make.Lik.ACDM.k <- function(vP){
par <- matrix(vP[-1], ncol = 1)
p <- c(vP[1] + posible.patterns %*% par)
logp <- log(p)
logq <- log(1 - p)
L <- sum(RNjjob[1,] * logp) + sum(RNjjob[3,] * logq)
return(-L)
}
make.Lik.GDINA.k <- function(pars){
p <- pars
logp <- log(p)
logq <- log(1 - p)
L <- sum(RNjjob[1,] * logp) + sum(RNjjob[3,] * logq)
return(-L)
}
est <- fit
if(!is.null(est)){
if(!is.null(est$extra$call)){ # package GDINA
Q <- est$options$Q
attpat <- GDINA::attributepattern(ncol(Q))
Rlj <- est$technicals$expectedCorrect
Nlj <- est$technicals$expectedTotal
catprob.parm <- est$catprob.parm
} else { # package CDM
Q <- est$q.matrix
attpat <- GDINA::attributepattern(ncol(Q))
attpat.s <- apply(attpat, 1, paste, collapse = "")
RLj <- est$control$R.lj
RLj <- RLj[,match(attpat.s, colnames(RLj))]
NLj <- est$control$I.lj
NLj <- NLj[,match(attpat.s, colnames(RLj))]
Rlj <- Nlj <- matrix(NA, nrow = nrow(Q), ncol = 2^max(rowSums(Q)))
catprob.parm <- list()
for(j in 1:nrow(Q)){
kj <- which(Q[j,] == 1)
tmp <- factor(apply(attpat[,kj, drop = F], 1, paste, collapse = ""))
tmp <- factor(tmp, levels = apply(unique(GDINA::attributepattern(length(kj))), 1, paste, collapse = ""))
for(l in 1:(2^length(kj))){
Rlj[j,l] <- sum(RLj[j, which(as.numeric(tmp) == l)])
Nlj[j,l] <- sum(NLj[j, which(as.numeric(tmp) == l)])
}
catprob.parm[[j]] <- est$probitem[est$probitem$itemno == j,]$prob
}
Rlj[is.na(Rlj)] <- 0
Nlj[is.na(Nlj)] <- 0
}
}
Kjs <- rowSums(Q)
Ks <- cumsum(2^Kjs)
item <- which(rowSums(Q) > 1)
J <- nrow(Q)
out <- list()
LR2 <- matrix(data = 0, nrow = J, ncol = 4)
LR2.p <- matrix(data = 0, nrow = J, ncol = 4)
df <- matrix(data = 0, nrow = J, ncol = 4)
for(jj in 1:J){
pars.jj <- catprob.parm[[jj]]
pars.jj[pars.jj < 0] <- 0
pars.jj[pars.jj > 1] <- 1
Kjj <- sum(Q[jj, ])
Kj <- length(pars.jj)
RNjjob <- rbind(Rlj[jj, 1:Kj], Nlj[jj, 1:Kj], Nlj[jj, 1:Kj] - Rlj[jj, 1:Kj])
classes <- 2^Kjs[jj]
posible.patterns <- GDINA::attributepattern(Kjj)
par.DINA <- constrOptim(theta = c(0.1, 0.1), f = make.Lik.DINA.k, grad = NULL,
ui = rbind(c(1, 0), c(0, 1), c(1, 1), c(-1, 0), c(0, -1), c(-1, -1)),
ci = c(.0001, .0001, .0001, -.9999, -.9999, -.9999))
par.DINO <- constrOptim(theta = c(0.1, 0.1), f = make.Lik.DINO.k, grad = NULL,
ui = rbind(c(1, 0), c(0, 1), c(1, 1), c(-1, 0), c(0, -1), c(-1, -1)),
ci = c(.0001, .0001, .0001, -.9999, -.9999 , -.9999))
par.ACDM <- constrOptim(theta = rep(0.1, Kjs[jj]+1), f = make.Lik.ACDM.k, grad = NULL,
ui = rbind(diag(Kjs[jj] + 1), -diag(Kjs[jj] + 1), rep(-1, Kjs[jj] + 1)),
ci = c(rep(.0001, Kjs[jj] + 1), rep(-.9999, Kjs[jj] + 2)))
par.GDINA.value <- make.Lik.GDINA.k(pars = pars.jj)
if(ncol(RNjjob) == 2){
LR2[jj,] <- LR2.p[jj,] <- df[jj,] <- cbind(jj, NA, NA, NA)
} else {
LR2DINA <- 2 * (par.GDINA.value * (-1) - par.DINA$value * (-1))
LR2DINO <- 2 * (par.GDINA.value * (-1) - par.DINO$value * (-1))
LR2ACDM <- 2 * (par.GDINA.value * (-1) - par.ACDM$value * (-1))
dfDINA <- dfDINO <- ncol(RNjjob) - 2
dfACDM <- ncol(RNjjob) - (Kjj + 1)
pDINA <- 1 - pchisq(LR2DINA, dfDINA)
pDINO <- 1 - pchisq(LR2DINO, dfDINO)
pACDM <- 1 - pchisq(LR2ACDM, dfACDM)
LR2[jj,] <- cbind(jj, LR2DINA, LR2DINO, LR2ACDM)
LR2.p[jj,] <- cbind(jj, pDINA, pDINO, pACDM)
df[jj,] <- cbind(jj, dfDINA, dfDINO, dfACDM)
}
}
if((sum(na.omit(LR2[, -1] == -Inf)) > 0) | (sum(is.nan(LR2[, -1])) > 0)) {
prob.items <- apply(LR2[, -1], 2, function(x) {which(x == -Inf)})[, 1]
warning(c("2LR statistic couldn't be computed for items ", paste(prob.items, collapse = ", "),
". G-DINA was retained for those items"))
}
LR2[, -1][which(LR2[, -1] == -Inf)] <- -9999
LR2[, -1][is.nan(LR2[, -1])] <- -9999
LR2.p[, -1][is.nan(LR2.p[, -1])] <- 0
LR2 <- na.omit(LR2)[, -1]
LR2.p <- na.omit(LR2.p)[, -1]
df <- na.omit(df)[, -1]
LR2.adjp <- LR2.p
LR2.adjp <- matrix(p.adjust(LR2.adjp, method = p.adjust.method), ncol = ncol(LR2.p), nrow = nrow(LR2.p))
model.alpha <- apply(LR2.adjp, 1, function(x){if(max(x, na.rm = T) > alpha.level){NA} else {return(0)}})
model.alpha[is.na(model.alpha)] <- apply(LR2.p[is.na(model.alpha),,drop = FALSE], 1, which.max)
models <- rep(0, nrow(Q))
models[which(rowSums(Q) != 1)] <- model.alpha
models.adjp <- models
models.adjp[which(models.adjp == 0)] <- "GDINA"
models.adjp[which(models.adjp == 1)] <- "DINA"
models.adjp[which(models.adjp == 2)] <- "DINO"
models.adjp[which(models.adjp == 3)] <- "ACDM"
colnames(LR2) <- colnames(LR2.p) <- colnames(LR2.adjp) <- colnames(df) <- c("DINA", "DINO", "ACDM")
rownames(LR2) <- rownames(LR2.p) <- rownames(LR2.adjp) <- rownames(df) <- paste("Item", item)
out <- list(LR2 = LR2, pvalues = LR2.p, adj.pvalues = LR2.adjp, df = df, models.adj.pvalues = models.adjp)
return(out)
}
miguel-sorrel/cdcatR documentation built on May 31, 2022, 9:42 p.m.
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Defines functions LR.2step
Documented in LR.2step
#' Item-level model comparison using 2LR test
#'
#' This function evaluates whether the saturated G-DINA model can be replaced by reduced CDMs without significant loss in model data fit for each item using two-step likelihood ratio test (2LR). Sorrel, de la Torre, Abad, and Olea (2017) and Ma & de la Torre (2018) can be consulted for details. Conducting this type of analysis can facilitate the calibration of the item bank and have implications for the CAT accuracy and item usage (Sorrel, Abad, & Nájera, 2021).
#'
#' @param fit Calibrated item bank with the \code{GDINA::GDINA} (Ma & de la Torre, 2020) or \code{CDM::gdina} (Robitzsch et al., 2020) R packages functions
#' @param p.adjust.method Scalar character. Correction method for \emph{p}-values. Possible values include \code{"holm"}, \code{"hochberg"}, \code{"hommel"}, \code{"bonferroni"}, \code{"BH"}, \code{"BY"}, \code{"fdr"}, and \code{"none"}. See \code{p.adjust} function from the \code{stats} R package for additional details. Default is \code{holm}
#' @param alpha.level Scalar numeric. Alpha level for decision. Default is \code{0.05}
#'
#' @return \code{LR2.step} returns an object of class \code{LR2.step}
#' \describe{
#' \item{LR2}{Numeric matrix. LR2 statistics}
#' \item{pvalues}{Numeric matrix. \emph{p}-values associated with the 2LR statistics}
#' \item{adj.pvalues}{Numeric matrix. Adjusted \emph{p}-values associated with the 2LR statistics}
#' \item{df}{Numeric matrix. Degrees of freedom}
#' \item{models.adj.pvalues}{Character vector denoting the model selected for each item using the \emph{largestp} rule (Ma et al., 2016). All statistics whose \emph{p}-values are less than \code{alpha.level} are rejected. All statistics with \emph{p}-value larger than \code{alpha.level} define the set of candidate reduced models. The G-DINA model is retained if all statistics are rejected. Whenever the set includes more than one model, the model with the largest \emph{p}-value is selected as the best model for that item}
#' }
#'
#' @references
#'
#' Ma, W. & de la Torre, J. (2018). Category-level model selection for the sequential G-DINA model. \emph{Journal of Educational and Behavorial Statistic, 44}, 45-77.
#'
#' Ma, W. & de la Torre, J. (2020). GDINA: The generalized DINA model framework. R package version 2.7.9. Retrived from https://CRAN.R-project.org/package=GDINA
#'
#' Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection and attribute classification.
#' \emph{Applied Psychological Measurement, 40}, 200-217.
#'
#' Robitzsch, A., Kiefer, T., George, A. C., & Uenlue, A. (2020). CDM: Cognitive Diagnosis Modeling. R package version 7.5-15. https://CRAN.R-project.org/package=CDM
#'
#' Sorrel, M. A., de la Torre, J., Abad, F. J., & Olea, J. (2017). Two-step likelihood ratio test for item-level model comparison in cognitive diagnosis models. \emph{Methodology, 13}, 39-47.
#'
#' Sorrel, M. A., Abad, F. J., & Nájera, P. (2021). Improving accuracy and usage by correctly selecting: The effects of model selection in cognitive diagnosis computerized adaptive testing. \emph{Applied Psychological Measurement, 45}, 112-129.
#'
#' @import stats
#'
#' @examples
#'Q <- sim180DINA$simQ
#'dat <- sim180DINA$simdat
#'resGDINA <- GDINA::GDINA(dat = dat, Q = Q, model = "GDINA",verbose = FALSE)
#'#resCDM <- CDM::gdina(data = dat, q.matrix = Q, rule = "GDINA", progress = FALSE)
#'LR2.GDINA <- LR.2step(fit = resGDINA) # GDINA package
#'#LR2.CDM <- LR.2step(fit = resCDM) # CDM package
#'mean(LR2.GDINA$models.adj.pvalues[which(rowSums(Q) != 1)] ==
#' sim180DINA$specifications$item.bank$specifications$model[which(rowSums(Q) != 1)])
#'#mean(LR2.CDM$models.adj.pvalues[which(rowSums(Q) != 1)] ==
#'# sim180DINA$specifications$item.bank$specifications$model[which(rowSums(Q) != 1)])
#'
#' @export
#'
LR.2step <- function(fit, p.adjust.method = "holm", alpha.level = 0.05)
{
if(!inherits(fit, what = c("GDINA", "gdina"))){stop("fit must be an object of class 'GDINA' or 'gdina'")}
if(!(p.adjust.method %in% c("holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none"))){stop("p.adjust.method must be one of the following: 'holm', 'hochberg', 'hommel', 'bonferroni', 'BH', 'BY', 'fdr', 'none'")}
if(alpha.level > 1 | alpha.level < 0){stop("alpha.level must be a value between 0 and 1.")}
make.Lik.DINA.k <- function(vP){
p <- rep(vP[1], classes - 1)
p[classes] <- vP[1] + vP[2]
logp <- log(p)
logq <- log(1 - p)
L <- sum(RNjjob[1,] * logp) + sum(RNjjob[3,] * logq)
return(-L)
}
make.Lik.DINO.k <- function(vP){
p <- rep(vP[1] + vP[2], classes)
p[1] <- vP[1]
logp <- log(p)
logq <- log(1 - p)
L <- sum(RNjjob[1,] * logp) + sum(RNjjob[3,] * logq)
return(-L)
}
make.Lik.ACDM.k <- function(vP){
par <- matrix(vP[-1], ncol = 1)
p <- c(vP[1] + posible.patterns %*% par)
logp <- log(p)
logq <- log(1 - p)
L <- sum(RNjjob[1,] * logp) + sum(RNjjob[3,] * logq)
return(-L)
}
make.Lik.GDINA.k <- function(pars){
p <- pars
logp <- log(p)
logq <- log(1 - p)
L <- sum(RNjjob[1,] * logp) + sum(RNjjob[3,] * logq)
return(-L)
}
est <- fit
if(!is.null(est)){
if(!is.null(est$extra$call)){ # package GDINA
Q <- est$options$Q
attpat <- GDINA::attributepattern(ncol(Q))
Rlj <- est$technicals$expectedCorrect
Nlj <- est$technicals$expectedTotal
catprob.parm <- est$catprob.parm
} else { # package CDM
Q <- est$q.matrix
attpat <- GDINA::attributepattern(ncol(Q))
attpat.s <- apply(attpat, 1, paste, collapse = "")
RLj <- est$control$R.lj
RLj <- RLj[,match(attpat.s, colnames(RLj))]
NLj <- est$control$I.lj
NLj <- NLj[,match(attpat.s, colnames(RLj))]
Rlj <- Nlj <- matrix(NA, nrow = nrow(Q), ncol = 2^max(rowSums(Q)))
catprob.parm <- list()
for(j in 1:nrow(Q)){
kj <- which(Q[j,] == 1)
tmp <- factor(apply(attpat[,kj, drop = F], 1, paste, collapse = ""))
tmp <- factor(tmp, levels = apply(unique(GDINA::attributepattern(length(kj))), 1, paste, collapse = ""))
for(l in 1:(2^length(kj))){
Rlj[j,l] <- sum(RLj[j, which(as.numeric(tmp) == l)])
Nlj[j,l] <- sum(NLj[j, which(as.numeric(tmp) == l)])
}
catprob.parm[[j]] <- est$probitem[est$probitem$itemno == j,]$prob
}
Rlj[is.na(Rlj)] <- 0
Nlj[is.na(Nlj)] <- 0
}
}
Kjs <- rowSums(Q)
Ks <- cumsum(2^Kjs)
item <- which(rowSums(Q) > 1)
J <- nrow(Q)
out <- list()
LR2 <- matrix(data = 0, nrow = J, ncol = 4)
LR2.p <- matrix(data = 0, nrow = J, ncol = 4)
df <- matrix(data = 0, nrow = J, ncol = 4)
for(jj in 1:J){
pars.jj <- catprob.parm[[jj]]
pars.jj[pars.jj < 0] <- 0
pars.jj[pars.jj > 1] <- 1
Kjj <- sum(Q[jj, ])
Kj <- length(pars.jj)
RNjjob <- rbind(Rlj[jj, 1:Kj], Nlj[jj, 1:Kj], Nlj[jj, 1:Kj] - Rlj[jj, 1:Kj])
classes <- 2^Kjs[jj]
posible.patterns <- GDINA::attributepattern(Kjj)
par.DINA <- constrOptim(theta = c(0.1, 0.1), f = make.Lik.DINA.k, grad = NULL,
ui = rbind(c(1, 0), c(0, 1), c(1, 1), c(-1, 0), c(0, -1), c(-1, -1)),
ci = c(.0001, .0001, .0001, -.9999, -.9999, -.9999))
par.DINO <- constrOptim(theta = c(0.1, 0.1), f = make.Lik.DINO.k, grad = NULL,
ui = rbind(c(1, 0), c(0, 1), c(1, 1), c(-1, 0), c(0, -1), c(-1, -1)),
ci = c(.0001, .0001, .0001, -.9999, -.9999 , -.9999))
par.ACDM <- constrOptim(theta = rep(0.1, Kjs[jj]+1), f = make.Lik.ACDM.k, grad = NULL,
ui = rbind(diag(Kjs[jj] + 1), -diag(Kjs[jj] + 1), rep(-1, Kjs[jj] + 1)),
ci = c(rep(.0001, Kjs[jj] + 1), rep(-.9999, Kjs[jj] + 2)))
par.GDINA.value <- make.Lik.GDINA.k(pars = pars.jj)
if(ncol(RNjjob) == 2){
LR2[jj,] <- LR2.p[jj,] <- df[jj,] <- cbind(jj, NA, NA, NA)
} else {
LR2DINA <- 2 * (par.GDINA.value * (-1) - par.DINA$value * (-1))
LR2DINO <- 2 * (par.GDINA.value * (-1) - par.DINO$value * (-1))
LR2ACDM <- 2 * (par.GDINA.value * (-1) - par.ACDM$value * (-1))
dfDINA <- dfDINO <- ncol(RNjjob) - 2
dfACDM <- ncol(RNjjob) - (Kjj + 1)
pDINA <- 1 - pchisq(LR2DINA, dfDINA)
pDINO <- 1 - pchisq(LR2DINO, dfDINO)
pACDM <- 1 - pchisq(LR2ACDM, dfACDM)
LR2[jj,] <- cbind(jj, LR2DINA, LR2DINO, LR2ACDM)
LR2.p[jj,] <- cbind(jj, pDINA, pDINO, pACDM)
df[jj,] <- cbind(jj, dfDINA, dfDINO, dfACDM)
}
}
if((sum(na.omit(LR2[, -1] == -Inf)) > 0) | (sum(is.nan(LR2[, -1])) > 0)) {
prob.items <- apply(LR2[, -1], 2, function(x) {which(x == -Inf)})[, 1]
warning(c("2LR statistic couldn't be computed for items ", paste(prob.items, collapse = ", "),
". G-DINA was retained for those items"))
}
LR2[, -1][which(LR2[, -1] == -Inf)] <- -9999
LR2[, -1][is.nan(LR2[, -1])] <- -9999
LR2.p[, -1][is.nan(LR2.p[, -1])] <- 0
LR2 <- na.omit(LR2)[, -1]
LR2.p <- na.omit(LR2.p)[, -1]
df <- na.omit(df)[, -1]
LR2.adjp <- LR2.p
LR2.adjp <- matrix(p.adjust(LR2.adjp, method = p.adjust.method), ncol = ncol(LR2.p), nrow = nrow(LR2.p))
model.alpha <- apply(LR2.adjp, 1, function(x){if(max(x, na.rm = T) > alpha.level){NA} else {return(0)}})
model.alpha[is.na(model.alpha)] <- apply(LR2.p[is.na(model.alpha),,drop = FALSE], 1, which.max)
models <- rep(0, nrow(Q))
models[which(rowSums(Q) != 1)] <- model.alpha
models.adjp <- models
models.adjp[which(models.adjp == 0)] <- "GDINA"
models.adjp[which(models.adjp == 1)] <- "DINA"
models.adjp[which(models.adjp == 2)] <- "DINO"
models.adjp[which(models.adjp == 3)] <- "ACDM"
colnames(LR2) <- colnames(LR2.p) <- colnames(LR2.adjp) <- colnames(df) <- c("DINA", "DINO", "ACDM")
rownames(LR2) <- rownames(LR2.p) <- rownames(LR2.adjp) <- rownames(df) <- paste("Item", item)
out <- list(LR2 = LR2, pvalues = LR2.p, adj.pvalues = LR2.adjp, df = df, models.adj.pvalues = models.adjp)
return(out)
}
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