Nothing
R/ddfMLR.R
In difNLR: DIF and DDF Detection by Non-Linear Regression Models
Defines functions
predict.ddfMLR
BIC.ddfMLR
AIC.ddfMLR
logLik.ddfMLR
coef.ddfMLR
plot.ddfMLR
print.ddfMLR
ddfMLR
Documented in
AIC.ddfMLR
BIC.ddfMLR
coef.ddfMLR
ddfMLR
logLik.ddfMLR
plot.ddfMLR
predict.ddfMLR
#' DDF detection for nominal data.
#'
#' @aliases ddfMLR
#'
#' @description Performs DDF detection procedure for nominal data
#' based on multinomial log-linear regression model and likelihood
#' ratio test of a submodel.
#'
#' @param Data data.frame or matrix: dataset which rows represent
#' unscored examinee answers (nominal) and columns correspond to the
#' items. In addition, \code{Data} can hold the vector of group
#' membership.
#' @param group numeric or character: a dichotomous vector of the same
#' length as \code{nrow(Data)} or a column identifier of
#' \code{Data}.
#' @param focal.name numeric or character: indicates the level of
#' \code{group} which corresponds to focal group.
#' @param key character: the answer key. Each element corresponds to
#' the correct answer of one item.
#' @param type character: type of DDF to be tested. Either
#' \code{"both"} for uniform and non-uniform DDF (i.e., difference
#' in parameters \code{"a"} and \code{"b"}) (default), or
#' \code{"udif"} for uniform DDF only (i.e., difference in
#' difficulty parameter \code{"b"}), or \code{"nudif"} for
#' non-uniform DDF only (i.e., difference in discrimination
#' parameter \code{"a"}). Can be specified as a single value (for
#' all items) or as an item-specific vector.
#' @param match numeric or character: matching criterion to be used as
#' an estimate of trait. Can be either \code{"zscore"} (default,
#' standardized total score), \code{"score"} (total test score), or
#' vector of the same length as number of observations in
#' \code{Data}.
#' @param anchor numeric or character: specification of DDF free
#' items. Either \code{NULL} (default), or a vector of item names
#' (column names of \code{Data}), or item identifiers (integers
#' specifying the column number) determining which items are
#' currently considered as anchor (DDF free) items. Argument is
#' ignored if \code{match} is not \code{"zscore"} or \code{"score"}.
#' @param purify logical: should the item purification be applied?
#' (default is \code{FALSE}).
#' @param nrIter numeric: the maximal number of iterations in the item
#' purification (default is 10).
#' @param p.adjust.method character: method for multiple comparison
#' correction. Possible values are \code{"holm"}, \code{"hochberg"},
#' \code{"hommel"}, \code{"bonferroni"}, \code{"BH"}, \code{"BY"},
#' \code{"fdr"}, and \code{"none"} (default). For more details see
#' \code{\link[stats]{p.adjust}}.
#' @param alpha numeric: significance level (default is 0.05).
#' @param parametrization deprecated. Use
#' \code{\link[difNLR]{coef.ddfMLR}} for different
#' parameterizations.
#'
#' @usage
#' ddfMLR(Data, group, focal.name, key, type = "both", match = "zscore", anchor = NULL,
#' purify = FALSE, nrIter = 10, p.adjust.method = "none",
#' alpha = 0.05, parametrization)
#'
#' @details
#' Performs DDF detection procedure for nominal data based on
#' multinomial log-linear regression model and likelihood ratio test
#' of submodel. Probability of selection the \eqn{k}-th category
#' (distractor) is
#' \deqn{P(y = k) = exp((a_k + a_kDif * g) * (x - b_k - b_kDif * g))) / (1 + \sum exp((a_l + a_lDif * g) * (x - b_l - b_lDif * g))), }
#' where \eqn{x} is by default standardized total score (also called
#' Z-score) and \eqn{g} is a group membership. Parameters \eqn{a_k}
#' and \eqn{b_k} are discrimination and difficulty for the \eqn{k}-th
#' category. Terms \eqn{a_kDif} and \eqn{b_kDif} then represent
#' differences between two groups (reference and focal) in relevant
#' parameters. Probability of correct answer (specified in argument
#' \code{key}) is
#' \deqn{P(y = k) = 1/(1 + \sum exp((a_l + a_lDif * g)*(x - b_l - b_lDif * g))). }
#' Parameters are estimated via neural networks. For more details see
#' \code{\link[nnet]{multinom}}.
#'
#' Missing values are allowed but discarded for item estimation. They
#' must be coded as \code{NA} for both, \code{Data} and \code{group}
#' arguments.
#'
#' @return The \code{ddfMLR()} function returns an object of class
#' \code{"ddfMLR"}. The output including values of the test
#' statistics, p-values, and items marked as DDF is displayed by the
#' \code{print()} method.
#'
#' A list of class \code{"ddfMLR"} with the following arguments:
#' \describe{
#' \item{\code{Sval}}{the values of likelihood ratio test statistics.}
#' \item{\code{mlrPAR}}{the estimates of final model.}
#' \item{\code{mlrSE}}{standard errors of the estimates of final model.}
#' \item{\code{parM0}}{the estimates of null model.}
#' \item{\code{parM1}}{the estimates of alternative model.}
#' \item{\code{llM0}}{log-likelihood of null model.}
#' \item{\code{llM1}}{log-likelihood of alternative model.}
#' \item{\code{AIC0}}{AIC of null model.}
#' \item{\code{AIC1}}{AIC of alternative model.}
#' \item{\code{BIC0}}{BIC of null model.}
#' \item{\code{BIC1}}{BIC of alternative model.}
#' \item{\code{DDFitems}}{either the column identifiers of the items which were detected as DDF, or
#' \code{"No DDF item detected"} in case no item was detected as DDF.}
#' \item{\code{type}}{character: type of DDF that was tested.}
#' \item{\code{purification}}{\code{purify} value.}
#' \item{\code{nrPur}}{number of iterations in item purification process. Returned only if \code{purify}
#' is \code{TRUE}.}
#' \item{\code{ddfPur}}{a binary matrix with one row per iteration of item purification and one column per item.
#' \code{"1"} in i-th row and j-th column means that j-th item was identified as DDF in i-th iteration. Returned only
#' if \code{purify} is \code{TRUE}.}
#' \item{\code{conv.puri}}{logical indicating whether item purification process converged before the maximal number
#' \code{nrIter} of iterations. Returned only if \code{purify} is \code{TRUE}.}
#' \item{\code{p.adjust.method}}{character: method for multiple comparison correction which was applied.}
#' \item{\code{pval}}{the p-values by likelihood ratio test.}
#' \item{\code{adj.pval}}{the adjusted p-values by likelihood ratio test using \code{p.adjust.method}.}
#' \item{\code{df}}{the degress of freedom of likelihood ratio test.}
#' \item{\code{alpha}}{numeric: significance level.}
#' \item{\code{Data}}{the data matrix.}
#' \item{\code{group}}{the vector of group membership.}
#' \item{\code{group.names}}{levels of grouping variable.}
#' \item{\code{key}}{key of correct answers.}
#' \item{\code{match}}{matching criterion.}
#' }
#'
#' For an object of class \code{"ddfMLR"} several methods are available (e.g. \code{methods(class = "ddfMLR")}).
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' Faculty of Mathematics and Physics, Charles University \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @references
#' Agresti, A. (2010). Analysis of ordinal categorical data. Second edition. John Wiley & Sons.
#'
#' Hladka, A. (2021). Statistical models for detection of differential item functioning. Dissertation thesis.
#' Faculty of Mathematics and Physics, Charles University.
#'
#' Hladka, A. & Martinkova, P. (2020). difNLR: Generalized logistic regression models for DIF and DDF detection.
#' The R Journal, 12(1), 300--323, \doi{10.32614/RJ-2020-014}.
#'
#' @seealso
#' \code{\link[difNLR]{plot.ddfMLR}} for graphical representation of item characteristic curves. \cr
#' \code{\link[difNLR]{coef.ddfMLR}} for extraction of item parameters with their standard errors. \cr
#' \code{\link[difNLR]{logLik.ddfMLR}}, \code{\link[difNLR]{AIC.ddfMLR}}, \code{\link[difNLR]{BIC.ddfMLR}}
#' for extraction of log-likelihood and information criteria. \cr
#'
#' \code{\link[stats]{p.adjust}} for multiple comparison corrections. \cr
#' \code{\link[nnet]{multinom}} for estimation function using neural networks.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # graphical devices
#' plot(x, item = "Item1", group.names = c("Group 1", "Group 2"))
#' plot(x, item = x$DDFitems)
#' plot(x, item = 1)
#'
#' # AIC, BIC, log-likelihood
#' AIC(x)
#' BIC(x)
#' logLik(x)
#'
#' # AIC, BIC, log-likelihood for the first item
#' AIC(x, item = 1)
#' BIC(x, item = 1)
#' logLik(x, item = 1)
#'
#' # estimated parameters
#' coef(x)
#' coef(x, SE = TRUE)
#' coef(x, SE = TRUE, simplify = TRUE)
#'
#' # testing both DDF effects with Benjamini-Hochberg adjustment method
#' ddfMLR(Data, group, focal.name = 1, key, p.adjust.method = "BH")
#'
#' # testing both DDF effects with item purification
#' ddfMLR(Data, group, focal.name = 1, key, purify = TRUE)
#'
#' # testing uniform DDF effects
#' ddfMLR(Data, group, focal.name = 1, key, type = "udif")
#' # testing non-uniform DDF effects
#' ddfMLR(Data, group, focal.name = 1, key, type = "nudif")
#'
#' # testing both DDF effects with total score as matching criterion
#' ddfMLR(Data, group, focal.name = 1, key, match = "score")
#' }
#'
#' @keywords DDF
#' @export
ddfMLR <- function(Data, group, focal.name, key, type = "both", match = "zscore", anchor = NULL,
purify = FALSE, nrIter = 10, p.adjust.method = "none",
alpha = 0.05, parametrization) {
# deprecated args handling
if (!missing(parametrization)) {
warning("Argument 'parametrization' is deprecated; please use 'coef.difORD()' method for different parameterizations. ",
call. = FALSE
)
}
if (!type %in% c("udif", "nudif", "both") | !is.character(type)) {
stop("'type' must be either 'udif', 'nudif', or 'both'.",
call. = FALSE
)
}
if (alpha > 1 | alpha < 0) {
stop("'alpha' must be between 0 and 1.",
call. = FALSE
)
}
# matching criterion
if (!(match[1] %in% c("score", "zscore"))) {
if (is.null(dim(Data))) {
no <- length(Data)
} else {
no <- dim(Data)[1]
}
if (length(match) != no) {
stop("Invalid value for 'match'. Possible values are 'zscore', 'score', or vector of the same length as number
of observations in 'Data'.")
}
}
# purification
if (purify & !(match[1] %in% c("score", "zscore"))) {
stop("Purification not allowed when matching variable is not 'zscore' or 'score'.", call. = FALSE)
}
internalMLR <- function() {
if (length(group) == 1) {
if (is.numeric(group)) {
GROUP <- Data[, group]
DATA <- Data[, (1:dim(Data)[2]) != group]
colnames(DATA) <- colnames(Data)[(1:dim(Data)[2]) != group]
} else {
GROUP <- Data[, colnames(Data) == group]
DATA <- Data[, colnames(Data) != group]
colnames(DATA) <- colnames(Data)[colnames(Data) != group]
}
} else {
GROUP <- group
DATA <- Data
}
if (length(levels(as.factor(GROUP))) != 2) {
stop("'group' must be binary vector", call. = FALSE)
}
if (is.matrix(DATA) | is.data.frame(DATA)) {
if (dim(DATA)[1] != length(GROUP)) {
stop("'Data' must have the same number of rows as is length of vector 'group'.",
call. = FALSE
)
}
} else {
stop("'Data' must be data frame or matrix of binary vectors.",
call. = FALSE
)
}
if (is.matrix(key) | is.data.frame(key)) {
KEY <- paste(unlist(key))
} else {
KEY <- key
}
if (length(KEY)[1] != dim(DATA)[2]) {
stop("Number of items in 'Data' is not equal to the length of 'key'.",
call. = FALSE
)
}
group.names <- unique(GROUP)[!is.na(unique(GROUP))]
if (group.names[1] == focal.name) {
group.names <- rev(group.names)
}
GROUP <- as.numeric(as.factor(GROUP) == focal.name)
if (length(match) == dim(DATA)[1]) {
df <- data.frame(DATA, GROUP, match, check.names = F)
} else {
df <- data.frame(DATA, GROUP, check.names = F)
}
df <- df[complete.cases(df), ]
if (dim(df)[1] == 0) {
stop("It seems that your 'Data' does not include any subjects that are complete.",
call. = FALSE
)
}
GROUP <- df[, "GROUP"]
DATA <- data.frame(df[, !(colnames(df) %in% c("GROUP", "match"))])
DATA[] <- lapply(DATA[], as.factor)
DATA[] <- lapply(DATA[], droplevels)
if (length(match) > 1) {
match <- df[, "match"]
}
if (!is.null(anchor)) {
if (is.numeric(anchor)) {
ANCHOR <- anchor
} else {
ANCHOR <- NULL
for (i in 1:length(anchor)) {
ANCHOR[i] <- (1:dim(DATA)[2])[colnames(DATA) == anchor[i]]
}
}
} else {
ANCHOR <- 1:dim(DATA)[2]
}
if (!purify | !(match[1] %in% c("zscore", "score")) | !is.null(anchor)) {
PROV <- suppressWarnings(MLR(
Data = DATA, group = GROUP,
key = KEY, match = match, anchor = ANCHOR,
type = type, p.adjust.method = p.adjust.method,
alpha = alpha
))
STATS <- PROV$Sval
ADJ.PVAL <- PROV$adjusted.pval
se.m1 <- PROV$se.m1
se.m0 <- PROV$se.m0
significant <- which(ADJ.PVAL < alpha)
if (length(significant) > 0) {
DDFitems <- significant
mlrPAR <- PROV$par.m0
mlrSE <- se.m0
for (idif in 1:length(DDFitems)) {
mlrPAR[[DDFitems[idif]]] <- PROV$par.m1[[DDFitems[idif]]]
mlrSE[[DDFitems[idif]]] <- se.m1[[DDFitems[idif]]]
}
} else {
DDFitems <- "No DDF item detected"
mlrPAR <- PROV$par.m0
mlrSE <- se.m0
}
nrow <- sapply(mlrPAR, nrow)
colnams <- lapply(mlrPAR, colnames)
rownams <- lapply(mlrPAR, rownames)
mlrSE <- lapply(1:length(mlrSE), function(x) {
matrix(mlrSE[[x]],
nrow = nrow[[x]],
dimnames = list(rownams[[x]], colnams[[x]])
)
})
RES <- list(
Sval = STATS,
mlrPAR = mlrPAR,
mlrSE = mlrSE,
parM0 = PROV$par.m0, parM1 = PROV$par.m1,
covM0 = PROV$cov.m0, covM1 = PROV$cov.m1,
llM0 = PROV$ll.m0, llM1 = PROV$ll.m1,
AICM0 = PROV$AIC.m0, AICM1 = PROV$AIC.m1,
BICM0 = PROV$BIC.m0, BICM1 = PROV$BIC.m1,
DDFitems = DDFitems,
type = type,
purification = purify,
p.adjust.method = p.adjust.method, pval = PROV$pval, adj.pval = PROV$adjusted.pval, df = PROV$df,
alpha = alpha,
Data = DATA, group = GROUP, group.names = group.names, key = c(KEY), match = match
)
} else {
nrPur <- 0
ddfPur <- NULL
noLoop <- FALSE
prov1 <- suppressWarnings(MLR(
Data = DATA, group = GROUP,
key = KEY, type = type,
p.adjust.method = p.adjust.method,
alpha = alpha
))
stats1 <- prov1$Sval
pval1 <- prov1$pval
significant1 <- which(pval1 < alpha)
if (length(significant1) == 0) {
PROV <- prov1
STATS <- stats1
DDFitems <- "No DDF item detected"
se.m1 <- PROV$se.m1
se.m0 <- PROV$se.m0
mlrPAR <- PROV$par.m0
mlrSE <- se.m0
noLoop <- TRUE
} else {
dif <- significant1
ddfPur <- rep(0, length(stats1))
ddfPur[dif] <- 1
repeat {
if (nrPur >= nrIter) {
break
} else {
nrPur <- nrPur + 1
nodif <- NULL
if (is.null(dif)) {
nodif <- 1:dim(DATA)[2]
} else {
for (i in 1:dim(DATA)[2]) {
if (sum(i == dif) == 0) {
nodif <- c(nodif, i)
}
}
}
prov2 <- suppressWarnings(MLR(
Data = DATA, group = GROUP,
key = KEY, anchor = nodif, type = type,
p.adjust.method = p.adjust.method,
alpha = alpha
))
stats2 <- prov2$Sval
pval2 <- prov2$pval
significant2 <- which(pval2 < alpha)
if (length(significant2) == 0) {
dif2 <- NULL
} else {
dif2 <- significant2
}
ddfPur <- rbind(ddfPur, rep(0, dim(DATA)[2]))
ddfPur[nrPur + 1, dif2] <- 1
if (length(dif) != length(dif2)) {
dif <- dif2
} else {
dif <- sort(dif)
dif2 <- sort(dif2)
if (sum(dif == dif2) == length(dif)) {
noLoop <- TRUE
break
} else {
dif <- dif2
}
}
}
}
PROV <- prov2
STATS <- stats2
significant1 <- which(PROV$adjusted.pval < alpha)
se.m1 <- PROV$se.m1
se.m0 <- PROV$se.m0
mlrPAR <- PROV$par.m0
mlrSE <- se.m0
if (length(significant1) > 0) {
DDFitems <- significant1
for (idif in 1:length(DDFitems)) {
mlrPAR[[DDFitems[idif]]] <- PROV$par.m1[[DDFitems[idif]]]
mlrSE[[DDFitems[idif]]] <- se.m1[[DDFitems[idif]]]
}
} else {
DDFitems <- "No DDF item detected"
}
}
if (!is.null(ddfPur)) {
rownames(ddfPur) <- paste("Step", 0:(dim(ddfPur)[1] - 1), sep = "")
colnames(ddfPur) <- colnames(DATA)
}
RES <- list(
Sval = STATS,
mlrPAR = mlrPAR,
mlrSE = mlrSE,
parM0 = PROV$par.m0, parM1 = PROV$par.m1,
covM0 = PROV$cov.m0, covM1 = PROV$cov.m1,
llM0 = PROV$ll.m0, llM1 = PROV$ll.m1,
AICM0 = PROV$AIC.m0, AICM1 = PROV$AIC.m1,
BICM0 = PROV$BIC.m0, BICM1 = PROV$BIC.m1,
DDFitems = DDFitems,
type = type,
purification = purify, nrPur = nrPur, ddfPur = ddfPur, conv.puri = noLoop,
p.adjust.method = p.adjust.method, pval = PROV$pval, adj.pval = PROV$adjusted.pval, df = PROV$df,
alpha = alpha,
Data = DATA, group = GROUP, group.names = group.names, key = c(KEY), match = match
)
}
class(RES) <- "ddfMLR"
return(RES)
}
resToReturn <- internalMLR()
return(resToReturn)
}
#' @export
print.ddfMLR <- function(x, ...) {
title <- switch(x$type,
both = "Detection of both types of Differential Distractor Functioning using multinomial log-linear regression model",
udif = "Detection of uniform Differential Distractor Functioning using multinomial log-linear regression model",
nudif = "Detection of non-uniform Differential Distractor Functioning using multinomial log-linear regression model"
)
cat(paste(strwrap(title, width = 60), collapse = "\n"))
cat("\n\nLikelihood-ratio chi-square statistics\n")
if (x$purification) word.iteration <- ifelse(x$nrPur <= 1, " iteration", " iterations")
cat(paste("\nItem purification was", ifelse(x$purification, " ", " not "), "applied",
ifelse(x$purification, paste(" with ", x$nrPur, word.iteration, sep = ""), ""), "\n",
sep = ""
))
if (x$purification) {
if (!x$conv.puri) {
cat(paste("WARNING: Item purification process not converged after "), x$nrPur, word.iteration, "\n",
" Results are based on last iteration of the item purification.\n",
sep = ""
)
}
}
if (x$p.adjust.method == "none") {
cat("No p-value adjustment for multiple comparisons\n\n")
} else {
cat(paste(
"Multiple comparisons made with",
switch(x$p.adjust.method,
holm = "Holm",
hochberg = "Hochberg",
hommel = "Hommel",
bonferroni = "Bonferroni",
BH = "Benjamini-Hochberg",
BY = "Benjamini-Yekutieli",
fdr = "FDR"
), "adjustment of p-values\n\n"
))
}
sign <- ifelse(is.na(x$adj.pval), " ",
symnum(x$adj.pval,
c(0, 0.001, 0.01, 0.05, 0.1, 1),
symbols = c("***", "**", "*", ".", "")
)
)
if (x$p.adjust.method == "none") {
tab <- format(round(cbind(x$Sval, x$pval), 4))
tab <- matrix(cbind(tab, sign), ncol = 3)
colnames(tab) <- c("Chisq-value", "P-value", "")
} else {
tab <- format(round(cbind(x$Sval, x$pval, x$adj.pval), 4))
tab <- matrix(cbind(tab, sign), ncol = 4)
colnames(tab) <- c("Chisq-value", "P-value", "Adj. P-value", "")
}
rownames(tab) <- colnames(x$Data)
print(tab, quote = F, digits = 4, zero.print = F)
cat("\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n")
if (is.character(x$DDFitems)) {
switch(x$type,
both = cat("\nNone of items is detected as DDF"),
udif = cat("\nNone of items is detected as uniform DDF"),
nudif = cat("\nNone of items is detected as non-uniform DDF")
)
} else {
switch(x$type,
both = cat("\nItems detected as DDF items:"),
udif = cat("\nItems detected as uniform DDF items:"),
nudif = cat("\nItems detected as non-uniform DDF items:")
)
cat("\n", paste(colnames(x$Data)[x$DDFitems], "\n", sep = ""))
}
}
#' ICC plots for an object of \code{"ddfMLR"} class.
#'
#' @description Plot method for an object of \code{"ddfMLR"} class
#' using \pkg{ggplot2}.
#'
#' The characteristic curves for an item specified in \code{item}
#' argument are plotted. Plotted curves represent the best model.
#'
#' @param x an object of \code{"ddfMLR"} class.
#' @param item numeric or character: either character \code{"all"} to
#' apply for all items (default), or a vector of item names (column
#' names of \code{Data}), or item identifiers (integers specifying
#' the column number).
#' @param group.names character: names of reference and focal group.
#' @param ... other generic parameters for \code{plot()} function.
#'
#' @return Returns list of objects of class \code{"ggplot"}.
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' Faculty of Mathematics and Physics, Charles University \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @seealso
#' \code{\link[difNLR]{ddfMLR}} for DDF detection. \cr
#' \code{\link[ggplot2]{ggplot}} for general function to plot a \code{"ggplot"} object.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # graphical devices
#' plot(x, item = "Item1", group.names = c("Group 1", "Group 2"))
#' plot(x, item = x$DDFitems)
#' plot(x, item = c(3, 1, 5))
#' }
#' @export
plot.ddfMLR <- function(x, item = "all", group.names, ...) {
m <- length(x$mlrPAR)
nams <- colnames(x$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
if (missing(group.names)) {
group.names <- x$group.names
if (all(group.names %in% c(0, 1))) group.names <- c("Reference", "Focal")
}
if (length(group.names) > 2) {
group.names <- group.names[1:2]
warning("Only first two values for 'group.names' argument are used. ")
} else {
if (length(group.names) < 2) {
group.names <- c("Reference", "Focal")
warning("Argument 'group.names' need to have length of two. Default value is used.")
}
}
if (x$purification) {
anchor <- c(1:m)[!c(1:m) %in% x$DDFitems]
} else {
anchor <- 1:m
}
if (x$match[1] == "zscore") {
matching <- c(scale(.score(as.data.frame(x$Data[, anchor]), x$key[anchor])))
xlab <- "Standardized total score"
} else {
if (x$match[1] == "score") {
matching <- c(.score(as.data.frame(x$Data[, anchor]), x$key[anchor]))
xlab <- "Total score"
} else {
if (length(x$match) == dim(x$Data)[1]) {
matching <- x$match
xlab <- "Matching criterion"
} else {
stop("Invalid value for 'match'. Possible values are 'score', 'zscore' or vector of the same length as number
of observations in 'Data'!")
}
}
}
match <- seq(min(matching, na.rm = TRUE), max(matching, na.rm = TRUE), length.out = 300)
plot_CC <- list()
for (i in items) {
TITLE <- colnames(x$Data)[i]
df.fitted <- data.frame(rbind(
cbind(Group = "0", Match = match, predict(x, item = i, match = match, group = 0)),
cbind(Group = "1", Match = match, predict(x, item = i, match = match, group = 1))
), check.names = FALSE)
df.fitted <- reshape(
data = df.fitted, direction = "long",
varying = list(colnames(df.fitted)[-c(1:2)]), v.names = "Probability",
idvar = c("Group", "Match"),
timevar = "Category", times = colnames(df.fitted)[-c(1:2)]
)
df.fitted$Category <- factor(df.fitted$Category)
df.fitted$Category <- relevel(df.fitted$Category, ref = paste(x$key[i]))
levels(df.fitted$Category) <- paste0("P(Y = ", levels(df.fitted$Category), ")")
n_cats <- length(levels(df.fitted$Category))
df.empirical <- rbind(
data.frame(prop.table(table(x$Data[x$group == 1, i], matching[x$group == 1]), 2),
table(x$Data[x$group == 1, i], matching[x$group == 1]),
group = "1"
),
data.frame(prop.table(table(x$Data[x$group == 0, i], matching[x$group == 0]), 2),
table(x$Data[x$group == 0, i], matching[x$group == 0]),
group = "0"
)
)
df.empirical <- data.frame(
Group = as.factor(df.empirical$group),
Match = as.numeric(paste(df.empirical$Var2)),
Category = relevel(df.empirical$Var1, ref = paste(x$key[i])),
Count = as.numeric(paste(df.empirical$Freq.1)),
Probability = as.numeric(paste(df.empirical$Freq))
)
levels(df.empirical$Category) <- paste0("P(Y = ", levels(df.empirical$Category), ")")
cbPalette <- c("#ffbe33", "#34a4e5", "#ce7eaa", "#00805e", "#737373", "#f4eb71", "#0072B2", "#D55E00")
n_col <- ceiling(n_cats / 8)
cols <- rep(cbPalette, n_col)[1:n_cats]
plot_CC[[i]] <- ggplot2::ggplot() +
ggplot2::geom_line(
data = df.fitted,
ggplot2::aes(
x = .data$Match, y = .data$Probability,
colour = .data$Category, linetype = .data$Group
),
linewidth = 0.8
) +
ggplot2::geom_point(
data = df.empirical,
ggplot2::aes(
x = .data$Match, y = .data$Probability,
colour = .data$Category, fill = .data$Category,
size = .data$Count
),
alpha = 0.5, shape = 21
) +
ggplot2::ylim(0, 1) +
ggplot2::ggtitle(TITLE) +
ggplot2::labs(
x = xlab,
y = "Probability of answer"
) +
ggplot2::scale_linetype_manual(
breaks = c(0, 1), labels = group.names,
values = c("solid", "dashed")
) +
ggplot2::scale_color_manual(values = cols) +
ggplot2::scale_fill_manual(values = cols) +
.plot.theme() +
# legend
.plot.theme.legend() +
ggplot2::guides(
size = ggplot2::guide_legend(title = "Count", order = 1),
colour = ggplot2::guide_legend(title = "Answer", order = 2),
fill = ggplot2::guide_legend(title = "Answer", order = 2),
linetype = ggplot2::guide_legend(title = "Group", order = 3)
)
}
plot_CC <- plot_CC[items]
names(plot_CC) <- nams[items]
return(plot_CC)
}
#' Extract model coefficients from an object of \code{"ddfMLR"} class.
#'
#' @description S3 method for extracting estimated model coefficients
#' from an object of \code{"ddfMLR"} class.
#' @aliases coefficients.ddfMLR
#'
#' @param object an object of \code{"ddfMLR"} class.
#' @param SE logical: should the standard errors of estimated
#' parameters be also returned? (default is \code{FALSE}).
#' @param simplify logical: should the estimated parameters be
#' simplified to a matrix? (default is \code{FALSE}).
#' @param IRTpars logical: should the estimated parameters be returned
#' in IRT parameterization? (default is \code{TRUE}).
#' @param CI numeric: level of confidence interval for parameters,
#' default is \code{0.95} for 95\% confidence interval.
#' @param ... other generic parameters for \code{coef()} function.
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' Faculty of Mathematics and Physics, Charles University \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @seealso
#' \code{\link[difNLR]{ddfMLR}} for DDF detection among nominal data. \cr
#' \code{\link[stats]{coef}} for generic function extracting model coefficients.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # estimated parameters
#' coef(x)
#' # includes standard errors
#' coef(x, SE = TRUE)
#' # includes standard errors and simplifies to matrix
#' coef(x, SE = TRUE, simplify = TRUE)
#' # intercept-slope parameterization
#' coef(x, IRTpars = FALSE)
#' # intercept-slope parameterization, simplifies to matrix, turn off confidence intervals
#' coef(x, IRTpars = FALSE, simplify = TRUE, CI = 0)
#' }
#' @export
coef.ddfMLR <- function(object, SE = FALSE, simplify = FALSE, IRTpars = TRUE, CI = 0.95, ...) {
if (!inherits(SE, "logical")) {
stop("Invalid value for 'SE'. 'SE' needs to be logical. ",
call. = FALSE
)
}
if (!inherits(simplify, "logical")) {
stop("Invalid value for 'simplify'. 'simplify' needs to be logical. ",
call. = FALSE
)
}
if (!inherits(IRTpars, "logical")) {
stop("Invalid value for 'IRTpars'. 'IRTpars' needs to be logical. ",
call. = FALSE
)
}
if (CI > 1 | CI < 0 | !is.numeric(CI)) {
stop("Invalid value for 'CI'. 'CI' must be numeric value between 0 and 1. ",
call. = FALSE
)
}
m <- dim(object$Data)[2]
nams <- colnames(object$Data)
if (!IRTpars) {
pars <- object$mlrPAR
se <- object$mlrSE
} else {
mlrPAR <- object$mlrPAR
mlrCOV <- ifelse(1:m %in% object$DDFitems, object$covM1, object$covM0)
mlrDM <- lapply(1:m, function(i) {
.deltamethod.MLR.log2irt(
par = mlrPAR[[i]], cov = mlrCOV[[i]]
)
})
se <- lapply(mlrDM, function(x) x$se)
pars <- lapply(1:m, function(i) {
if (any(is.null(dim(mlrDM[[i]]$par)))) {
par_names <- names(mlrDM[[i]]$par)
} else {
par_names <- colnames(mlrDM[[i]]$par)
}
matrix(mlrDM[[i]]$par,
nrow = nrow(mlrPAR[[i]]), ncol = ncol(mlrPAR[[i]]),
dimnames = list(rownames(mlrPAR[[i]]), par_names)
)
})
}
cats <- lapply(1:m, function(i) rownames(pars[[i]]))
names(pars) <- names(cats) <- names(se) <- nams
if (SE) {
se_matrix <- lapply(1:m, function(i) {
matrix(se[[i]],
nrow = nrow(pars[[i]]), ncol = ncol(pars[[i]]),
dimnames = list(rownames(pars[[i]]), colnames(pars[[i]]))
)
})
coefs <- lapply(1:m, function(i) rbind(pars[[i]], se_matrix[[i]]))
coefs <- lapply(1:m, function(i) {
rownames(coefs[[i]]) <- paste(rep(c("estimate", "SE"), each = nrow(coefs[[i]]) / 2), cats[[i]], sep = "_")
coefs[[i]]
})
} else {
coefs <- pars
}
names(coefs) <- nams
if (CI > 0) {
alpha <- (1 - CI) / 2
CIlow <- lapply(1:m, function(i) pars[[i]] - qnorm(1 - alpha) * se[[i]])
CIupp <- lapply(1:m, function(i) pars[[i]] + qnorm(1 - alpha) * se[[i]])
coefs <- lapply(1:m, function(i) rbind(coefs[[i]], CIlow[[i]], CIupp[[i]]))
names(coefs) <- nams
if (SE) {
tmp <- c("estimate", "SE", paste0("CI", 100 * alpha), paste0("CI", 100 * (1 - alpha)))
} else {
tmp <- c("estimate", paste0("CI", 100 * alpha), paste0("CI", 100 * (1 - alpha)))
}
coefs <- lapply(1:m, function(i) {
rownames(coefs[[i]]) <- paste(rep(tmp, each = nrow(coefs[[i]]) / length(tmp)), cats[[i]], sep = "_")
coefs[[i]]
})
names(coefs) <- nams
}
if (simplify) {
res <- as.data.frame(plyr::ldply(coefs, rbind, .id = NULL))
id <- unlist(lapply(nams, function(i) paste(i, rownames(coefs[[i]]))))
rownames(res) <- id
res[is.na(res)] <- 0
} else {
res <- coefs
}
return(res)
}
#' Log-likelihood and information criteria for an object of \code{"ddfMLR"} class.
#'
#' @aliases AIC.ddfMLR BIC.ddfMLR
#' @rdname logLik.ddfMLR
#'
#' @description S3 methods for extracting log-likelihood, Akaike's
#' information criterion (AIC) and Schwarz's Bayesian criterion
#' (BIC) for an object of \code{"ddfMLR"} class.
#'
#' @param object an object of \code{"ddfMLR"} class.
#' @param item numeric or character: either character \code{"all"} to
#' apply for all converged items (default), or a vector of item
#' names (column names of \code{Data}), or item identifiers
#' (integers specifying the column number).
#' @param ... other generic parameters for S3 methods.
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' Faculty of Mathematics and Physics, Charles University \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @seealso
#' \code{\link[difNLR]{ddfMLR}} for DDF detection among nominal data. \cr
#' \code{\link[stats]{logLik}} for generic function extracting log-likelihood. \cr
#' \code{\link[stats]{AIC}} for generic function calculating AIC and BIC.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # AIC, BIC, log-likelihood
#' AIC(x)
#' BIC(x)
#' logLik(x)
#'
#' # AIC, BIC, log-likelihood for the first item
#' AIC(x, item = 1)
#' BIC(x, item = 1)
#' logLik(x, item = 1)
#' }
#' @export
logLik.ddfMLR <- function(object, item = "all", ...) {
m <- length(object$mlrPAR)
nams <- colnames(object$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
val <- ifelse(items %in% object$DDFitems,
object$llM1[items],
object$llM0[items]
)
df <- ifelse(items %in% object$DDFitems,
sapply(object$parM1, length)[items],
sapply(object$parM0, length)[items]
)
if (length(items) == 1) {
attr(val, "df") <- df
class(val) <- "logLik"
}
return(val)
}
#' @rdname logLik.ddfMLR
#' @aliases BIC.ddfMLR logLik.ddfMLR
#' @export
AIC.ddfMLR <- function(object, item = "all", ...) {
m <- length(object$mlrPAR)
nams <- colnames(object$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
AIC <- ifelse(items %in% object$DDFitems, object$AICM1[items], object$AICM0[items])
return(AIC)
}
#' @rdname logLik.ddfMLR
#' @aliases AIC.ddfMLR logLik.ddfMLR
#' @export
BIC.ddfMLR <- function(object, item = "all", ...) {
m <- length(object$mlrPAR)
nams <- colnames(object$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
BIC <- ifelse(items %in% object$DDFitems, object$BICM1[items], object$BICM0[items])
return(BIC)
}
#' Predicted values for an object of \code{"ddfMLR"} class.
#'
#' @description S3 method for predictions from the model used in the
#' object of \code{"ddfMLR"} class.
#'
#' @param object an object of \code{"ddfMLR"} class.
#' @param item numeric or character: either character \code{"all"} to
#' apply for all converged items (default), or a vector of item
#' names (column names of \code{Data}), or item identifiers
#' (integers specifying the column number).
#' @param match numeric: matching criterion for new observations.
#' @param group numeric: group membership for new observations.
#' @param ... other generic parameters for \code{predict()} function.
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @references
#' Hladka, A. & Martinkova, P. (2020). difNLR: Generalized logistic regression models for DIF and DDF detection.
#' The R Journal, 12(1), 300--323, \doi{10.32614/RJ-2020-014}.
#'
#' @seealso
#' \code{\link[difNLR]{ddfMLR}} for DDF detection among nominal data using multinomial log-linear regression model. \cr
#' \code{\link[stats]{predict}} for generic function for prediction.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # fitted values
#' predict(x, item = 1)
#'
#' # predicted values
#' predict(x, item = 1, match = 0, group = c(0, 1))
#' predict(x, item = x$DDFitems, match = 0, group = c(0, 1))
#' }
#'
#' @export
predict.ddfMLR <- function(object, item = "all", match, group, ...) {
m <- dim(object$Data)[2]
nams <- colnames(object$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
if (object$purification) {
anchor <- c(1:m)[!c(1:m) %in% object$DIFitems]
} else {
anchor <- 1:m
}
if (missing(match)) {
if (length(object$match) > 1) {
match <- object$match
} else {
if (object$match == "score") {
match <- c(.score(as.data.frame(object$Data[, anchor]), object$key))
} else {
match <- c(scale(.score(as.data.frame(object$Data[, anchor]), object$key)))
}
}
}
if (missing(group)) {
group <- object$group
}
if (length(match) != length(group)) {
if (length(match) == 1) {
match <- rep(match, length(group))
} else if (length(group) == 1) {
group <- rep(group, length(match))
} else {
stop("Arguments 'match' and 'group' must be of the same length.",
call. = FALSE
)
}
}
mat <- cbind("(Intercept)" = 1, "x" = match, "group" = group, "x:group" = match * group)
coefs_all <- coef(object, IRTpars = FALSE, CI = 0)
res <- list()
for (i in items) {
coefs <- coefs_all[[i]]
if (is.null(dim(coefs))) coefs <- matrix(coefs, ncol = length(coefs))
if (dim(coefs)[2] == 2) {
coefs <- as.matrix(data.frame(coefs, 0, 0))
}
if (dim(coefs)[2] == 3) {
coefs <- as.matrix(data.frame(coefs, 0))
}
cats <- c(object$key[i], rownames(coefs))
df.probs <- as.data.frame(t(exp(coefs %*% t(mat))))
df.probs <- sapply(df.probs, function(x) x / (rowSums(df.probs) + 1))
df.probs <- data.frame(1 - rowSums(df.probs), df.probs)
colnames(df.probs) <- cats
res[[i]] <- df.probs
}
res <- res[items]
names(res) <- nams[items]
if (length(res) == 1) {
res <- res[[1]]
} else {
names(res) <- nams[items]
}
return(res)
}
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Defines functions predict.ddfMLR BIC.ddfMLR AIC.ddfMLR logLik.ddfMLR coef.ddfMLR plot.ddfMLR print.ddfMLR ddfMLR
Documented in AIC.ddfMLR BIC.ddfMLR coef.ddfMLR ddfMLR logLik.ddfMLR plot.ddfMLR predict.ddfMLR
#' DDF detection for nominal data.
#'
#' @aliases ddfMLR
#'
#' @description Performs DDF detection procedure for nominal data
#' based on multinomial log-linear regression model and likelihood
#' ratio test of a submodel.
#'
#' @param Data data.frame or matrix: dataset which rows represent
#' unscored examinee answers (nominal) and columns correspond to the
#' items. In addition, \code{Data} can hold the vector of group
#' membership.
#' @param group numeric or character: a dichotomous vector of the same
#' length as \code{nrow(Data)} or a column identifier of
#' \code{Data}.
#' @param focal.name numeric or character: indicates the level of
#' \code{group} which corresponds to focal group.
#' @param key character: the answer key. Each element corresponds to
#' the correct answer of one item.
#' @param type character: type of DDF to be tested. Either
#' \code{"both"} for uniform and non-uniform DDF (i.e., difference
#' in parameters \code{"a"} and \code{"b"}) (default), or
#' \code{"udif"} for uniform DDF only (i.e., difference in
#' difficulty parameter \code{"b"}), or \code{"nudif"} for
#' non-uniform DDF only (i.e., difference in discrimination
#' parameter \code{"a"}). Can be specified as a single value (for
#' all items) or as an item-specific vector.
#' @param match numeric or character: matching criterion to be used as
#' an estimate of trait. Can be either \code{"zscore"} (default,
#' standardized total score), \code{"score"} (total test score), or
#' vector of the same length as number of observations in
#' \code{Data}.
#' @param anchor numeric or character: specification of DDF free
#' items. Either \code{NULL} (default), or a vector of item names
#' (column names of \code{Data}), or item identifiers (integers
#' specifying the column number) determining which items are
#' currently considered as anchor (DDF free) items. Argument is
#' ignored if \code{match} is not \code{"zscore"} or \code{"score"}.
#' @param purify logical: should the item purification be applied?
#' (default is \code{FALSE}).
#' @param nrIter numeric: the maximal number of iterations in the item
#' purification (default is 10).
#' @param p.adjust.method character: method for multiple comparison
#' correction. Possible values are \code{"holm"}, \code{"hochberg"},
#' \code{"hommel"}, \code{"bonferroni"}, \code{"BH"}, \code{"BY"},
#' \code{"fdr"}, and \code{"none"} (default). For more details see
#' \code{\link[stats]{p.adjust}}.
#' @param alpha numeric: significance level (default is 0.05).
#' @param parametrization deprecated. Use
#' \code{\link[difNLR]{coef.ddfMLR}} for different
#' parameterizations.
#'
#' @usage
#' ddfMLR(Data, group, focal.name, key, type = "both", match = "zscore", anchor = NULL,
#' purify = FALSE, nrIter = 10, p.adjust.method = "none",
#' alpha = 0.05, parametrization)
#'
#' @details
#' Performs DDF detection procedure for nominal data based on
#' multinomial log-linear regression model and likelihood ratio test
#' of submodel. Probability of selection the \eqn{k}-th category
#' (distractor) is
#' \deqn{P(y = k) = exp((a_k + a_kDif * g) * (x - b_k - b_kDif * g))) / (1 + \sum exp((a_l + a_lDif * g) * (x - b_l - b_lDif * g))), }
#' where \eqn{x} is by default standardized total score (also called
#' Z-score) and \eqn{g} is a group membership. Parameters \eqn{a_k}
#' and \eqn{b_k} are discrimination and difficulty for the \eqn{k}-th
#' category. Terms \eqn{a_kDif} and \eqn{b_kDif} then represent
#' differences between two groups (reference and focal) in relevant
#' parameters. Probability of correct answer (specified in argument
#' \code{key}) is
#' \deqn{P(y = k) = 1/(1 + \sum exp((a_l + a_lDif * g)*(x - b_l - b_lDif * g))). }
#' Parameters are estimated via neural networks. For more details see
#' \code{\link[nnet]{multinom}}.
#'
#' Missing values are allowed but discarded for item estimation. They
#' must be coded as \code{NA} for both, \code{Data} and \code{group}
#' arguments.
#'
#' @return The \code{ddfMLR()} function returns an object of class
#' \code{"ddfMLR"}. The output including values of the test
#' statistics, p-values, and items marked as DDF is displayed by the
#' \code{print()} method.
#'
#' A list of class \code{"ddfMLR"} with the following arguments:
#' \describe{
#' \item{\code{Sval}}{the values of likelihood ratio test statistics.}
#' \item{\code{mlrPAR}}{the estimates of final model.}
#' \item{\code{mlrSE}}{standard errors of the estimates of final model.}
#' \item{\code{parM0}}{the estimates of null model.}
#' \item{\code{parM1}}{the estimates of alternative model.}
#' \item{\code{llM0}}{log-likelihood of null model.}
#' \item{\code{llM1}}{log-likelihood of alternative model.}
#' \item{\code{AIC0}}{AIC of null model.}
#' \item{\code{AIC1}}{AIC of alternative model.}
#' \item{\code{BIC0}}{BIC of null model.}
#' \item{\code{BIC1}}{BIC of alternative model.}
#' \item{\code{DDFitems}}{either the column identifiers of the items which were detected as DDF, or
#' \code{"No DDF item detected"} in case no item was detected as DDF.}
#' \item{\code{type}}{character: type of DDF that was tested.}
#' \item{\code{purification}}{\code{purify} value.}
#' \item{\code{nrPur}}{number of iterations in item purification process. Returned only if \code{purify}
#' is \code{TRUE}.}
#' \item{\code{ddfPur}}{a binary matrix with one row per iteration of item purification and one column per item.
#' \code{"1"} in i-th row and j-th column means that j-th item was identified as DDF in i-th iteration. Returned only
#' if \code{purify} is \code{TRUE}.}
#' \item{\code{conv.puri}}{logical indicating whether item purification process converged before the maximal number
#' \code{nrIter} of iterations. Returned only if \code{purify} is \code{TRUE}.}
#' \item{\code{p.adjust.method}}{character: method for multiple comparison correction which was applied.}
#' \item{\code{pval}}{the p-values by likelihood ratio test.}
#' \item{\code{adj.pval}}{the adjusted p-values by likelihood ratio test using \code{p.adjust.method}.}
#' \item{\code{df}}{the degress of freedom of likelihood ratio test.}
#' \item{\code{alpha}}{numeric: significance level.}
#' \item{\code{Data}}{the data matrix.}
#' \item{\code{group}}{the vector of group membership.}
#' \item{\code{group.names}}{levels of grouping variable.}
#' \item{\code{key}}{key of correct answers.}
#' \item{\code{match}}{matching criterion.}
#' }
#'
#' For an object of class \code{"ddfMLR"} several methods are available (e.g. \code{methods(class = "ddfMLR")}).
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' Faculty of Mathematics and Physics, Charles University \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @references
#' Agresti, A. (2010). Analysis of ordinal categorical data. Second edition. John Wiley & Sons.
#'
#' Hladka, A. (2021). Statistical models for detection of differential item functioning. Dissertation thesis.
#' Faculty of Mathematics and Physics, Charles University.
#'
#' Hladka, A. & Martinkova, P. (2020). difNLR: Generalized logistic regression models for DIF and DDF detection.
#' The R Journal, 12(1), 300--323, \doi{10.32614/RJ-2020-014}.
#'
#' @seealso
#' \code{\link[difNLR]{plot.ddfMLR}} for graphical representation of item characteristic curves. \cr
#' \code{\link[difNLR]{coef.ddfMLR}} for extraction of item parameters with their standard errors. \cr
#' \code{\link[difNLR]{logLik.ddfMLR}}, \code{\link[difNLR]{AIC.ddfMLR}}, \code{\link[difNLR]{BIC.ddfMLR}}
#' for extraction of log-likelihood and information criteria. \cr
#'
#' \code{\link[stats]{p.adjust}} for multiple comparison corrections. \cr
#' \code{\link[nnet]{multinom}} for estimation function using neural networks.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # graphical devices
#' plot(x, item = "Item1", group.names = c("Group 1", "Group 2"))
#' plot(x, item = x$DDFitems)
#' plot(x, item = 1)
#'
#' # AIC, BIC, log-likelihood
#' AIC(x)
#' BIC(x)
#' logLik(x)
#'
#' # AIC, BIC, log-likelihood for the first item
#' AIC(x, item = 1)
#' BIC(x, item = 1)
#' logLik(x, item = 1)
#'
#' # estimated parameters
#' coef(x)
#' coef(x, SE = TRUE)
#' coef(x, SE = TRUE, simplify = TRUE)
#'
#' # testing both DDF effects with Benjamini-Hochberg adjustment method
#' ddfMLR(Data, group, focal.name = 1, key, p.adjust.method = "BH")
#'
#' # testing both DDF effects with item purification
#' ddfMLR(Data, group, focal.name = 1, key, purify = TRUE)
#'
#' # testing uniform DDF effects
#' ddfMLR(Data, group, focal.name = 1, key, type = "udif")
#' # testing non-uniform DDF effects
#' ddfMLR(Data, group, focal.name = 1, key, type = "nudif")
#'
#' # testing both DDF effects with total score as matching criterion
#' ddfMLR(Data, group, focal.name = 1, key, match = "score")
#' }
#'
#' @keywords DDF
#' @export
ddfMLR <- function(Data, group, focal.name, key, type = "both", match = "zscore", anchor = NULL,
purify = FALSE, nrIter = 10, p.adjust.method = "none",
alpha = 0.05, parametrization) {
# deprecated args handling
if (!missing(parametrization)) {
warning("Argument 'parametrization' is deprecated; please use 'coef.difORD()' method for different parameterizations. ",
call. = FALSE
)
}
if (!type %in% c("udif", "nudif", "both") | !is.character(type)) {
stop("'type' must be either 'udif', 'nudif', or 'both'.",
call. = FALSE
)
}
if (alpha > 1 | alpha < 0) {
stop("'alpha' must be between 0 and 1.",
call. = FALSE
)
}
# matching criterion
if (!(match[1] %in% c("score", "zscore"))) {
if (is.null(dim(Data))) {
no <- length(Data)
} else {
no <- dim(Data)[1]
}
if (length(match) != no) {
stop("Invalid value for 'match'. Possible values are 'zscore', 'score', or vector of the same length as number
of observations in 'Data'.")
}
}
# purification
if (purify & !(match[1] %in% c("score", "zscore"))) {
stop("Purification not allowed when matching variable is not 'zscore' or 'score'.", call. = FALSE)
}
internalMLR <- function() {
if (length(group) == 1) {
if (is.numeric(group)) {
GROUP <- Data[, group]
DATA <- Data[, (1:dim(Data)[2]) != group]
colnames(DATA) <- colnames(Data)[(1:dim(Data)[2]) != group]
} else {
GROUP <- Data[, colnames(Data) == group]
DATA <- Data[, colnames(Data) != group]
colnames(DATA) <- colnames(Data)[colnames(Data) != group]
}
} else {
GROUP <- group
DATA <- Data
}
if (length(levels(as.factor(GROUP))) != 2) {
stop("'group' must be binary vector", call. = FALSE)
}
if (is.matrix(DATA) | is.data.frame(DATA)) {
if (dim(DATA)[1] != length(GROUP)) {
stop("'Data' must have the same number of rows as is length of vector 'group'.",
call. = FALSE
)
}
} else {
stop("'Data' must be data frame or matrix of binary vectors.",
call. = FALSE
)
}
if (is.matrix(key) | is.data.frame(key)) {
KEY <- paste(unlist(key))
} else {
KEY <- key
}
if (length(KEY)[1] != dim(DATA)[2]) {
stop("Number of items in 'Data' is not equal to the length of 'key'.",
call. = FALSE
)
}
group.names <- unique(GROUP)[!is.na(unique(GROUP))]
if (group.names[1] == focal.name) {
group.names <- rev(group.names)
}
GROUP <- as.numeric(as.factor(GROUP) == focal.name)
if (length(match) == dim(DATA)[1]) {
df <- data.frame(DATA, GROUP, match, check.names = F)
} else {
df <- data.frame(DATA, GROUP, check.names = F)
}
df <- df[complete.cases(df), ]
if (dim(df)[1] == 0) {
stop("It seems that your 'Data' does not include any subjects that are complete.",
call. = FALSE
)
}
GROUP <- df[, "GROUP"]
DATA <- data.frame(df[, !(colnames(df) %in% c("GROUP", "match"))])
DATA[] <- lapply(DATA[], as.factor)
DATA[] <- lapply(DATA[], droplevels)
if (length(match) > 1) {
match <- df[, "match"]
}
if (!is.null(anchor)) {
if (is.numeric(anchor)) {
ANCHOR <- anchor
} else {
ANCHOR <- NULL
for (i in 1:length(anchor)) {
ANCHOR[i] <- (1:dim(DATA)[2])[colnames(DATA) == anchor[i]]
}
}
} else {
ANCHOR <- 1:dim(DATA)[2]
}
if (!purify | !(match[1] %in% c("zscore", "score")) | !is.null(anchor)) {
PROV <- suppressWarnings(MLR(
Data = DATA, group = GROUP,
key = KEY, match = match, anchor = ANCHOR,
type = type, p.adjust.method = p.adjust.method,
alpha = alpha
))
STATS <- PROV$Sval
ADJ.PVAL <- PROV$adjusted.pval
se.m1 <- PROV$se.m1
se.m0 <- PROV$se.m0
significant <- which(ADJ.PVAL < alpha)
if (length(significant) > 0) {
DDFitems <- significant
mlrPAR <- PROV$par.m0
mlrSE <- se.m0
for (idif in 1:length(DDFitems)) {
mlrPAR[[DDFitems[idif]]] <- PROV$par.m1[[DDFitems[idif]]]
mlrSE[[DDFitems[idif]]] <- se.m1[[DDFitems[idif]]]
}
} else {
DDFitems <- "No DDF item detected"
mlrPAR <- PROV$par.m0
mlrSE <- se.m0
}
nrow <- sapply(mlrPAR, nrow)
colnams <- lapply(mlrPAR, colnames)
rownams <- lapply(mlrPAR, rownames)
mlrSE <- lapply(1:length(mlrSE), function(x) {
matrix(mlrSE[[x]],
nrow = nrow[[x]],
dimnames = list(rownams[[x]], colnams[[x]])
)
})
RES <- list(
Sval = STATS,
mlrPAR = mlrPAR,
mlrSE = mlrSE,
parM0 = PROV$par.m0, parM1 = PROV$par.m1,
covM0 = PROV$cov.m0, covM1 = PROV$cov.m1,
llM0 = PROV$ll.m0, llM1 = PROV$ll.m1,
AICM0 = PROV$AIC.m0, AICM1 = PROV$AIC.m1,
BICM0 = PROV$BIC.m0, BICM1 = PROV$BIC.m1,
DDFitems = DDFitems,
type = type,
purification = purify,
p.adjust.method = p.adjust.method, pval = PROV$pval, adj.pval = PROV$adjusted.pval, df = PROV$df,
alpha = alpha,
Data = DATA, group = GROUP, group.names = group.names, key = c(KEY), match = match
)
} else {
nrPur <- 0
ddfPur <- NULL
noLoop <- FALSE
prov1 <- suppressWarnings(MLR(
Data = DATA, group = GROUP,
key = KEY, type = type,
p.adjust.method = p.adjust.method,
alpha = alpha
))
stats1 <- prov1$Sval
pval1 <- prov1$pval
significant1 <- which(pval1 < alpha)
if (length(significant1) == 0) {
PROV <- prov1
STATS <- stats1
DDFitems <- "No DDF item detected"
se.m1 <- PROV$se.m1
se.m0 <- PROV$se.m0
mlrPAR <- PROV$par.m0
mlrSE <- se.m0
noLoop <- TRUE
} else {
dif <- significant1
ddfPur <- rep(0, length(stats1))
ddfPur[dif] <- 1
repeat {
if (nrPur >= nrIter) {
break
} else {
nrPur <- nrPur + 1
nodif <- NULL
if (is.null(dif)) {
nodif <- 1:dim(DATA)[2]
} else {
for (i in 1:dim(DATA)[2]) {
if (sum(i == dif) == 0) {
nodif <- c(nodif, i)
}
}
}
prov2 <- suppressWarnings(MLR(
Data = DATA, group = GROUP,
key = KEY, anchor = nodif, type = type,
p.adjust.method = p.adjust.method,
alpha = alpha
))
stats2 <- prov2$Sval
pval2 <- prov2$pval
significant2 <- which(pval2 < alpha)
if (length(significant2) == 0) {
dif2 <- NULL
} else {
dif2 <- significant2
}
ddfPur <- rbind(ddfPur, rep(0, dim(DATA)[2]))
ddfPur[nrPur + 1, dif2] <- 1
if (length(dif) != length(dif2)) {
dif <- dif2
} else {
dif <- sort(dif)
dif2 <- sort(dif2)
if (sum(dif == dif2) == length(dif)) {
noLoop <- TRUE
break
} else {
dif <- dif2
}
}
}
}
PROV <- prov2
STATS <- stats2
significant1 <- which(PROV$adjusted.pval < alpha)
se.m1 <- PROV$se.m1
se.m0 <- PROV$se.m0
mlrPAR <- PROV$par.m0
mlrSE <- se.m0
if (length(significant1) > 0) {
DDFitems <- significant1
for (idif in 1:length(DDFitems)) {
mlrPAR[[DDFitems[idif]]] <- PROV$par.m1[[DDFitems[idif]]]
mlrSE[[DDFitems[idif]]] <- se.m1[[DDFitems[idif]]]
}
} else {
DDFitems <- "No DDF item detected"
}
}
if (!is.null(ddfPur)) {
rownames(ddfPur) <- paste("Step", 0:(dim(ddfPur)[1] - 1), sep = "")
colnames(ddfPur) <- colnames(DATA)
}
RES <- list(
Sval = STATS,
mlrPAR = mlrPAR,
mlrSE = mlrSE,
parM0 = PROV$par.m0, parM1 = PROV$par.m1,
covM0 = PROV$cov.m0, covM1 = PROV$cov.m1,
llM0 = PROV$ll.m0, llM1 = PROV$ll.m1,
AICM0 = PROV$AIC.m0, AICM1 = PROV$AIC.m1,
BICM0 = PROV$BIC.m0, BICM1 = PROV$BIC.m1,
DDFitems = DDFitems,
type = type,
purification = purify, nrPur = nrPur, ddfPur = ddfPur, conv.puri = noLoop,
p.adjust.method = p.adjust.method, pval = PROV$pval, adj.pval = PROV$adjusted.pval, df = PROV$df,
alpha = alpha,
Data = DATA, group = GROUP, group.names = group.names, key = c(KEY), match = match
)
}
class(RES) <- "ddfMLR"
return(RES)
}
resToReturn <- internalMLR()
return(resToReturn)
}
#' @export
print.ddfMLR <- function(x, ...) {
title <- switch(x$type,
both = "Detection of both types of Differential Distractor Functioning using multinomial log-linear regression model",
udif = "Detection of uniform Differential Distractor Functioning using multinomial log-linear regression model",
nudif = "Detection of non-uniform Differential Distractor Functioning using multinomial log-linear regression model"
)
cat(paste(strwrap(title, width = 60), collapse = "\n"))
cat("\n\nLikelihood-ratio chi-square statistics\n")
if (x$purification) word.iteration <- ifelse(x$nrPur <= 1, " iteration", " iterations")
cat(paste("\nItem purification was", ifelse(x$purification, " ", " not "), "applied",
ifelse(x$purification, paste(" with ", x$nrPur, word.iteration, sep = ""), ""), "\n",
sep = ""
))
if (x$purification) {
if (!x$conv.puri) {
cat(paste("WARNING: Item purification process not converged after "), x$nrPur, word.iteration, "\n",
" Results are based on last iteration of the item purification.\n",
sep = ""
)
}
}
if (x$p.adjust.method == "none") {
cat("No p-value adjustment for multiple comparisons\n\n")
} else {
cat(paste(
"Multiple comparisons made with",
switch(x$p.adjust.method,
holm = "Holm",
hochberg = "Hochberg",
hommel = "Hommel",
bonferroni = "Bonferroni",
BH = "Benjamini-Hochberg",
BY = "Benjamini-Yekutieli",
fdr = "FDR"
), "adjustment of p-values\n\n"
))
}
sign <- ifelse(is.na(x$adj.pval), " ",
symnum(x$adj.pval,
c(0, 0.001, 0.01, 0.05, 0.1, 1),
symbols = c("***", "**", "*", ".", "")
)
)
if (x$p.adjust.method == "none") {
tab <- format(round(cbind(x$Sval, x$pval), 4))
tab <- matrix(cbind(tab, sign), ncol = 3)
colnames(tab) <- c("Chisq-value", "P-value", "")
} else {
tab <- format(round(cbind(x$Sval, x$pval, x$adj.pval), 4))
tab <- matrix(cbind(tab, sign), ncol = 4)
colnames(tab) <- c("Chisq-value", "P-value", "Adj. P-value", "")
}
rownames(tab) <- colnames(x$Data)
print(tab, quote = F, digits = 4, zero.print = F)
cat("\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n")
if (is.character(x$DDFitems)) {
switch(x$type,
both = cat("\nNone of items is detected as DDF"),
udif = cat("\nNone of items is detected as uniform DDF"),
nudif = cat("\nNone of items is detected as non-uniform DDF")
)
} else {
switch(x$type,
both = cat("\nItems detected as DDF items:"),
udif = cat("\nItems detected as uniform DDF items:"),
nudif = cat("\nItems detected as non-uniform DDF items:")
)
cat("\n", paste(colnames(x$Data)[x$DDFitems], "\n", sep = ""))
}
}
#' ICC plots for an object of \code{"ddfMLR"} class.
#'
#' @description Plot method for an object of \code{"ddfMLR"} class
#' using \pkg{ggplot2}.
#'
#' The characteristic curves for an item specified in \code{item}
#' argument are plotted. Plotted curves represent the best model.
#'
#' @param x an object of \code{"ddfMLR"} class.
#' @param item numeric or character: either character \code{"all"} to
#' apply for all items (default), or a vector of item names (column
#' names of \code{Data}), or item identifiers (integers specifying
#' the column number).
#' @param group.names character: names of reference and focal group.
#' @param ... other generic parameters for \code{plot()} function.
#'
#' @return Returns list of objects of class \code{"ggplot"}.
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' Faculty of Mathematics and Physics, Charles University \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @seealso
#' \code{\link[difNLR]{ddfMLR}} for DDF detection. \cr
#' \code{\link[ggplot2]{ggplot}} for general function to plot a \code{"ggplot"} object.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # graphical devices
#' plot(x, item = "Item1", group.names = c("Group 1", "Group 2"))
#' plot(x, item = x$DDFitems)
#' plot(x, item = c(3, 1, 5))
#' }
#' @export
plot.ddfMLR <- function(x, item = "all", group.names, ...) {
m <- length(x$mlrPAR)
nams <- colnames(x$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
if (missing(group.names)) {
group.names <- x$group.names
if (all(group.names %in% c(0, 1))) group.names <- c("Reference", "Focal")
}
if (length(group.names) > 2) {
group.names <- group.names[1:2]
warning("Only first two values for 'group.names' argument are used. ")
} else {
if (length(group.names) < 2) {
group.names <- c("Reference", "Focal")
warning("Argument 'group.names' need to have length of two. Default value is used.")
}
}
if (x$purification) {
anchor <- c(1:m)[!c(1:m) %in% x$DDFitems]
} else {
anchor <- 1:m
}
if (x$match[1] == "zscore") {
matching <- c(scale(.score(as.data.frame(x$Data[, anchor]), x$key[anchor])))
xlab <- "Standardized total score"
} else {
if (x$match[1] == "score") {
matching <- c(.score(as.data.frame(x$Data[, anchor]), x$key[anchor]))
xlab <- "Total score"
} else {
if (length(x$match) == dim(x$Data)[1]) {
matching <- x$match
xlab <- "Matching criterion"
} else {
stop("Invalid value for 'match'. Possible values are 'score', 'zscore' or vector of the same length as number
of observations in 'Data'!")
}
}
}
match <- seq(min(matching, na.rm = TRUE), max(matching, na.rm = TRUE), length.out = 300)
plot_CC <- list()
for (i in items) {
TITLE <- colnames(x$Data)[i]
df.fitted <- data.frame(rbind(
cbind(Group = "0", Match = match, predict(x, item = i, match = match, group = 0)),
cbind(Group = "1", Match = match, predict(x, item = i, match = match, group = 1))
), check.names = FALSE)
df.fitted <- reshape(
data = df.fitted, direction = "long",
varying = list(colnames(df.fitted)[-c(1:2)]), v.names = "Probability",
idvar = c("Group", "Match"),
timevar = "Category", times = colnames(df.fitted)[-c(1:2)]
)
df.fitted$Category <- factor(df.fitted$Category)
df.fitted$Category <- relevel(df.fitted$Category, ref = paste(x$key[i]))
levels(df.fitted$Category) <- paste0("P(Y = ", levels(df.fitted$Category), ")")
n_cats <- length(levels(df.fitted$Category))
df.empirical <- rbind(
data.frame(prop.table(table(x$Data[x$group == 1, i], matching[x$group == 1]), 2),
table(x$Data[x$group == 1, i], matching[x$group == 1]),
group = "1"
),
data.frame(prop.table(table(x$Data[x$group == 0, i], matching[x$group == 0]), 2),
table(x$Data[x$group == 0, i], matching[x$group == 0]),
group = "0"
)
)
df.empirical <- data.frame(
Group = as.factor(df.empirical$group),
Match = as.numeric(paste(df.empirical$Var2)),
Category = relevel(df.empirical$Var1, ref = paste(x$key[i])),
Count = as.numeric(paste(df.empirical$Freq.1)),
Probability = as.numeric(paste(df.empirical$Freq))
)
levels(df.empirical$Category) <- paste0("P(Y = ", levels(df.empirical$Category), ")")
cbPalette <- c("#ffbe33", "#34a4e5", "#ce7eaa", "#00805e", "#737373", "#f4eb71", "#0072B2", "#D55E00")
n_col <- ceiling(n_cats / 8)
cols <- rep(cbPalette, n_col)[1:n_cats]
plot_CC[[i]] <- ggplot2::ggplot() +
ggplot2::geom_line(
data = df.fitted,
ggplot2::aes(
x = .data$Match, y = .data$Probability,
colour = .data$Category, linetype = .data$Group
),
linewidth = 0.8
) +
ggplot2::geom_point(
data = df.empirical,
ggplot2::aes(
x = .data$Match, y = .data$Probability,
colour = .data$Category, fill = .data$Category,
size = .data$Count
),
alpha = 0.5, shape = 21
) +
ggplot2::ylim(0, 1) +
ggplot2::ggtitle(TITLE) +
ggplot2::labs(
x = xlab,
y = "Probability of answer"
) +
ggplot2::scale_linetype_manual(
breaks = c(0, 1), labels = group.names,
values = c("solid", "dashed")
) +
ggplot2::scale_color_manual(values = cols) +
ggplot2::scale_fill_manual(values = cols) +
.plot.theme() +
# legend
.plot.theme.legend() +
ggplot2::guides(
size = ggplot2::guide_legend(title = "Count", order = 1),
colour = ggplot2::guide_legend(title = "Answer", order = 2),
fill = ggplot2::guide_legend(title = "Answer", order = 2),
linetype = ggplot2::guide_legend(title = "Group", order = 3)
)
}
plot_CC <- plot_CC[items]
names(plot_CC) <- nams[items]
return(plot_CC)
}
#' Extract model coefficients from an object of \code{"ddfMLR"} class.
#'
#' @description S3 method for extracting estimated model coefficients
#' from an object of \code{"ddfMLR"} class.
#' @aliases coefficients.ddfMLR
#'
#' @param object an object of \code{"ddfMLR"} class.
#' @param SE logical: should the standard errors of estimated
#' parameters be also returned? (default is \code{FALSE}).
#' @param simplify logical: should the estimated parameters be
#' simplified to a matrix? (default is \code{FALSE}).
#' @param IRTpars logical: should the estimated parameters be returned
#' in IRT parameterization? (default is \code{TRUE}).
#' @param CI numeric: level of confidence interval for parameters,
#' default is \code{0.95} for 95\% confidence interval.
#' @param ... other generic parameters for \code{coef()} function.
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' Faculty of Mathematics and Physics, Charles University \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @seealso
#' \code{\link[difNLR]{ddfMLR}} for DDF detection among nominal data. \cr
#' \code{\link[stats]{coef}} for generic function extracting model coefficients.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # estimated parameters
#' coef(x)
#' # includes standard errors
#' coef(x, SE = TRUE)
#' # includes standard errors and simplifies to matrix
#' coef(x, SE = TRUE, simplify = TRUE)
#' # intercept-slope parameterization
#' coef(x, IRTpars = FALSE)
#' # intercept-slope parameterization, simplifies to matrix, turn off confidence intervals
#' coef(x, IRTpars = FALSE, simplify = TRUE, CI = 0)
#' }
#' @export
coef.ddfMLR <- function(object, SE = FALSE, simplify = FALSE, IRTpars = TRUE, CI = 0.95, ...) {
if (!inherits(SE, "logical")) {
stop("Invalid value for 'SE'. 'SE' needs to be logical. ",
call. = FALSE
)
}
if (!inherits(simplify, "logical")) {
stop("Invalid value for 'simplify'. 'simplify' needs to be logical. ",
call. = FALSE
)
}
if (!inherits(IRTpars, "logical")) {
stop("Invalid value for 'IRTpars'. 'IRTpars' needs to be logical. ",
call. = FALSE
)
}
if (CI > 1 | CI < 0 | !is.numeric(CI)) {
stop("Invalid value for 'CI'. 'CI' must be numeric value between 0 and 1. ",
call. = FALSE
)
}
m <- dim(object$Data)[2]
nams <- colnames(object$Data)
if (!IRTpars) {
pars <- object$mlrPAR
se <- object$mlrSE
} else {
mlrPAR <- object$mlrPAR
mlrCOV <- ifelse(1:m %in% object$DDFitems, object$covM1, object$covM0)
mlrDM <- lapply(1:m, function(i) {
.deltamethod.MLR.log2irt(
par = mlrPAR[[i]], cov = mlrCOV[[i]]
)
})
se <- lapply(mlrDM, function(x) x$se)
pars <- lapply(1:m, function(i) {
if (any(is.null(dim(mlrDM[[i]]$par)))) {
par_names <- names(mlrDM[[i]]$par)
} else {
par_names <- colnames(mlrDM[[i]]$par)
}
matrix(mlrDM[[i]]$par,
nrow = nrow(mlrPAR[[i]]), ncol = ncol(mlrPAR[[i]]),
dimnames = list(rownames(mlrPAR[[i]]), par_names)
)
})
}
cats <- lapply(1:m, function(i) rownames(pars[[i]]))
names(pars) <- names(cats) <- names(se) <- nams
if (SE) {
se_matrix <- lapply(1:m, function(i) {
matrix(se[[i]],
nrow = nrow(pars[[i]]), ncol = ncol(pars[[i]]),
dimnames = list(rownames(pars[[i]]), colnames(pars[[i]]))
)
})
coefs <- lapply(1:m, function(i) rbind(pars[[i]], se_matrix[[i]]))
coefs <- lapply(1:m, function(i) {
rownames(coefs[[i]]) <- paste(rep(c("estimate", "SE"), each = nrow(coefs[[i]]) / 2), cats[[i]], sep = "_")
coefs[[i]]
})
} else {
coefs <- pars
}
names(coefs) <- nams
if (CI > 0) {
alpha <- (1 - CI) / 2
CIlow <- lapply(1:m, function(i) pars[[i]] - qnorm(1 - alpha) * se[[i]])
CIupp <- lapply(1:m, function(i) pars[[i]] + qnorm(1 - alpha) * se[[i]])
coefs <- lapply(1:m, function(i) rbind(coefs[[i]], CIlow[[i]], CIupp[[i]]))
names(coefs) <- nams
if (SE) {
tmp <- c("estimate", "SE", paste0("CI", 100 * alpha), paste0("CI", 100 * (1 - alpha)))
} else {
tmp <- c("estimate", paste0("CI", 100 * alpha), paste0("CI", 100 * (1 - alpha)))
}
coefs <- lapply(1:m, function(i) {
rownames(coefs[[i]]) <- paste(rep(tmp, each = nrow(coefs[[i]]) / length(tmp)), cats[[i]], sep = "_")
coefs[[i]]
})
names(coefs) <- nams
}
if (simplify) {
res <- as.data.frame(plyr::ldply(coefs, rbind, .id = NULL))
id <- unlist(lapply(nams, function(i) paste(i, rownames(coefs[[i]]))))
rownames(res) <- id
res[is.na(res)] <- 0
} else {
res <- coefs
}
return(res)
}
#' Log-likelihood and information criteria for an object of \code{"ddfMLR"} class.
#'
#' @aliases AIC.ddfMLR BIC.ddfMLR
#' @rdname logLik.ddfMLR
#'
#' @description S3 methods for extracting log-likelihood, Akaike's
#' information criterion (AIC) and Schwarz's Bayesian criterion
#' (BIC) for an object of \code{"ddfMLR"} class.
#'
#' @param object an object of \code{"ddfMLR"} class.
#' @param item numeric or character: either character \code{"all"} to
#' apply for all converged items (default), or a vector of item
#' names (column names of \code{Data}), or item identifiers
#' (integers specifying the column number).
#' @param ... other generic parameters for S3 methods.
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' Faculty of Mathematics and Physics, Charles University \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @seealso
#' \code{\link[difNLR]{ddfMLR}} for DDF detection among nominal data. \cr
#' \code{\link[stats]{logLik}} for generic function extracting log-likelihood. \cr
#' \code{\link[stats]{AIC}} for generic function calculating AIC and BIC.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # AIC, BIC, log-likelihood
#' AIC(x)
#' BIC(x)
#' logLik(x)
#'
#' # AIC, BIC, log-likelihood for the first item
#' AIC(x, item = 1)
#' BIC(x, item = 1)
#' logLik(x, item = 1)
#' }
#' @export
logLik.ddfMLR <- function(object, item = "all", ...) {
m <- length(object$mlrPAR)
nams <- colnames(object$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
val <- ifelse(items %in% object$DDFitems,
object$llM1[items],
object$llM0[items]
)
df <- ifelse(items %in% object$DDFitems,
sapply(object$parM1, length)[items],
sapply(object$parM0, length)[items]
)
if (length(items) == 1) {
attr(val, "df") <- df
class(val) <- "logLik"
}
return(val)
}
#' @rdname logLik.ddfMLR
#' @aliases BIC.ddfMLR logLik.ddfMLR
#' @export
AIC.ddfMLR <- function(object, item = "all", ...) {
m <- length(object$mlrPAR)
nams <- colnames(object$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
AIC <- ifelse(items %in% object$DDFitems, object$AICM1[items], object$AICM0[items])
return(AIC)
}
#' @rdname logLik.ddfMLR
#' @aliases AIC.ddfMLR logLik.ddfMLR
#' @export
BIC.ddfMLR <- function(object, item = "all", ...) {
m <- length(object$mlrPAR)
nams <- colnames(object$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
BIC <- ifelse(items %in% object$DDFitems, object$BICM1[items], object$BICM0[items])
return(BIC)
}
#' Predicted values for an object of \code{"ddfMLR"} class.
#'
#' @description S3 method for predictions from the model used in the
#' object of \code{"ddfMLR"} class.
#'
#' @param object an object of \code{"ddfMLR"} class.
#' @param item numeric or character: either character \code{"all"} to
#' apply for all converged items (default), or a vector of item
#' names (column names of \code{Data}), or item identifiers
#' (integers specifying the column number).
#' @param match numeric: matching criterion for new observations.
#' @param group numeric: group membership for new observations.
#' @param ... other generic parameters for \code{predict()} function.
#'
#' @author
#' Adela Hladka (nee Drabinova) \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{hladka@@cs.cas.cz} \cr
#'
#' Patricia Martinkova \cr
#' Institute of Computer Science of the Czech Academy of Sciences \cr
#' \email{martinkova@@cs.cas.cz} \cr
#'
#' @references
#' Hladka, A. & Martinkova, P. (2020). difNLR: Generalized logistic regression models for DIF and DDF detection.
#' The R Journal, 12(1), 300--323, \doi{10.32614/RJ-2020-014}.
#'
#' @seealso
#' \code{\link[difNLR]{ddfMLR}} for DDF detection among nominal data using multinomial log-linear regression model. \cr
#' \code{\link[stats]{predict}} for generic function for prediction.
#'
#' @examples
#' \dontrun{
#' # loading data
#' data(GMATtest, GMATkey)
#' Data <- GMATtest[, 1:20] # items
#' group <- GMATtest[, "group"] # group membership variable
#' key <- GMATkey # correct answers
#'
#' # testing both DDF effects
#' (x <- ddfMLR(Data, group, focal.name = 1, key))
#'
#' # fitted values
#' predict(x, item = 1)
#'
#' # predicted values
#' predict(x, item = 1, match = 0, group = c(0, 1))
#' predict(x, item = x$DDFitems, match = 0, group = c(0, 1))
#' }
#'
#' @export
predict.ddfMLR <- function(object, item = "all", match, group, ...) {
m <- dim(object$Data)[2]
nams <- colnames(object$Data)
if (inherits(item, "character")) {
if (any(item != "all") & !all(item %in% nams)) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
}
if (any(item == "all")) {
items <- 1:m
} else {
items <- which(nams %in% item)
}
} else {
if (!inherits(item, "integer") & !inherits(item, "numeric")) {
stop("Invalid value for 'item'. Item must be either character 'all', or
numeric vector corresponding to column identifiers, or name of the item.",
call. = FALSE
)
} else {
if (!all(item %in% 1:m)) {
stop("Invalid number for 'item'.",
call. = FALSE
)
} else {
items <- item
}
}
}
if (object$purification) {
anchor <- c(1:m)[!c(1:m) %in% object$DIFitems]
} else {
anchor <- 1:m
}
if (missing(match)) {
if (length(object$match) > 1) {
match <- object$match
} else {
if (object$match == "score") {
match <- c(.score(as.data.frame(object$Data[, anchor]), object$key))
} else {
match <- c(scale(.score(as.data.frame(object$Data[, anchor]), object$key)))
}
}
}
if (missing(group)) {
group <- object$group
}
if (length(match) != length(group)) {
if (length(match) == 1) {
match <- rep(match, length(group))
} else if (length(group) == 1) {
group <- rep(group, length(match))
} else {
stop("Arguments 'match' and 'group' must be of the same length.",
call. = FALSE
)
}
}
mat <- cbind("(Intercept)" = 1, "x" = match, "group" = group, "x:group" = match * group)
coefs_all <- coef(object, IRTpars = FALSE, CI = 0)
res <- list()
for (i in items) {
coefs <- coefs_all[[i]]
if (is.null(dim(coefs))) coefs <- matrix(coefs, ncol = length(coefs))
if (dim(coefs)[2] == 2) {
coefs <- as.matrix(data.frame(coefs, 0, 0))
}
if (dim(coefs)[2] == 3) {
coefs <- as.matrix(data.frame(coefs, 0))
}
cats <- c(object$key[i], rownames(coefs))
df.probs <- as.data.frame(t(exp(coefs %*% t(mat))))
df.probs <- sapply(df.probs, function(x) x / (rowSums(df.probs) + 1))
df.probs <- data.frame(1 - rowSums(df.probs), df.probs)
colnames(df.probs) <- cats
res[[i]] <- df.probs
}
res <- res[items]
names(res) <- nams[items]
if (length(res) == 1) {
res <- res[[1]]
} else {
names(res) <- nams[items]
}
return(res)
}
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