% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/dif.R, R/summary.GDINA.R
\name{dif}
\alias{dif}
\alias{summary.dif}
\title{Differential item functioning for cognitive diagnosis models}
\usage{
dif(dat, Q, group, method = "wald", p.adjust.methods = "bonferroni",
  LR.type = "free.all", LR.approx = FALSE, difitem = "all", digits = 4,
  SE.type = 2, ...)

\method{summary}{dif}(object, ...)
}
\arguments{
\item{dat}{A required \eqn{N \times J} \code{matrix} or \code{data.frame} consisting of the
responses of \eqn{N} individuals to \eqn{J} items. Missing values need to be coded as \code{NA}.}

\item{Q}{A required matrix; The number of rows occupied by a single-strategy dichotomous item is 1, by a polytomous item is
the number of nonzero categories, and by a mutiple-strategy dichotomous item is the number of strategies.
The number of column is equal to the number of attributes if all items are single-strategy dichotomous items, but
the number of attributes + 2 if any items are polytomous or have multiple strategies.
For a polytomous item, the first column represents the item number and the second column indicates the nonzero category number.
For a multiple-strategy dichotomous item, the first column represents the item number and the second column indicates the strategy number.
For binary attributes, 1 denotes the attributes are measured by the items and 0 means the attributes are not
   measured. For polytomous attributes, non-zero elements indicate which level
   of attributes are needed (see Chen, & de la Torre, 2013).  See \code{Examples}.}

\item{group}{a numerical vector with integer 1, 2, ..., # of groups indicating the group each individual belongs to. It must start from 1 and its
length must be equal to the number of individuals.}

\item{method}{DIF detection method; It can be \code{"wald"} for Hou, de la Torre, and Nandakumar's (2014)
Wald test method, and \code{"LR"} for likelihood ratio test (Ma, Terzi, Lee,& de la Torre, 2017).}

\item{p.adjust.methods}{adjusted p-values for multiple hypothesis tests. This is conducted using \code{p.adjust} function in \pkg{stats},
and therefore all adjustment methods supported by \code{p.adjust} can be used, including \code{"holm"},
\code{"hochberg"}, \code{"hommel"}, \code{"bonferroni"}, \code{"BH"} and \code{"BY"}. See \code{p.adjust}
for more details. \code{"bonferroni"} is the default.}

\item{LR.type}{Type of likelihood ratio test for DIF detection. It can be \code{'free.all'} or
\code{'free.one'}.}

\item{LR.approx}{Whether an approximated LR test is implemented? If TRUE, anchor item parameters will not be re-estimated but fixed.}

\item{difitem}{Items for the DIF detection. By default, all items will be examined.}

\item{digits}{How many decimal places in each number? The default is 4.}

\item{SE.type}{Type of standard error estimation methods for the Wald test.}

\item{...}{Other arguments passed to GDINA function for model calibration}

\item{object}{GDINA object for various S3 methods}
}
\value{
A data frame giving the Wald statistics and associated p-values.
}
\description{
This function is used to detect differential item functioning based on the models estimated
in the \code{\link{GDINA}} function using the Wald test (Hou, de la Torre, & Nandakumar, 2014) and the likelihood ratio
test (Ma, Terzi, Lee, & de la Torre, 2017). It can only detect DIF for two groups currently.
}
\section{Methods (by generic)}{
\itemize{
\item \code{summary}: print summary information
}}

\examples{
\dontrun{
set.seed(123456)
N <- 3000
Q <- sim10GDINA$simQ
gs <- matrix(c(0.1,0.2,
                       0.1,0.2,
                       0.1,0.2,
                       0.1,0.2,
                       0.1,0.2,
                       0.1,0.2,
                       0.1,0.2,
                       0.1,0.2,
                       0.1,0.2,
                       0.1,0.2),ncol = 2, byrow = TRUE)
# By default, individuals are simulated from uniform distribution
# and deltas are simulated randomly
sim1 <- simGDINA(N,Q,gs.parm = gs,model="DINA")
sim2 <- simGDINA(N,Q,gs.parm = gs,model=c(rep("DINA",9),"DINO"))
dat <- rbind(extract(sim1,"dat"),extract(sim2,"dat"))
gr <- c(rep(1,N),rep(2,N))
dif.out <- dif(dat,Q,group=gr)
dif.out2 <- dif(dat,Q,group=gr,method="LR")
}
}
\references{
Hou, L., de la Torre, J., & Nandakumar, R. (2014). Differential item functioning assessment in cognitive diagnostic modeling: Application of the Wald test to
investigate DIF in the DINA model. \emph{Journal of Educational Measurement, 51}, 98-125.

Ma, W., Terzi, R., Lee, S., & de la Torre, J. (2017, April). Multiple group cognitive diagnosis models and their applications in detecting differential item functioning. Paper presented at the Annual Meeting ofthe American Educational Research Association, San Antonio, TX.
}
\seealso{
\code{\link{GDINA}}
}
\author{
{Wenchao Ma, The University of Alabama, \email{wenchao.ma@ua.edu} \cr Jimmy de la Torre, The University of Hong Kong}
}