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\encoding{UTF-8}
\name{stepwiseIt}
\alias{stepwiseIt}
\alias{stepwiseIt.eRm}
\alias{print.step}
%- Also NEED an '\alias' for EACH other topic documented here.
\title{Stepwise item elimination}
\description{This function eliminates items stepwise according to one of the following
criteria: itemfit, Wald test, Andersen's LR-test
}
\usage{
\method{stepwiseIt}{eRm}(object, criterion = list("itemfit"), alpha = 0.05,
verbose = TRUE, maxstep = NA)
}
\arguments{
\item{object}{Object of class \code{eRm}.}
\item{criterion}{List with either \code{"itemfit"}, \code{"Waldtest"} or \code{"LRtest"} as first element.
Optionally, for the Waldtest and LRtest a second element containing the split criterion can be specified (see details).}
\item{alpha}{Significance level.}
\item{verbose}{If \code{TRUE} intermediate results are printed out. }
\item{maxstep}{Maximum number of elimination steps. If \code{NA} the procedure stops when the itemset is Rasch homogeneous.}
}
\details{If \code{criterion = list("itemfit")} the elimination stops when none of the p-values
in itemfit is significant. Within each step the item with the largest chi-squared
itemfit value is excluded.
If \code{criterion = list("Waldtest")} the elimination stops when none of the p-values
resulting from the Wald test is significant. Within each step the item with the largest z-value in
Wald test is excluded.
If \code{criterion = list("LRtest")} the elimination stops when Andersen's LR-test is not
significant. Within each step the item with the largest z-value in Wald test is excluded.
}
\value{
The function returns an object of class \code{step} containing:
\item{X}{Reduced data matrix (bad items eliminated)}
\item{fit}{Object of class \code{eRm} with the final item parameter elimination}
\item{it.elim}{Vector contaning the names of the eliminated items}
\item{res.wald}{Elimination results for Wald test criterion}
\item{res.itemfit}{Elimination results for itemfit criterion}
\item{res.LR}{Elimination results for LR-test criterion}
\item{nsteps}{Number of elimination steps}
}
\seealso{ \code{\link{LRtest.Rm}}, \code{\link{Waldtest.Rm}}, \code{\link{itemfit.ppar}}
}
\examples{
## 2pl-data, 100 persons, 10 items
set.seed(123)
X <- sim.2pl(500, 10, 0.4)
res <- RM(X)
## elimination according to itemfit
stepwiseIt(res, criterion = list("itemfit"))
## Wald test based on mean splitting
stepwiseIt(res, criterion = list("Waldtest","mean"))
## Andersen LR-test based on random split
set.seed(123)
groupvec <- sample(1:3, 500, replace = TRUE)
stepwiseIt(res, criterion = list("LRtest",groupvec))
}
\keyword{models}
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