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\name{itempar}
\alias{itempar}
\alias{itempar.btmodel}
\alias{itempar.raschmodel}
\alias{itempar.rsmodel}
\alias{itempar.pcmodel}
\alias{itempar.plmodel}
\alias{itempar.gpcmodel}
\alias{itempar.raschtree}
\alias{itempar.bttree}
\alias{coef.itempar}
\alias{print.itempar}
\alias{vcov.itempar}
\title{Extract Item Parameters of Item Response Models}
\description{
A class and generic function for representing and extracting the item
parameters of a given item response model.
}
\usage{
itempar(object, \dots)
\method{itempar}{raschmodel}(object, ref = NULL, alias = TRUE, vcov = TRUE, \dots)
\method{itempar}{rsmodel}(object, ref = NULL, alias = TRUE, vcov = TRUE, \dots)
\method{itempar}{pcmodel}(object, ref = NULL, alias = TRUE, vcov = TRUE, \dots)
\method{itempar}{plmodel}(object, ref = NULL, alias = TRUE, vcov = TRUE, \dots)
\method{itempar}{gpcmodel}(object, ref = NULL, alias = TRUE, vcov = TRUE, \dots)
\method{itempar}{btmodel}(object, ref = NULL, alias = TRUE, vcov = TRUE, log = FALSE, \dots)
}
\arguments{
\item{object}{a fitted model or tree object whose item parameters should be extracted.}
\item{ref}{a vector of labels or position indices of item parameters or a
contrast matrix which should be used as restriction/for normalization. If
\code{NULL} (the default) for all models except models estimated via MML,
all items are used (sum zero restriction). For models estimated via MML
(\code{plmodel}s and \code{gpcmodel}s), the parameters are by default
identified via the distributional parameters of the person parameters (mean
and variance of a normal distribution). Nevertheless, a restriction on the
interval scale can be applied.}
\item{alias}{logical. If \code{TRUE} (the default), the aliased parameter is
included in the return vector (and in the variance-covariance matrix if
\code{vcov} = TRUE). If \code{FALSE}, it is removed. If the restriction
given in \code{ref} depends on several parameters, the first parameter of
the restriction specified is (arbitrarily) chosen to be removed if
\code{alias} is \code{FALSE}.}
\item{vcov}{logical. If \code{TRUE} (the default), the (transformed)
variance-covariance matrix of the item parameters is attached as
attribute \code{vcov}. If \code{FALSE}, an \code{NA}-matrix is attached.}
\item{log}{logical. Whether to return the estimated model parameters
on the logit (\code{TRUE}) or preference scale (\code{FALSE}).}
\item{\dots}{further arguments which are currently not used.}
}
\details{
\code{itempar} is both, a class to represent item parameters of item
response models as well as a generic function. The generic function can be
used to extract the item parameters of a given item response model.
For Rasch models and n-parameter logistic models, \code{itempar} returns the
estimated item difficulty parameters \eqn{\hat{\beta}_{j}} under the
restriction specified in argument \code{ref}. For rating scale models,
\code{itempar} returns computed item location parameters \eqn{\hat{\beta}_{j}}
under the restriction specified in argument \code{ref}. These are computed
from the estimated item-specific parameters \eqn{\hat{\xi}_{j}} (who mark the
location of the first category of an item on the latent theta axis). For
partial credit models and generalized partial credit models, \code{itempar}
returns \sQuote{mean} absolute item threshold parameters, \eqn{\hat{\beta}_{j}
= \frac{1}{p_{j}} \sum_{k = 1}^{p_{j}}\hat{\delta}_{jk}}, i.e., a single
parameter per item is returned which results as the mean of the absolute item
threshold parameters \eqn{\hat{\delta}_{jk}} of this item. Based upon these
\sQuote{mean} absolute item threshold parameters \eqn{\hat{\beta}_{j}}, the
restriction specified in argument \code{ref} is applied. For all models, the
variance-covariance matrix of the returned item parameters is adjusted
according to the multivariate delta rule.
For objects of class \code{itempar}, several methods to standard generic
functions exist: \code{print}, \code{coef}, \code{vcov}. \code{coef} and
\code{vcov} can be used to extract the estimated calculated item parameters
and their variance-covariance matrix without additional attributes. Based on
this Wald tests or confidence intervals can be easily computed, e.g., via
\code{confint}.
Two-sample item-wise Wald tests for DIF in the item parameters can be
carried out using the function \code{\link{anchortest}}.
}
\value{
A named vector with item parameters of class \code{itempar} and additional
attributes \code{model} (the model name), \code{ref} (the items or parameters
used as restriction/for normalization), \code{alias} (either \code{FALSE} or a
named character vector with the removed aliased parameter, and \code{vcov}
(the adjusted covariance matrix of the estimates if \code{vcov = TRUE} or an
\code{NA}-matrix otherwise).
}
\seealso{\code{\link{personpar}}, \code{\link{threshpar}},
\code{\link{discrpar}}, \code{\link{guesspar}}, \code{\link{upperpar}}}
\examples{
o <- options(digits = 4)
## load verbal aggression data
data("VerbalAggression", package = "psychotools")
## fit a Rasch model to dichotomized verbal aggression data
raschmod <- raschmodel(VerbalAggression$resp2)
## extract item parameters with sum zero or use last two items as anchor
ip1 <- itempar(raschmod)
ip2a <- itempar(raschmod, ref = 23:24) # with position indices
ip2b <- itempar(raschmod, ref = c("S4WantShout", "S4DoShout")) # with item label
ip1
ip2a
all.equal(ip2a, ip2b)
## extract vcov
vc1 <- vcov(ip1)
vc2 <- vcov(ip2a)
## adjusted standard errors,
## smaller with more items used as anchors
sqrt(diag(vc1))
sqrt(diag(vc2))
## Wald confidence intervals
confint(ip1)
confint(ip2a)
options(digits = o$digits)
}
\keyword{classes}
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