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\name{predict.pcmodel}
\alias{predict.pcmodel}
\alias{predict.rsmodel}
\alias{predict.raschmodel}
\alias{predict.gpcmodel}
\alias{predict.plmodel}
\title{Predict Methods for Item Response Models}
\description{
Prediction of (cumulated) response probabilities and responses based on fitted
item response models.
}
\usage{
\S3method{predict}{pcmodel}(object, newdata = NULL, type = c("probability",
"cumprobability", "mode", "median", "mean", "category-information",
"item-information", "test-information"), ref = NULL, \dots)
}
\arguments{
\item{object}{a fitted model object whose item parameters should be used for
prediction.}
\item{newdata}{an optional (possibly named) vector of person parameters
used for prediction. If \code{NULL} (the default), the person parameters of
the subjects used to fit the model in \code{object} are used.}
\item{type}{character of length one which determines the type of
prediction (see details below).}
\item{ref}{arguments passed over to internal calls of \code{itempar} or
\code{threshpar}. Not used for models estimated via MML.}
\item{\dots}{further arguments which are currently not used.}
}
\details{
Depending on the value of \code{type} either probabilities, responses or
some form of information under the model specified in \code{object} are
returned:
If \code{type} is \code{"probability"}, the category response probabilities
are returned.
If \code{type} is \code{"cumprobability"}, the cumulated category response
probabilities are returned, i.e., \eqn{P(X_{ij} \geq k)} with \eqn{k}
corresponding to the categories of item \eqn{j}.
If \code{type} is \code{"mode"}, the most probable category response for a
given subject and item is returned.
If \code{type} is \code{"median"}, the first category \eqn{k} where
\eqn{P(X_{ij} = k) \geq 0.5} is returned.
If \code{type} is \code{"mean"}, the rounded expected category response,
i.e., \eqn{E(X_{ij}|\theta_{i})}, is returned.
If \code{type} is \code{"category-information"}, the item-category
information as suggested by Bock (1972) is returned.
If \code{type} is \code{"item-information"}, the item information as
suggested by Samejima (1974) is returned.
If \code{type} is \code{"test-information"}, the sum over the individual
item information values is returned.
}
\value{
A (possibly named) numeric matrix with rows corresponding to subjects and
columns corresponding to the whole test, the single items or categories. The
exact content depends on the value of \code{type} (see details above).
}
\references{
Bock RD (1972).
Estimating Item Parameters and Latent Ability When Responses Are Scored in
Two or More Nominal Categories.
\emph{Psychometrika}, \bold{37}(1), 29--51.
Samejima F (1974).
Normal Ogive Model on the Continuous Response Level in the Multidimensional
Latent Space.
\emph{Psychometrika}, \bold{39}(1), 111--121.
}
\seealso{
The help page of the generic function \code{\link{predict}} and other
predict methods (e.g., \code{\link{predict.lm}}, \code{\link{predict.glm}},
\dots)
}
\examples{
o <- options(digits = 4)
## load verbal aggression data
data("VerbalAggression", package = "psychotools")
## fit a partial credit model to first ten items
pcmod <- pcmodel(VerbalAggression$resp[, 1:10])
## predicted response probabilities for each subject and category (the default)
head(predict(pcmod), 3)
## predicted mode (most probable category) for certain subjects whose person
## parameters are given via argument "newdata"
predict(pcmod, type = "mode",
newdata = c("Sarah" = 1.2, "Michael" = 0.1, "Arnd" = -0.8))
## rounded expected category value for the same subjects
predict(pcmod, type = "mean",
newdata = c("Sarah" = 1.2, "Michael" = 0.1, "Arnd" = -0.8))
## in the Rasch model mode, mean and median are the same
raschmod <- raschmodel(VerbalAggression$resp2[, 1:10])
med <- predict(raschmod, type = "median")
mn <- predict(raschmod, type = "mean")
mod <- predict(raschmod, type = "mode")
head(med, 3)
all.equal(med, mn)
all.equal(mod, mn)
options(digits = o$digits)
}
\keyword{regression}
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