psychotools (version 0.4-0)

personpar: Extract Person Parameters of Item Response Models

Description

A class and generic function for representing and estimating the person parameters of a given item response model.

Usage

personpar(object, ...)
"personpar"(object, ref = NULL, vcov = TRUE, interval = NULL, tol = 1e-8, ...)
"personpar"(object, ref = NULL, vcov = TRUE, interval = NULL, tol = 1e-8, ...)
"personpar"(object, ref = NULL, vcov = TRUE, interval = NULL, tol = 1e-8, ...)

Arguments

object

a fitted model object for which person parameters should be estimated.

ref

a vector of labels or position indices of item parameters or a contrast matrix which should be used as restriction/for normalization. If NULL (the default), all items are used (sum zero restriction). This argument will passed over to internal calls of itempar.

vcov

logical. Should a covariance matrix be estimated (based on the joint log-likelihood) for the person parameter estimates? See also details below.

interval

numeric vector of length two, specifying an interval for uniroot to search for the person parameter estimates.

tol

numeric tolerance passed to uniroot.

...

further arguments which are passed to optim in case of vcov = TRUE.

Value

A named vector with estimated person parmeters of class personpar and additional attributes "model" (the model name), and "vcov" (the covariance matrix of the estimates if vcov = TRUE or an NA-matrix otherwise).

Details

personpar is both, a class to represent person parameters of item response models as well as a generic function. The generic function can be used to estimate the person parameters of a given item response model.

Person parameters are estimated via uniroot() with the estimation equations given by Hoijtink & Boomsma (1995) as well as Andersen (1995). This approach is fast and estimates for all possible raw scores are available. If the covariance matrix of the estimated person parameters is requested (vcov = TRUE), an additional call of optim is necessary to obtain the Hessian. With this approach, person parameters are available only for observed raw scores.

For objects of class personpar, several methods to standard generic functions exist: print, coef, vcov. coef and vcov can be used to extract the person parameters and covariance matrix without additional attributes. Based on this Wald tests or confidence intervals can be easily computed, e.g., via confint.

References

Erling B. Andersen. Polytomous Rasch Models and Their Estimation. In Gerhard H. Fischer, and Ivo W. Molenaar, (1995). Rasch Models: Foundations, Recent Developments, and Applications.

Herbert Hoijtink, and Anne Boomsma. On Person Parameter Estimation in the Dichotomous Rasch Model. In Gerhard H. Fischer, and Ivo W. Molenaar, (1995). Rasch Models: Foundations, Recent Developments, and Applications.

See Also

itempar, threshpar, discrpar

Examples

o <- options(digits = 4)

## load verbal aggression data
data("VerbalAggression", package = "psychotools")

## fit a Rasch model to dichotomized verbal aggression data and
ram <- raschmodel(VerbalAggression$resp2)

## extract person parameters
rap <- personpar(ram)
rap

## extract variance-covariance matrix and standard errors
vc <- vcov(rap)
sqrt(diag(vc))

## Wald confidence intervals
confint(rap)

## person parameters for RSM/PCM fitted to original polytomous data
rsm <- rsmodel(VerbalAggression$resp)
pcm <- pcmodel(VerbalAggression$resp)
cbind(personpar(rsm, vcov = FALSE), personpar(pcm, vcov = FALSE))

options(digits = o$digits)