R/LRT.R

In pcIRT: IRT Models for Polytomous and Continuous Item Responses

#' Computes Andersen's Likelihood Ratio Test for the multidimensional
#' polytomous Rasch model
#' 
#' Andersen's Likelihood Ratio Test is a model test for Rasch models (based on
#' CML estimation) and splits the data set into subsamples to test the person
#' homogeneity
#' 
#' The default split criterion \code{"score"} computes the raw score of every
#' person according to the category values in the data set. The sample is split
#' by the median of this raw score.
#' 
#' @aliases LRT summary.aLR print.aLR LRT.MPRM LRT.DRM
#' @param object Object of class \code{MPRM} or \code{DRM} or \code{aLR}
#' @param splitcrit Vector or the character vector \code{"score"} to define the
#' split criterion. The default split criterion \code{"score"} splits the
#' sample according to the median of the raw score. Vector can be numeric,
#' factor or character. (see details)
#' @return \item{emp_Chi2}{\eqn{\chi^2} distributed value of the Likelihood
#' Ratio test} \item{df}{degrees of freedom of the test statistic}
#' \item{pval}{p value of the test statistic} \item{itempar}{estimated item
#' parameters for each subsample} \item{item_se}{estimated standard errors for
#' the item parameters for each subsample}
#' @author Christine Hohensinn
#' @seealso \code{\link{MPRM}} \code{\link{dLRT}}
#' @references Andersen, E. B. (1973). A goodness of fit test for the Rasch
#' model. Psychometrika, 38, 123- 140.
#' 
#' Fischer, G. H. (1974). Einfuehrung in die Theorie psychologischer Tests
#' [Introduction to test theory]. Bern: Huber.
#' 
#' @rdname lrt
#' 
#' @examples
#' 
#' #simulate data set
#' simdat <- simMPRM(rbind(matrix(c(-1.5,0.5,0.5,1,0.8,-0.3, 0.2,-1.2), 
#'                   ncol=4),0), 500)
#' 
#' #estimate MPRM item parameters
#' res_mprm <- MPRM(simdat$datmat)
#' 
#' #compute Andersen's Likelihood Ratio test
#' res_lrt <- LRT(res_mprm)
#' summary(res_lrt)
#'   
#' @export
LRT <-
  function(object,...)UseMethod("LRT")