Mixture Distribution Rasch Models

Abstract

This chapter deals with the generalization of the Rasch model to a discrete mixture distribution model. Its basic assumption is that the Rasch model holds within subpopulations of individuals, but with different parameter values in each subgroup. These subpopulations are not defined by manifest indicators, rather they have to be identified by applying the model. Model equations are derived by conditioning out the class-specific ability parameters and introducing class-specific score probabilities as model parameters. The model can be used to test the fit of the ordinary Rasch model. By means of an example it is illustrated that this goodness-of-fit test can be more powerful for detecting model violations than the conditional likelihood ratio test by Andersen.