Comparing two maximum likelihood algorithms for mixture Rasch models

Abstract

The mixture Rasch model is gaining popularity as it allows items to perform differently across subpopulations and hence addresses the violation of the unidimensionality assumption with traditional Rasch models. This study focuses on comparing two common maximum likelihood methods for estimating such models using Monte Carlo simulations. The conditional maximum likelihood (CML) and joint maximum likelihood (JML) estimations, as implemented in three popular R packages are compared by evaluating parameter recovery and class accuracy. The results suggest that in general, CML is preferred in parameter recovery and JML is preferred in identifying the correct number of classes. A set of guidelines is also provided regarding how sample sizes, test lengths or actual class probabilities affect the accuracy of estimation and number of classes, as well as how different information criteria compare in achieving class accuracy. Specific issues regarding the performance of particular R packages are highlighted in the study as well.