Rasch Mixture Models for DIF Detection: A Comparison of Old and New Score Specifications

Rasch mixture models can be a useful tool when checking the assumption of measurement invariance for a single Rasch model. They provide advantages compared to manifest DIF tests when the DIF groups are only weakly correlated with the manifest covariates available. Unlike in single Rasch models, estimation of Rasch mixture models is sensitive to the specification of the ability distribution even when the conditional maximum likelihood approach is used. It is demonstrated in a simulation study how differences in ability can influence the latent classes of a Rasch mixture model. If the aim is only DIF detection, it is not of interest to uncover such ability differences as one is only interested in a latent group structure regarding the item difficulties. To avoid any confounding effect of ability differences (or impact), a score distribution for the Rasch mixture model is introduced here which is restricted to be equal across latent classes. This causes the estimation of the Rasch mixture model to be independent of the ability distribution and thus restricts the mixture to be sensitive to latent structure in the item difficulties only. Its usefulness is demonstrated in a simulation study and its application is illustrated in a study of verbal aggression.