Mixture Rasch (MixRasch) models conventionally assume normal distributions for latent ability. Previous research has shown that the assumption of normality is often unmet in educational and psychological measurement. When normality is assumed, asymmetry in the actual latent ability distribution has been shown to result in extraction of spurious…

Covariates have been used in mixture IRT models to help explain why examinees are classed into different latent classes. Previous research has considered manifest variables as covariates in a mixture Rasch analysis for prediction of group membership. Latent covariates, however, are more likely to have higher correlations with the latent class…

The purpose of this study was to explore what may be contributing to differences in performance in mathematics on the Trends in International Mathematics and Science Study 2007. This was done by using a mixture item response theory modeling approach to first detect latent classes in the data and then to examine differences in performance on items…