Robustness of mixture IRT models to violations of latent normality
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Unlike the traditional item response theory (IRT) models, mixture IRT (MixIRT) models can be useful when subpopulations are suspected. The usual MixIRT model is typically estimated assuming normally distributed latent ability. Research on finite mixture models suggests that spurious latent classes can be extracted even in the absence of population heterogeneity if the distribution of the data is non-normal. In this study, we conducted two simulation studies and an empirical study to examine the robustness of MixIRT models to violations of latent normality. Single class IRT data sets were generated using different ability distributions and then analyzed with MixIRT models to determine the impact of these distributions on the extraction of latent classes. Results suggest that estimation of mixed Rasch models resulted in spurious latent class problems in the data when distributions were bimodal and uniform. Mixture 2PL and mixture 3PL IRT models were found to be more robust to latent non-normality. Akaike's information criterion (AIC) and the Bayesian information criterion (BIC), were used to inform model selection. For most conditions, the performance of the BIC index was better than the AIC index for selection of the correct model.