Robustness of Mixture IRT Models to Violations of Latent Normality

Abstract

Unidimensional item response theory (IRT) models assume that a single model applies to all people in the population. Mixture IRT models can be useful when subpopulations are suspected. The usual mixture IRT model is typically estimated assuming normally distributed latent ability. Research on normal finite mixture models suggests that latent classes potentially can be extracted even in the absence of population heterogeneity if the distribution of the data is nonnormal. Empirical evidence suggests, in fact, that test data may not always be normal. In this study, we examined the sensitivity of mixture IRT models to latent nonnormality. Single-class IRT data sets were generated using different ability distributions and then analyzed with mixture IRT models to determine the impact of these distributions on the extraction of latent classes. Preliminary 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 nonnormal latent ability distributions. Two popular information criterion indices, Akaike’s information criterion (AIC) and the Bayesian information criterion (BIC), were used to inform model selection. For most conditions, the performance of BIC index was better than the AIC for selection of the correct model.