The Impact of Non-Normality on Extraction of Spurious Latent Classes in Mixture IRT Models.

Abstract

Unidimensional, item response theory (IRT) models assume a single homogeneous population. Mixture IRT (MixIRT) models can be useful when subpopulations are suspected. The usual MixIRT model is typically estimated assuming a 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 non-normal. In this study, the authors examined the sensitivity of MixIRT models to latent non-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 two-parameter logistic (2PL) and mixture three-parameter logistic (3PL) IRT models were found to be more robust to latent non-normality.