A Multilevel Mixture IRT Model With an Application to DIF

Abstract

Mixture item response theory models have been suggested as a potentially useful methodology for identifying latent groups formed along secondary, possibly nuisance dimensions. In this article, we describe a multilevel mixture item response theory (IRT) model (MMixIRTM) that allows for the possibility that this nuisance dimensionality may function differently at different levels. A MMixIRT model is described that enables simultaneous detection of differences in latent class composition at both examinee and school levels. The MMixIRTM can be viewed as a combination of an IRT model, an unrestricted latent class model, and a multilevel model. A Bayesian estimation of the MMixIRTM is described including analysis of label switching, use of priors, and model selection strategies. Results of a simulation study indicated that the generated parameters were recovered very well for the conditions considered. Use of MMixIRTM also was illustrated with the standardized mathematics test.