Model Selection Methods for Mixture Dichotomous IRT Models

Abstract

This study examines model selection indices for use with dichotomous mixture item response theory (IRT) models. Five indices are considered: Akaike's information coefficient (AIC), Bayesian information coefficient (BIC), deviance information coefficient (DIC), pseudo-Bayes factor (PsBF), and posterior predictive model checks (PPMC). The five indices provide somewhat different recommendations for a set of real data. Results from a simulation study indicate that BIC selects the correct (i.e., the generating) model well under most conditions simulated and for all three of the dichotomous mixture IRT models considered. PsBF is almost as effective. AIC and PPMC tend to select the more complex model under some conditions. DIC is least effective for this use.