Empirical evaluation of fully Bayesian information criteria for mixture IRT models using NUTS

Abstract

This study is to evaluate the performance of fully Bayesian information criteria, namely, LOO, WAIC and WBIC in terms of the accuracy in determining the number of latent classes of a mixture IRT model while comparing it to the conventional model via non-random walk MCMC algorithms and to further compare their performance with conventional information criteria including AIC, BIC, CAIC, SABIC, and DIC. Monte Carlo simulations were carried out to evaluate these criteria under different situations. The results indicate that AIC, BIC, and their related CAIC and SABIC tend to select the simpler model and are not recommended when the actual data involve multiple latent classes. For the three fully Bayesian measures, WBIC can be used for detecting the number of latent classes for tests with at least 30 items, while WAIC and LOO are suggested to be used together with their effective number of parameters in choosing the correct number of latent classes.