Does model misspecification lead to spurious latent classes? An evaluation of model comparison indices

Abstract

This study examined whether model misspecification leads to the extraction of spurious latent classes in the mixture Rasch model, and assessed the performance of model-fit statistics in selecting the number of latent classes in examinee population. A simulation was conducted to investigate whether disregarding variant item discrimination, as well as guessing and slipping parameters, contributes to the over-extraction of latent classes in the mixture Rasch model. Data were generated under the one-class four-parameter logistic item response theory (IRT) model and were estimated by the mixture Rasch model. This study assessed how model misspecification influences the extraction of spurious latent classes under varied sample sizes and test lengths. An empirical application was also conducted with two real data sets. The first was extracted from the PIRLS 2006 assessment, which was originally calibrated using the two-parameter or three-parameter logistic IRT model. The second data set was extracted from the 2005 Monitoring the Future national survey, which has been demonstrated to fit a four-parameter logistic IRT model well. Findings from the current study suggest BIC as a suitable index for identifying the number of latent classes. If BIC is used, less concern exists over the extraction of spurious latent classes resulting from model misspecification.