Latent profile analysis with nonnormal mixtures: A Monte Carlo examination of model selection using fit indices

Abstract

The performances of fit indices used for model selection in cross-sectional mixture modeling with nonnormally distributed indicators were examined in two studies using Monte Carlo methods. Simulation conditions were selected to mirror conditions found in educational and psychological research. The design factors under investigation were: indicator distribution, number of indicators, sample size, and profile prevalence. All models contained five, ten, or 15 continuous indicators with varying departures from normality. The fit indices examined were Akaike’s information criterion (AIC), corrected Akaike’s information criterion (AICc), consistent Akaike’s information criterion (CAIC), Bayesian information criterion (BIC), sample size-adjusted Bayesian information criterion (SSBIC), Draper’s information criterion (DIC), integrated classification likelihood criterion with Bayesian-type approximation (ICL), entropy, and the adjusted Lo–Mendell–Rubin likelihood ratio test (LMR). In the first study, nonnormally distributed data were used to estimate the mixture models. No fit index uniformly identified the simulated number of profiles using nonnormal indicators. The fit indices that tended to identify the simulated number of profiles more frequently than others were BIC, SSBIC, CAIC, and LMR although the condition(s) in which this was observed varied. In the second study, the raw data were transformed using van der Waerden quantile normal scores. Despite deflating the indicator variances, the use of normal scores increased the frequency with which fit indices identified the simulated number of profiles across most conditions.