The Efficacy of Common Fit Indices for Enumerating Classes in Growth Mixture Models When Nested Data Structure Is Ignored

Abstract

Growth mixture model (GMM) is a flexible statistical technique for analyzing longitudinal data when there are unknown heterogeneous subpopulations with different growth trajectories. When individuals are nested within clusters, multilevel growth mixture model (MGMM) should be used to account for the clustering effect. A review of recent literature shows that a higher level of nesting was described in 43% of articles using GMM, none of which used MGMM to account for the clustered data. We conjecture that researchers sometimes ignore the higher level to reduce analytical complexity, but in other situations, ignoring the nesting is unavoidable. This Monte Carlo study investigated whether the correct number of classes can still be retrieved when a higher level of nesting in MGMM is ignored. We investigated six commonly used model selection indices: Akaike information criterion (AIC), consistent AIC (CAIC), Bayesian information criterion (BIC), sample size–adjusted BIC (SABIC), Vuong–Lo–Mendell–Rubin likelihood ratio test (VLMR), and adjusted Lo–Mendell–Rubin likelihood ratio test (ALMR). Results showed that accuracy of class enumeration decreased for all six indices when the higher level is ignored. BIC, CAIC, and SABIC were the most effective model selection indices under the misspecified model. BIC and CAIC were preferable when sample size was large and/or intraclass correlation (ICC) was small, whereas SABIC performed better when sample size was small and/or ICC was large. In addition, SABIC and VLMR/ALMR tended to overextract the number of classes when there are more than two subpopulations and the sample size is large.