The Effect of Model Misspecification on Growth Mixture Model Class Enumeration

Multiple criteria have been proposed to aid in deciding how many latent classes to extract in growth mixture models; however, studies are just beginning to investigate the performance of these criteria under non-ideal conditions. We review these previous studies and conduct a simulation study to address the performance of fit criteria under two previously uninvestigated assumption violations: (1) linearity of covariates and (2) proper specification of the growth factor covariance matrix. Results show that, provided that estimation is carried out with a large number of random starts and final stage optimizations, BIC and the bootstrap likelihood ratio test perform exceedingly well at identifying whether the data are homogenous or whether latent classes may be present, even with misspecifications present. Results were far less favorable when software default estimation choices were selected. We discuss implications to empirical studies and speculate on the relation between estimation choices and fit criteria perform.