How Well Does Growth Mixture Modeling Identify Heterogeneous Growth Trajectories? A Simulation Study Examining GMM's Performance Characteristics

Abstract

Growth mixture modeling (GMM) has become a more popular statistical method for modeling population heterogeneity in longitudinal data, but the performance characteristics of GMM enumeration indexes in correctly identifying heterogeneous growth trajectories are largely unknown. Few empirical studies have addressed this issue. This study considered both homogeneous (a k = 1 growth trajectory) and heterogeneous (k = 3 different but unobserved growth trajectories) situations, and examined the performance of GMM in correctly identifying the latent trajectories in sample data. Four design conditions were manipulated: (a) sample size, (b) latent trajectory class proportions, (c) shapes of latent growth trajectories, and (d) degree of separation among latent growth trajectories. The findings suggest that, for k = 1 condition (1 homogenous growth trajectory), GMM's performance is reasonable in correctly identifying 1 latent growth trajectory (cf. Type I error control). However, for the k = 3 conditions (3 heterogeneous latent growth trajectories), GMM's general performance is very questionable (cf. Type II error). Different enumeration indexes varied considerably in their respective performances. Comparing the current results with previous GMM studies, the limitations of this study and future GMM enumeration research avenues are all discussed.

Keywords:

• entropy
• enumeration indexes
• growth mixture modeling
• information criteria

Notes

^al and m are undefined if k = 1.

^aBold entries in parentheses represent correct data generation model identification percentages under unequal k-trajectory proportions.