A Two-Step Estimator for Growth Mixture Models with Covariates in the Presence of Direct Effects

Growth mixture models (GMMs) are popular approaches for modeling unobserved population heterogeneity over time. GMMs can be extended with covariates, predicting latent class (LC) membership, the within-class growth trajectories, or both. However, current estimators are sensitive to misspecifications in complex models. We propose extending the two-step estimator for LC models to GMMs, which provides robust estimation against model misspecifications (namely, ignored and overfitted the direct effects) for simpler LC models. We conducted several simulation studies, comparing the performance of the proposed two-step estimator to the commonly-used one- and three-step estimators. Three different population models were considered, including covariates that predicted only the LC membership (I), adding direct effects to the latent intercept (II), or to both growth factors (III). Results show that when predicting LC membership alone, all three estimators are unbiased when the measurement model is strong, with weak measurement model results being more nuanced. Alternatively, when including covariate effects on the growth factors, the two-step, and three-step estimators show consistent robustness against misspecifications with unbiased estimates across simulation conditions while tending to underestimate the standard error estimates while the one-step estimator is most sensitive to misspecifications.