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 populationheterogeneity over time. GMMs can be extended with covariates, predicting latent class (LC)membership, the within-class growth trajectories, or both. However current estimators aresensitive to misspecifications in complex models. We propose extending the two-step estimatorfor LC models to GMMs, which provides robust estimation against modelmisspecifications for simpler LC models.We conducted several simulation studies, comparing the performance of the proposedtwo-step estimator to the commonly-used one- and three-step estimators.Three different population models were considered, including covariates that predicted only theLC 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 morenuanced. Alternatively, when including covariate effects on the growth factors, the two-step, andthree-step estimators show consistent robustness against misspecifications with unbiased estimates across simulation conditions while tending to underestimate the standard error estimateswhile the one-step estimator is most sensitive to misspecifications.