Bayesian Approach to Non-ignorable Missingness in Latent Growth Models

Abstract

Latent growth curve models (LGCMs) are becoming increasingly important among growth models because they can effectively capture individuals' latent growth trajectories and also explain the factors that influence such growth by analyzing the repeatedly measured manifest variables. However, with the increase in complexity of LGCMs, there is an increase in issues on model estimation. This research proposes a Bayesian approach to LGCMs to address the perennial problem of almost all longitudinal research, namely, missing data. First, different missingness models are formulated. We focus on non-ignorable missingness in this article. Specifically, these models include the latent intercept dependent missingness, the latent slope dependent missingness, and the potential outcome dependent missingness. To implement the model estimation, this study proposes a full Bayesian approach through data augmentation algorithm and Gibbs sampling procedure. Simulation studies are conducted and results show that the proposed method accurately recover model parameters and the mis-specified missingness may result in severely misleading conclusions. Finally, the implications of the approach and future research directions are discussed.