Bayesian Methods and Model Selection for Latent Growth Curve Models with Missing Data

With an increase in complexity of latent growth curve models (LGCMs), comes an increase in problems estimating the models. This research first proposes new growth models to address the perennial problems of almost all longitudinal research, namely, missing data. Different non-ignorable missingness models are formulated. These models include the latent coefficient (intercept or slope)-dependent missingness, in which the missing data rates vary across different latent individual initial levels or slopes; and the potential outcome-dependent missingness, in which the missing data rates on each occasion depend on potential outcomes. Second, this study proposes a full Bayesian approach to estimate the proposed LGCMs with non-ignorable missing data through data augmentation algorithm and Gibbs sampling procedure. And third, model selecting criteria are proposed in a Bayesian context to identify the best-fit model.Simulation studies were conducted. Conclusions include the proposed method can accurately recover model parameters, the mis-specified missingness may result in severely misleading conclusions, and almost all the model selection criteria can correctly identify the true model with high certainty. The application of the model and the method are illustrated with a longitudinal data set showing growth in mathematical ability. Finally, related implications of the approach and future research directions are discussed.

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