Bayesian Estimation and Model Selection in Group-Based Trajectory Models

Abstract

This paper makes three contributions to the literature on group-based trajectory models. First, although a small literature exists applying Bayesian methods to single trajectory models, their expositions are targeted toward biostatisticians. We bridge this gap by developing a model for normally distributed outcomes in congruence with standard social science references in order to facilitate more widespread adoption. Second, we extend this model to the first Bayesian dual trajectory model with a joint distribution specified over dual group memberships. Finally, we develop a Bayesian model averaging technique for efficient selection of the trajectories' functional forms. Model averaging provides additional flexibility in specifying trajectory shapes and saves researchers time by eliminating the need to fit functional forms separately and compare model fits. We also argue that the exact finite sample inference for model parameters and arbitrary functions thereof inherent in our Bayesian approach provides a compelling advantage over maximum likelihood methods.