Bayesian Estimation and Model Selection in Group-Based Trajectory Models

Translational Abstract We develop a Bayesian group-based trajectory model (GBTM) for the estimation of single and dual trajectories, with normal, censored normal, binary, and ordered outcomes. The main advantage of our method compared to the frequentist GBTM is that we incorporate the Bayesian model averaging technique to substantially simplify and improve the model selection process. GBTMs require the researcher to specify a functional relationship between time and the outcome within each latent group. These relationships are generally polynomials with varying degrees in each group, but can also include additional covariates or other functions of time. When the number of groups is large, the model space can grow prohibitively complex, requiring a time-consuming brute-force search over potentially thousands of models. The approach developed in this article requires just one model fit and has the additional advantage of accounting for uncertainty in model selection. In addition, our Bayesian approach produces more accurate estimates when the sample size is small and makes the calculation of standard errors easier compared to the conventional GBTMs. We develop a Bayesian group-based trajectory model (GBTM) and extend it to incorporate dual trajectories and Bayesian model averaging for model selection. Our framework lends itself to many of the standard distributions used in GBTMs, including normal, censored normal, binary, and ordered outcomes. On the model selection front, GBTMs require the researcher to specify a functional relationship between time and the outcome within each latent group. These relationships are generally polynomials with varying degrees in each group, but can also include additional covariates or other functions of time. When the number of groups is large, the model space can grow prohibitively complex, requiring a time-consuming brute-force search over potentially thousands of models. The approach developed in this article requires just one model fit and has the additional advantage of accounting for uncertainty in model selection.