Jointly modeling latent trajectories and a subsequent outcome variable: A Bayesian approach.

Abstract

The general class of models described in this dissertation was motivated by research questions that come from two linked longitudinal datasets. We are interested in whether the growth and decline in young adolescents' various problem behaviors from 5<super>th</super> to 10<super>th</super> grade explain subsequent involvement in serious motor vehicle offenses. However, trajectories of problem behaviors are not directly observed and require estimation from data at several discrete time points. Thus, in stage 1 of the model, latent trajectories are summarized by a few latent trajectory variables. For example, in subject-specific polynomial models, the coefficients for linear or quadratic terms are the latent trajectory variables. In longitudinal analyses, the objective is often to treat these latent trajectory variables as outcome variables in order to investigate both systematic and random variation. However, the research questions addressed here require using latent trajectory variables as predictors of a subsequent outcome in stage 2 of the model. In this dissertation, we propose a general class of models that treats latent trajectory variables summarized in stage 1 of the model as predictors of a subsequent outcome. This general class of models allows for a variety of trajectory shapes and can incorporate outcomes that come from the exponential family of distributions. Furthermore, the model can be extended to multivariate latent trajectories as predictors of a future outcome. Because currently used methods do not provide flexibility, we propose a fully Bayesian approach to fit this model. Details on the implementation of the Bayesian approach are provided in the dissertation. We apply the Bayesian approach and two competing approaches to study trajectories of adolescent alcohol use as predictors of motor vehicle offenses incurred during later adolescence. Results from a simulation study done to evaluate the performance of the Bayesian method are also reported. To illustrate the flexibility of the Bayesian approach, we apply the Bayesian approach to examine a number of research questions that require the modeling of multivariate latent trajectories.