Bayesian Hierarchical Poisson Regression Models: An Application to a Driving Study with Kinematic Events
Paul S. Albert, NICHD/NIH  Zhen Chen, NICHD/NIH  *Sung Duk Kim, NICHD/NIH  Bruce G. Simons-Morton, NICHD/NIH  Zhiwei Zhang, NICHD/NIH 

Keywords: Longitudinal Count Data, Over-dispersion, Random effect, Serial correlation, Teenage driving

In this paper, we propose a Bayesian hierarchical Poisson regression model with a latent process for the long and unequally spaced sequences of count data. The latent process consists of terms for a decaying serial correlation, heterogeneity, and over-dispersion. In addition, we propose to use nonparametric regression methodology to model the longitudinal trajectory to account for time varying patterns of the outcome. Our interest is on examining how the event rates change over time and understanding the effect of important covariates. We are also interested in understanding the between- and within-individual variation in the event rates over time. Analysis is carried out with a hierarchical Bayesian framework using reversible jump Markov chain Monte Carlo algorithms to accommodate the flexible mean structure. The deviance information criterion measure is used for guiding the choice of models. This methodology will be useful for other intensively collected longitudinal count data, where event rates are low and interest focuses on estimating the mean and variance structure of the process. We applied the proposed approach to the data from the Naturalistic Teenage Driving Study.