Bayesian Hierarchical Poisson Regression Models: An Application to a Driving Study With Kinematic Events

Abstract

Although there is evidence that teenagers are at a high risk of crashes in the early months after licensure, the driving behavior of these teenagers is not well understood. The Naturalistic Teenage Driving Study (NTDS) is the first U.S. study to document continuous driving performance of newly licensed teenagers during their first 18 months of licensure. Counts of kinematic events such as the number of rapid accelerations are available for each trip, and their incidence rates represent different aspects of driving behavior. We propose a hierarchical Poisson regression model incorporating overdispersion, heterogeneity, and serial correlation as well as a semiparametric mean structure. Analysis of the NTDS data is carried out with a hierarchical Bayesian framework using reversible jump Markov chain Monte Carlo algorithms to accommodate the flexible mean structure. We show that driving with a passenger and night driving decrease kinematic events, while having risky friends increases these events. Further the within-subject variation in these events is comparable to the between-subject variation. 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. Supplementary materials for this article are available online.

KEY WORDS:

• Longitudinal count data
• Over-dispersion
• Random effect
• Serial correlation
• Teenage driving

Acknowledgments

The authors thank the Editor, the Associate Editor, and two referees for their helpful comments and suggestions that have improved the article. This research was supported by the intramural research program of the National Institutes of Health, Eunice Kennedy Shriver National Institute of Child Health and Human Development (contract # N01-HD-5-3405).

Notes

*Range of the subject-specific means across the 42 subjects.