Bayesian multivariate Poisson-lognormal regression for crash prediction on rural two-lane highways

Roadway safety is a major concern for the general public and public agencies. Roadway crashes claim many lives and cause substantial economic losses each year. The situation is of particular interest on rural two-lane roadways, which experience significantly higher fatality rates than urban roads. There have been numerous efforts devoted to investigating crash occurrence as related to roadway design features, environmental and traffic conditions. However, most of the research has relied on univariate count models; that is, traffic crash counts at different levels of severity are estimated separately. The widely used univariate count data models ignore the following issues: (1) interdependence may exist between crash counts at different levels of severity for a specific segment of vii roadway, and (2) road geometric design features, road use, and environmental conditions may have distinct effects on crashes of different severity.;The objective of this research is to model correlated traffic crash counts simultaneously at different levels of severity using multivariate Poisson-lognormal (MVPLN) models. The MVPLN specification allows for a more general correlation structure as well as overdispersion. This approach addresses some questions that are difficult to answer by estimating them separately. With recent advancements in crash modeling and Bayesian statistics, the parameter estimation is done within the Bayesian paradigm, using a Gibbs Sampler and the Metropolis-Hastings (M-H) algorithms.;As an illustration, the MVPLN specification is empirically applied to investigate crash frequency by severity using crashes that occurred on Washington State rural two-lane highways in the Puget Sound region in 2002. Thanks to MCMC simulation techniques, the marginal posterior distributions of all parameters of interest were obtained. The estimation results from the MVPLN approach did show statistically significant correlations between crash counts at different levels of injury severity. The non-zero diagonal elements suggested an existence of overdispersion crash counts at all levels of severity. The results lend themselves to several recommendations for highway safety treatments and design policies. For example, wide lanes and shoulders are key for reducing crash frequencies, as are longer vertical curves. Moreover, using a cost-benefit approach and assumptions about travel speed changes, model results suggest that time savings from raising speed limits 10 mi/h (from 50 to 60 mi/h) may not be worth the added crash cost.