Turner-Fairbank Highway Research Center

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Bayesian Multivariate Poisson-Lognormal Regression for Crash Prediction on Rural Two-Lane Highways.

Product Type

Other Publication


Ma, J., K.M. Kockelman, and P. Damien




Numerous efforts have been 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, which may neglect shared information in unobserved error terms, reduce efficiency in parameter estimates, and lead to potential biases in sample databases. This paper offers a multivariate Poisson-lognormal (MVPLN) specification that simultaneously models injuries by severity. 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 for crashes on Washington State rural two-lane highways. 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 overdispersion in 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 (say from 50 to 60 mi/h) may not be worth the added crash cost.

Link To Other Publication

Bayesian Multivariate Poisson-Lognormal Regression for Crash Prediction on Rural Two-Lane Highways.
(search on Paper #07-0664)


Bayesian inference
Bayes' theorem
Gibbs sampler
highway safety
Metropolis-Hastings algorithm
Markov chain Monte Carlo (MCMC) simulation
multivariate Poisson-lognormal regression

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