Bayesian Multivariate Poisson Log-Normal Models for Crash Severity Modeling and Site Ranking.

Traditionally, univariate Poisson or Negative Binomial distributions havebeing used to model crash counts for different crash severities in highway safety analysis. However, these crash counts are multivariate in nature since unobservables or omitted variables are shared across severity levels. This research uses Full Bayes Multivariate Poisson Log-Normal models to estimate the expected crash frequency for different crash severity levels and then compares those estimates to the independent or Univariate PoissonLog-Normal estimates. Using data from rural central Pennsylvania, the multivariate model fits better than the univariate and has improved crash frequency estimate precision: the standard deviation of the crash frequency estimates was reduced 20% overall and 40 and 48% for fatal and major injury crashes, respectively. The covariances and correlations among crash severities are high (correlations range from 0.47 to 0.97) with highest valuesbetween contiguous severity levels. Explicitly considering this correlation between severity levels results in the improved precision of the expected number of crashes (i.e. ôborrowing strengthö from contiguous severity levels yields substantial improvements in precision). The multivariate estimates are next used with cost data from the Pennsylvania Department of Transportation (PennDOT) to develop the expected crash cost per segment (and excess expected cost) which is then used to rank sites for safety improvements. The multivariate-based top ranked segments have consistently higher costs and excess costs than the univariate estimates, a result of higher multivariate estimates of fatalities and major injuries (due to the random effects parameter). The higher estimated frequencies, in turn, produce different rankings for the multivariate and independent models. The finding of high correlation between contiguous severity levels is consistent with some of the literature, but additional tests of multivariate models are recommended. The improved precision has important implication for identification of sites with promise (SWiPs) as one formulation includes the standarddeviation of crash frequencies for similar sites as part of the assessment of SWiPs.