Bayesian Multivariate Poisson Lognormal Models for Crash Severity Modeling and Site Ranking

Abstract

Traditionally, highway safety analyses have used univariate Poisson or negative binomial distributions to model crash counts for different levels of crash severity. Because unobservables or omitted variables are shared across severity levels, however, crash counts are multivariate in nature. This research uses full Bayes multivariate Poisson lognormal models to estimate the expected crash frequency for different levels of crash severity and then compares those estimates to independent or univariate Poisson lognormal estimates. The multivariate Poisson log-normal model fits better than the univariate model and improves the precision in crash-frequency estimates. The covariances and correlations among crash severities are high (correlations range from 0.47 to 0.97), with the highest values found between contiguous severity levels. Considering this correlation between severity levels improves the precision of the expected number of crashes. The multivariate estimates are used with cost data from the Pennsylvania Department of Transportation to develop the expected crash cost (and excess expected cost) per segment, which is then used to rank sites for safety improvements. The multivariate-based top-ranked segments are found to have consistently higher costs and excess costs than the univariate estimates, which is due to higher multivariate estimates of fatalities and major injuries (due to the random effects parameter). These higher estimated frequencies, in turn, produce different rankings for the multivariate and independent models. The finding of a 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 implications for the identification of sites with promise (SWiPs), because one formulation includes the standard deviation of crash frequencies for similar sites as part of the assessment of SWiPs.

Full Bayesian evaluation of the safety effects of reducing the posted speed limit in urban residential area

“…The multivariate approach takes into account that crash data of different severities or types are correlated, while the univariate approach fails to do so. Empirical evidence showed that the multivariate method of modelling crash data improves a model's goodness of fit (Aguero-Valverde and Jovanis, 2009;El-Basyouny and Sayed, 2009a;Ma et al, 2008;Park and Lord, 2007;Tunaru, 2002). However, despite the conceptual understanding and empirical evidence supporting the superiority of the multivariate approach over the univariate, its application to before-after safety evaluations has not been very common.…”

On accommodating spatial dependence in bicycle and pedestrian injury counts by severity level

“…A second common approach is to use a mixing structure, in which one or more (typically) normally distributed random terms are introduced in the parameterization of the expected value of the discrete distribution (so that the expected value is not only a function of exogenous variables, but also includes one or more additive random terms within the exponentiation). If the same error term enters in the means of multiple count variables, this generates correlation (see Chib and Winkelmann, 2001, Lee et al, 2006, Park and Lord, 2007, Aguero-Valverde and Jovanis, 2009, and El-Basyouny and Sayed, 2009 for examples of such an approach). A similar, but slightly different mixing approach, has been used recently by Chiou and Fu (2012), who developed a multinomial-generalized Poisson model for the joint analysis of crash frequency and injury severity.…”

Predicting accident frequency at their severity levels and its application in site ranking using a two-stage mixed multivariate model

“…Several multivariate models have been employed such as multivariate spatial models (Song, 2004;Song et al, 2006), multivariate Poisson (MVP) models (Ma and Kockelman, 2006), and multivariate Poisson-lognormal (MVPLN) models (Park and Lord, 2007;Ma et al, 2008;Aguero-Valverde and Jovanis, 2009;El-Basyouny and Sayed, 2009). Compared to the univariate modelling approach, the multivariate models (i.e.…”