Examination of Crash Variances Estimated by Poisson–Gamma and Conway–Maxwell–Poisson Models

The Poisson–gamma (negative binomial or NB) distribution is still the most common probabilistic distribution used by transportation safety analysts to model motor vehicle crashes. Recent studies have shown that the Conway–Maxwell–Poisson (COM–Poisson) distribution also is promising for developing crash prediction models. The objectives of this study were to investigate and compare the estimation of crash variance predicted by the COM–Poisson generalized linear model (GLM) and the traditional NB model. The comparison analysis was carried out with the most commonly employed functional forms, which linked crashes to the entering flows and other explanatory variables at intersections or on segments. To accomplish the objectives of the study, several NB and COM–Poisson GLMs (including flow-only models and models with several covariates) were developed and compared by using two data sets. The first data set contained crash data collected at signalized, four-legged intersections in Toronto, Ontario, Canada. The second data set included data collected on rural, four-lane, undivided highways in Texas. The results of this study show that the trend of crash variance prediction by COM–Poisson GLM is similar to that predicted by the NB model. The Spearman's rank correlation coefficients between the crash variance predicted by the COM–Poisson and the NB model confirmed that there was a perfect monotone increasing, and the values were highly correlated. This correlation means that a site characterized by a large variance would essentially be identified as such, whether the NB model or the COM–Poisson model was used.