Multivariate Poisson-Lognormal Models for Jointly Modeling Crash Frequency by Severity

This paper introduces a new multivariate approach for jointly modeling crash counts by severity data based on Multivariate Poisson-Lognormal models. Although the crash frequency by severity data are multivariate in nature, they have often been analyzed by modeling each severity level separately without taking into account correlations that exist among different severity levels. The new Multivariate Poisson-Lognormal regression approach can cope with both overdispersion and a fully general correlation structure in the data as opposed to the recently suggested Multivariate Poisson regression approach that allows for neither over-dispersion nor a general correlation structure in the data. The new method is applied to the multivariate crash counts obtained from the intersections in California for 10 years. The results show promise towards the goal of obtaining more accurate estimates by accounting for correlations in the multivariate crash counts and over-dispersion.