A new multivariate approach is introduced for jointly modeling data on crash counts by severity on the basis of multivariate Poisson-lognormal models. Although the data on crash frequency by severity 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, which allows for neither overdispersion nor a general correlation structure in the data. The new method is applied to the multivariate crash counts obtained from intersections in California for 10 years. The results show promise toward the goal of obtaining more accurate estimates by accounting for correlations in the multivariate crash counts and overdispersion.

Park, E.S. and D. Lord. Multivariate Poisson-Lognormal Models for Jointly Modeling Crash Frequency by Severity. In Transportation Research Record: Journal of the Transportation Research Board, No. 2019, Transportation Research Board, National Research Council, Washington, D.C., 2007, pp. 1-6.