In practice, crash and injury counts are modeled by using a single equation or a series of independently specified equations, which may neglect shared information in unobserved error terms, reduce efficiency in parameter estimates, and lead to biases in sample databases. This paper offers a multivariate Poisson specification that simultaneously models injuries by severity. Parameter estimation is performed within the Bayesian paradigm with a Gibbs sampler for crashes on Washington State highways. Parameter estimates and goodness-of-fit measures are compared with a series of independent Poisson equations, and a costbenefit analysis of a 10-mph speed limit change is provided as an example application.

Ma, J. and K.M. Kockelman. Bayesian Multivariate Poisson Regression for Models of Injury Count, by Severity. In Transportation Research Record: Journal of the Transportation Research Board, No. 1950, Transportation Research Board, National Research Council, Washington, D.C., 2006, pp. 24-34