Bayesian analysis for the bivariate Poisson regression model: Applications to road safety countermeasures

Abstract

Abstract We consider a bivariate Poisson regression model to analyze discrete count datawhen two dependent variables are present. We estimate the regression coecients as-sociated with several safety countermeasures. We use Markov chain and Monte Carlotechniques to execute some computations. A simulation and real data analysis are per-formed to demonstrate model tting performances of the proposed model.Keywords: Accident prediction model, bivariate Poisson distribution, Gibbs sampler,Metropolis-Hastings algorithm, safety countermeasure. 1. Introduction Analysis of discrete count data has been done in various elds, including applied sciences,economics, and transportation engineering. Several models have been proposed in recentdecades to analyze these count data, especially trac crash data. Modeling these data beginswith the multiple linear regression model (MLR) in conjunction with normality assumptionsand homoscedasticity on error terms. The MLR is conceptually sound and computationallyfeasible in estimating regression coecients and explaining correlations between variables.However, these conditions are not compatible with characteristics of crash data. Jovanis andChang (1986) initially propose the Poisson regression model (PRM) to circumvent theselimitations. However, because the Poisson distribution has the same mean and variance, itdoes not often reect typical characteristics such as substantial overdispersion contained incount data. A great deal of work regarding model building for crash data has been basedon the negative binomial regression model (NBRM). See Persaud (1991, 1994), Persaud andDzbik (1993), Lord and Persaud (2004) for the related work based on the NBRM.