Fast Bayesian inference for modeling multivariate crash counts
This paper investigates the multivariate Poisson Lognormal modeling of counts for different types of crashes. This multivariate model can account for the overdispersion as well as positive and/or negative association between counts. Approximate Bayesian inference via the Integrated Nested Laplace Approximations significantly decreases computational time which makes it attractive for researchers. The models are developed for single vehicle, same direction and opposite direction crash types using three years (2009 2011) of crash data on Connecticut divided limited access highway segments. Annual average daily traffic, segment length, and road specific covariates (median type, shoulder width, area type, and on ramp indicator) are used as predictor variables. The results from the multivariate Poisson Lognormal model suggest that an increase in the annual average daily traffic, segment length, and shoulder width together with urban area type and presence of an on ramp are associated with in an increase in crashes. The median type covariate has a mixed effect for different median types on different type of crashes. The multivariate Poisson Lognormal model results are compared with the results obtained from two univariate regression models, univariate Poisson Lognormal and univariate negative binomial, with respect to model implications and precision on analysis of crash counts. The results show that the coefficient estimates of predictors have almost similar effects across all three crash type count models; however, standard errors in the multivariate Poisson Lognormal model are smaller than standard errors from other two univariate models in most cases. Results on posterior means for the correlation coefficients between crash types indicate that there are significant correlations exist between the crash count vectors, which indicate that ignoring such a correlation could possibly lead to incorrect variance estimation for the parameters. Results on predicted mean absolute error (PMAE) indicate that Bayesian multivariate Poisson Lognormal model provides up to 33% less prediction error compared to the univariate negative binomial model, although there are no significant difference of PMAE values between multivariate and univariate Poisson Lognormal models results. The analysis results demonstrated that the Bayesian multivariate Poisson Lognormal model provides correct estimates for parameters in predicting crash counts by accounting for correlations in the multivariate crash counts.