Multivariate poisson lognormal modeling of crashes by type and severity on rural two lane highways

In an effort to improve traffic safety, there has been considerable interest in estimating crash prediction models and identifying factors contributing to crashes. To account for crash frequency variations among crash types and severities, crash prediction models have been estimated by type and severity. The univariate crash count models have been used by researchers to estimate crashes by crash type or severity, in which the crash counts by type or severity are assumed to be independent of one another and modelled separately. When considering crash types and severities simultaneously, this may neglect the potential correlations between crash counts due to the presence of shared unobserved factors across crash types or severities for a specific roadway intersection or segment, and might lead to biased parameter estimation and reduce model accuracy. The focus on this study is to estimate crashes by both crash type and crash severity using the Integrated Nested Laplace Approximation (INLA) Multivariate Poisson Lognormal (MVPLN) model, and identify the different effects of contributing factors on different crash type and severity counts on rural two-lane highways. The INLA MVPLN model can simultaneously model crash counts by crash type and crash severity by accounting for the potential correlations among them and significantly decreases the computational time compared with a fully Bayesian fitting of the MVPLN model using Markov Chain Monte Carlo (MCMC) method. This paper describes estimation of MVPLN models for three-way stop controlled (3ST) intersections, four-way stop controlled (4ST) intersections, four-way signalized (4SG) intersections, and roadway segments on rural two-lane highways. Annual Average Daily traffic (AADT) and variables describing roadway conditions (including presence of lighting, presence of left-turn/right-turn lane, lane width and shoulder width) were used as predictors. A Univariate Poisson Lognormal (UPLN) was estimated by crash type and severity for each highway facility, and their prediction results are compared with the MVPLN model based on the Average Predicted Mean Absolute Error (APMAE) statistic. A UPLN model for total crashes was also estimated to compare the coefficients of contributing factors with the models that estimate crashes by crash type and severity. The model coefficient estimates show that the signs of coefficients for presence of left-turn lane, presence of right-turn lane, land width and speed limit are different across crash type or severity counts, which suggest that estimating crashes by crash type or severity might be more helpful in identifying crash contributing factors. The standard errors of covariates in the MVPLN model are slightly lower than the UPLN model when the covariates are statistically significant, and the crash counts by crash type and severity are significantly correlated. The model prediction comparisons illustrate that the MVPLN model outperforms the UPLN model in prediction accuracy. Therefore, when predicting crash counts by crash type and crash severity for rural two-lane highways, the MVPLN model should be considered to avoid estimation error and to account for the potential correlations among crash type counts and crash severity counts.