An efficient parallel sampling technique for Multivariate Poisson-Lognormal model: Analysis with two crash count datasets

Abstract

Our study investigates the Multivariate Poisson-lognormal (MVPLN) model that jointly models crash frequency and severity accounting for correlations. The ordinary univariate count models analyze crashes of different severity level separately ignoring the correlations among severity levels. The MVPLN model is capable to incorporate the general correlation structure and takes account of the over dispersion in the data that leads to a superior data fitting. But, the traditional estimation approach for MVPLN model is computationally expensive, which often limits the use of MVPLN model in practice. In this work, a parallel sampling scheme is introduced to improve the original Markov Chain Monte Carlo (MCMC) estimation approach of the MVPLN model, which significantly reduces the model estimation time. Two MVPLN models are developed using the pedestrian vehicle crash data collected in New York City from 2002 to 2006, and the highway-injury data from Washington State (5-year data from 1990 to 1994) The Deviance Information Criteria (DIC) is used to evaluate the model fitting. The estimation results show that the MVPLN models provide a superior fit over univariate Poisson-lognormal (PLN), univariate Poisson, and Negative Binomial models. Moreover, the correlations among the latent effects of different severity levels are found significant in both datasets that justifies the importance of jointly modeling crash frequency and severity accounting for correlations.