Developing a Random Parameters Negative Binomial-Lindley Model to analyze highly over-dispersed crash count data

The existence of preponderant zero crash sites and/or sites with large crash counts can present challenges during the statistical analysis of crash count data. Additionally, unobserved heterogeneity in crash data due to the absence of important variables could negatively impact the estimated model parameters. The traditional negative binomial (NB) model with fixed parameters might not adequately handle highly over-dispersed data or unobserved heterogeneity. Many research efforts that have involved the negative binomial-Lindley (NB-L) model or the random parameters negative binomial (RPNB) model, for example, have attempted to improve the inference of estimated coefficients by explicitly accounting for extra variation in crash data. The NB-L is a mixed modeling approach which provides flexibility to account for additional dispersion in data. The RP modeling approach accommodates the effect of unobserved variables by allowing the model parameters to vary from one observation to another. The following study proposes a combination of these models - the random parameters NB-L (RPNB-L) generalized linear model (GLM) - to account for underlying heterogeneity and address excess over-dispersion. The results show that the RPNB-L model not only provides a superior goodness-of-fit (GOF) with the sample data, but also offers a better understanding about the effects of potential contributing factors. The paper uses the Bayesian framework to provide a strategy for eliminating the potential for poor mixing in the Markov Chain Monte Carlo (MCMC) chains during the estimation of the RPNB-L model.