Statistical Approaches to Crash Frequency Modelling: An overview of Poisson and Negative Binomial Models

This paper provides an insight and comparison of the Poisson model and Poisson-Gamma model (also known as the Negative Binomial Model), the two most popular methodological approaches for crash frequency study. Despite the acceptance of Poisson model as one of the preliminary models, the model fails to understand over- and under-dispersed data and tends to produce biased result for small samples. The problem of the over-dispersed data is resolved in the Negative Binomial model. However, the model is unable to handle the data when it is under-dispersed and characterised by low sample-mean values and small sample sizes. A zero-inflated model has been introduced for both the Poisson and Negative Binomial model, to address the excess zero density. The zero inflated model is found to accommodate the significant number of zeros of a traditional count structure, which helps to model crash-free versus crash-prone zone of a roadway segment.