Comparison of Two Negative Binomial Regression Techniques in Developing Accident Prediction Models

Abstract

There are several regression techniques to develop accident prediction models. Model development and subsequently the results are affected by the choice of regression technique. The objective of this paper is to compare two types of regression techniques: the traditional negative binomial (TNB) and the modified negative binomial (MNB). The TNB approach assumes that the shape parameter of the negative binomial distribution is fixed for all locations, while the MNB approach assumes that this shape parameter varies with the location's characteristics. The difference between the two approaches in terms of their goodness of fit and the identification and ranking of accident-prone locations is investigated. The study makes use of a sample of accident, volume, and geometric data corresponding to 392 arterial segments in British Columbia, Canada. Both models appear to fit the data well. However, the MNB approach provides a statistically significant improvement in model fit over the TNB approach. A total of 100 locations were identified as accident-prone by both approaches. A comparison between the ranks showed a close agreement in the general trend of ranking between the two models. While the MNB approach appears to fit the data better than the TNB approach, there was little difference in the results of the identification and ranking of accident-prone locations. This is likely due to the nature of the application and the data set used. The difference in results will depend on the extent to which deviant sites exist in the data set.