Application of generalized link functions in developing accident prediction models

The Bayesian Poisson–Gamma hierarchy, leading to the negative binomial distribution, has been the standard practice in developing accident prediction models. To linearize the relationship connecting the mean of the negative binomial distribution to relevant covariates, a canonical log link has traditionally been used. Typically, little information is available regarding the choice of a particular link. To avoid link misspecification, it is proposed to nest the canonical log link model within a generalized link family and subsequently use the full Bayes method for parameter estimation, performance evaluation and inference. The proposed approach was applied to a sample of accident and traffic volume data corresponding to 99 intersections in the city of Edmonton, Alberta. The results showed that both the generalized link model and the traditional canonical link model provided adequate fit to the data. However, the Bayes factor provided a clear statistical support for the use of the generalized link approach. A procedure for link validation is also described. It allows the users (e.g., road authorities) to consider the changes in predicted accidents that will result if a generalized link is used instead of a canonical link. If a certain maximal change is tolerated, the canonical link can be used to analyze the data; otherwise the generalized link is worth the extra efforts and should be adopted. When compared with the traditional approach, the generalized link model was found to predict a lower number of accidents whenever there is a heavy traffic at the major approach, especially if combined with light flow on the minor approach. The paper concludes by identifying out areas for further research.