The Poisson Inverse Gaussian (PIG) Generalized Linear Regression Model for Analyzing Motor Vehicle Crash Data

This paper documents the application of the Poisson Inverse Gaussian (PIG) regression model for modeling motor vehicle crash data. The PIG distribution, which mixes the Poisson distribution and Inverse Gaussian distribution, has the potential for modeling highly dispersed count data due to the flexibility of Inverse Gaussian distribution. The objectives of this paper were to evaluate the application of PIG regression model for analyzing motor vehicle crash data and compare the results with Negative binomial (NB) model, especially when varying dispersion parameter is introduced. To accomplish the objectives, both NB and PIG models were developed with fixed and varying dispersion parameters and compared using two datasets. The Texas undivided rural highway segments dataset includes five years of crash data, while the divided highway segments Washington dataset includes four years. The results of this study show that PIG models perform better than the NB models in terms of goodness-of-fit (GOF) statistics. Moreover, PIG models can perform similarly well in capturing the variance of crash to the NB models. Lastly, PIG models demonstrate almost the same prediction performance compared to NB models. Considering the simple form of PIG model and its easiness of applications, PIG model could be used as a potential alternative to the NB model for analyzing crash data.