Modeling Zonal Traffic Accident Counts with the Regression under Zero-adjusted Inverse Gaussian Distribution

Abstract

Statistical analyses on crash counts/rates are important steps for transportation safety planning and evaluations of certain transportation facilities. Even there are various types of regression models in connecting between the response variable and characteristics of transportation facilities in relevance with considerations of different aspects of the frequency distribution of crashes, due to the complicated data generating process, past models still lack sufficient precision for accounting for several issues of crash counts especially the widely mentioned problem of excessive zero counts of accidents. Towards to this end, this study seeks to provide an alternative approach for predicating and inferring the response variable through a set of explanatory variables. As the crash rates fundamentally follow a mixed distribution such that non-zero probability will be associated with zero point in the domain, the zero-adjusted inverse Gaussian regression is introduced to overcome these issues as well as provide new thoughts in this field. Based on an observed dataset of accidents aggregated for the level of traffic analysis zone (TAZ), the regression model is developed and estimated using the principle of maximum likelihood estimation. The results discover that several attributes related to the zonal social economic, average traffic condition as well as roadway geometric design characteristics are statistically significant. Under such empirical analysis, the zero-adjusted inverse Gaussian distribution is appropriate to reflect the distributional characteristics of crash rates and provide a new direction of approaches in the field of crash data analyses.