Modelling crash frequencies at signalized intersections with a truncated count data model

Modelling crash frequencies provides comprehensive insights into the safety effects of explanatory variables contributing to crash occurrence, and thus a variety of modelling techniques have been employed depending on what variable is of interest. Since accident frequencies are count data which are discrete and non-negative integers, Poisson and negative binomial regression models are used to fit count data with the entire distribution of counts. However, some of the crash counts might be omitted from a sample due to the limits of observability, hence resulting in the truncation of the sample. Without accounting for truncation, the parameters estimated will be biased and inconsistent, and thus careful attention should be paid to the estimation of count data models when a truncation problem exists. This paper describes the development of a truncated Poisson model with zero-truncated count data and the demonstration of differences in estimation results by comparing the results from truncated and untruncated Poisson models with truncated data. The major difference in estimation results is that significant factors included in the both models are not exactly the same. However, it is found that there is no difference in the directions of associations with safety of the significant variables included in the both models.