A negative binomial crash sum model for time invariant heterogeneity in panel crash data: Some insights

This paper presents a negative binomial crash sum model as an alternative for modeling time invariant heterogeneity in short panel crash data. Time invariant heterogeneity arising through multiple years of observation for each segment is viewed as a common unobserved effect at the segment level, and typically treated with panel models involving fixed or random effects. Random effects model unobserved heterogeneity through the error term, typically following a gamma or normal distribution. We take advantage of the fact that gamma heterogeneity in a multi-period Poisson count modeling framework is equivalent to a negative binomial distribution for a dependent variable which is the summation of crashes across years. The Poisson panel model referred to in this paper is the random effects Poisson gamma (REPG). In the REPG model, the dependent variable is an annual number of a specific crash type. The multi-year crash sum model is a negative binomial (NB) model that is based on three consecutive years of crash data (2005–2007). In the multi-year crash sum model, the dependent variable is the sum of crashes of a specific type for the three-year period. Four categories (in addition to total crashes) of crash types are considered in this study including rear end, sideswipe, fixed objects and all-other types. The empirical results show that when time effects are insignificant in short panels such as the one used in this study, the three-year crash sum model is a computationally simpler alternative to a panel model for modeling time invariant heterogeneity while imposing fewer data requirements such as annual measurements.