Modeling traffic crash rates of road segments through a lognormal hurdle framework with flexible scale parameter

This study examines distributional characteristics of crash rates for road segments using observed accident data. The results indicate that the distribution of crash rates is mixed and right‐skewed, which motivates the consideration of non‐normal distributions. With the aid of Kolmogorov–Smirnov tests, kernel density plots, and Q–Q plots, the lognormal distribution is verified as an appropriate candidate for representing the positive domain of crash rates. Then, a lognormal hurdle model was developed and also compared with gamma and Weibull hurdle models. Further, the lognormal hurdle model was revised by allowing the scale parameter to vary with respect to explanatory variables. Such a modification enables the heterogeneous skewness of samples to be captured while enhancing the modeling flexibility. The proposed model was also compared with a Tobit model, an alternative approach that treats crash rates as censored data. Among all these models, the proposed lognormal hurdle model with flexible scale parameter presents the best modeling performance, and the analyses also reveal that several explanatory variables affect crash rates through not only the location parameter but also the scale parameter in the lognormal model. This study finally attempted to inspect crash rates through count models, and it discovered that the proposed hurdle model is superior because it is able to output the whole distribution form of crash rates, whereas the crash count model can only provide the expected value of crash rates, provided the exposure variable servers as an offset term in the link function of the mean parameter. Copyright © 2015 John Wiley & Sons, Ltd.