A challenge in modeling crash frequency is an excess of sites with no crashes, few sites with a large number of crashes, or both. When there are excess zeros in the data or when the variance of the response is greater than the mean, the data are overdispersed. Recently, a few promising modeling techniques, such as the negative binomial–Lindley (NB-L) and negative binomial–generalized exponential (NB-GE) mixed distribution generalized linear models (GLMs), have been developed to handle count data overdispersion while keeping the core strength of the NB model. This study expanded the discussion on NB-L and NB-GE GLMs by focusing on their capability for modeling crash data as well as quantifying the safety impact of crash contributing factors. The mixed distribution models along with the conventional NB model were applied to a rural two-lane, two-way highway data set. The results showed that both NB-L and NB-GE GLMs could yield results similar to those of the NB model in addition to having mixed distribution probabilities to account for overdispersion. All modeling approaches successfully estimated the combined effects of lane width and shoulder width and identified the same combination with the optimal safety benefits. Both NB-L and NB-GE can be considered viable alternatives for the NB model if better goodness of fit is desired.
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