A nested grouped random parameter negative binomial model for modeling segment-level crash counts.

In this study, a nested grouped random parameter negative binomial framework is proposed to model crash counts at the segment level, a three-level longitudinal framework. The proposed model accounts for correlations along county routes and over time and thus includes a time variable, the year index, to analyze crash counts. The model is applied to crashes on undivided two-lane arterial roads in Ohio from 2012 to 2017. The results present two variants of the model: one with varying intercepts and fixed slopes and the other with varying intercepts and slopes. Both variants have comparable interpretations concerning the fixed parameters, but the latter variant exhibits a significantly improved fit and provides additional information on the interpretations. The results show a significant quadratic relationship between the time variable and the crash count, indicating that, on average, the crash count of segments increases with a decreasing rate as time variable increases. Regarding random parameters, the findings show that 17% of segments within routes and 2% of routes exhibit crash counts that decrease at accelerating downward trend as time variable increases. The effect of the natural logarithm of the segment length varies significantly across different routes, with an increase in this value primarily leading to an increase in crashes. On the other hand, the effect of the total shoulder width also varies across routes, but unlike the former, an increase in this value generally results in a decrease in crashes. The proposed model shows high forecast accuracy for crash count prediction, making it a valuable tool for informed decision-making in safety improvement.