Adequacy of negative binomial models for managing safety on rural local roads

Count models, such as negative binomial regression, are well-established statistical methods for analyzing road safety. Although count models are widely used for arterial roads, their application to rural local roads is sparse, partly due to the concern of possible estimation bias caused by low crash counts. This paper revisits the matter to further evaluate the suitability of negative binomial models for rural local roads with low crash frequencies, comparing the performance of the model to probabilistic regression (ordered probit) proposed in the past. The negative binomial model was estimated to predict crashes for rural local intersections and compared to predictions obtained from the ordered probit model. Bivariate versions of both models were applied to improve model efficiency by incorporating correlation between two severity outcomes, fatal/injury (FI) and property damage only (PDO) crashes. The estimated models included several significant variables with intuitive signs. These results are discussed in the paper to support the claim that both models are adequate. Furthermore, the cumulative sums of the model-predicted and observed crashes conditioned on the estimated effects were compared to detect any systematic bias in the results. Although both models showed similar performance and no obvious biases could be detected, the negative binomial model seemed to behave slightly better than the ordered probit model, demonstrating the model's suitability in the analyzed case. The results point to the possibility of applying the Highway Safety Manual methodology to lower-volume county roads with focus shifted from individual high-crash locations to safety-deficient road features present at multiple locations.