A mixed grouped response ordered logit count model framework

The study proposes and estimates a new econometric framework for analysing crash count events labeled as the Mixed Grouped Response Ordered Logit Count model. The proposed framework relates the crash count propensity to the observed counts directly while also accommodating for heteroscedasticity and unobserved heterogeneity. The proposed model is demonstrated by using Traffic Analysis Zone level bicycle crash count data for the Island of Montreal. The model framework employs a comprehensive set of exogenous variables − accessibility measures, exposure measures, built environment, road network characteristics, sociodemographic and socioeconomic characteristics. Further, we also compare the performance of the proposed model to the most commonly used negative binomial model and the generalized ordered logit count model by generating a comprehensive set of measures to evaluate model performance and data fit. The alternative modeling approaches considered for the comparison exercise include: (1) negative binomial model without parameterized overdispersion, (2) negative binomial model with parameterized overdispersion, and (3) mixed negative binomial model with parameterized overdispersion, (4) generalized ordered logit count model and (5) mixed generalized ordered logit count model, (6) grouped response ordered logit count model without parameterized variance, (7) grouped response ordered logit count model with parameterized variance and (8) mixed grouped response ordered logit count model with parameterized variance. The comparison exercise clearly highlights that the proposed mixed grouped response ordered logit count model with parameterized variance relative to the mixed negative binomial model with parameterized overdispersion offers either equivalent or superior data fit across various measures in the current study context. The fit measures for comparing the predictive performance also indicate that the proposed grouped response model offers better predictions both at the aggregate and disaggregate levels. Overall, the results from this comparison exercise points out that the grouped response ordered logit count model is a promising alternate econometric framework for examining crash count events.