Partial proportional odds model for analyzing pedestrian crashes, threshold heterogeneity by scale and proportional odds factor

Despite low traffic in Wyoming, pedestrian crash severity accounts for a high number of fatalities in the state. Thus this study was conducted to highlights factors contributing to those crashes. The results highlighted that drivers under influence, type of vehicle, location of crashes, estimated speed of vehicles, driving over the recommended speed are some of factors contributing to the severity of crashes. In this study, we used proportional odds model which assumes that the impact of each attribute is consistent or proportional across various threshold values. However, it has been argued that this assumption might be unrealistic, especially at the presence of extreme values. Thus, the assumption was relaxed in this study by shifting the thresholds based on some explanatory attributes, or proportional odds effects. In addition, we accounted for the spread rate, or scale, of the model's latent distribution of pedestrian crashes. The results highlighted that the partial proportional odds model through proportional odds factor and scale effects result in a significant improvement in model fit compared with the standard proportional odds model. Comparisons were also made across standard normal, simple partial ordinal model, and partial ordinal accounting for scale heterogeneity. In addition, various potential threshold structures such as symmetric and flexible were considered, but similar goodness of fits were observed across all those models. Extensive discussion has been made regarding the formulation of the implemented methodology, and its implications.