A note on generalized ordered outcome models

• Equivalence between Generalized Ordered Logit (GOL) model and Partial Proportional Odds Logit (PPO) model is shown.
• Model estimation and interpretation guidelines for GOL and PPO models.
• Mixed Partial Proportional Odds model is developed.
• Computational difficulties that may arise in estimating mixed versions are discussed.

While there is growing application of generalized ordered outcome model variants (widely known as Generalized Ordered Logit (GOL) model and Partial Proportional Odds Logit (PPO) model) in crash injury severity analysis, there are several aspects of these approaches that are not well documented in extant safety literature. The current research note presents the relationship between these two variants of generalized ordered outcome models and elaborates on model interpretation issues. While these variants arise from different mathematical approaches employed to enhance the traditional ordered outcome model, we establish that these are mathematically identical. We also discuss how one can facilitate estimation and interpretation while building on the ordered outcome model estimates – a useful process for practitioners considering upgrading their existing traditional ordered logit/probit injury severity models. Finally, the note presents the differences within GOL and PPO model frameworks, for accommodating the effect of unobserved heterogeneity, referred to as Mixed Generalized Ordered Logit (MGOL) and Mixed Partial Proportional Odds Logit (MPPO) models while also discussing the computational difficulties that may arise in estimating these models.