Implied probabilities of polytomous response functions for model-based prediction and comparison

Polytomous response models are typically motivated by assumptions about specific dichotomizations. We build on this by considering a broader range of dichotomizations. We first enumerate all possible dichotomizations for an outcome in a given number of categories. We then show that many of these dichotomizations lead to ``implied probabilities'' that have dramatically different forms when computed for different models. We finally illustrate how differences can be used to evaluate model fit. This consideration of the full range of possible dichotomizations and how the resulting implied probabilities may behave is of both conceptual and applied interest.