Ordinal & Multinomial Models

Summary

Distinguishes nominal from ordinal categorical outcomes and warns against treating ordered categories as numeric, then builds the proportional odds model through cumulative logits at K minus one cutpoints with a shared slope assumption tested by the Brant and score tests. Develops the latent-variable interpretation under which predictors act on an underlying continuum that is coarsened into observed bins, illustrated with pain severity and self-rated health. Extends to multinomial logistic regression with a reference category for unordered outcomes like cancer type or insurance status, then closes with adjacent-category and continuation-ratio models for special structures.