C25. Proportional odds
What is the proportional-odds assumption in an ordinal regression model?
Worked answer (click to show)
Definitions/notation. For ordered categories 1,\ldots,K, use the upper-tail convention \gamma_k(x)=\mathbb{P}(Y\ge k\mid x) and \operatorname{logit}\gamma_k(x)=a_k+x^\top\beta, k=2,\ldots,K. The slope vector \beta is common to all cutpoints, so a unit change in x_j multiplies every cumulative odds by e^{\beta_j}, holding the other covariates fixed.