Proportional-odds model ($\mathrm{logit}P(Y\le l\mid x)={\theta }_l-x^T\beta$)

For ordered response categories, ordered thresholds ${\theta }_l$ and a common slope vector define this cumulative logistic regression. Increasing $x^T\beta$ shifts probability toward higher categories. A covariate contrast multiplies all corresponding cumulative odds by the same factor. This model is not a canonical baseline-category multinomial logistic regression, so the latter's design-weighted count margins are not generally sufficient for it.