Proportional-odds model (source code)

= Proportional-odds model
{title2=$\operatorname{logit}P(Y\le l\mid x)=\theta_l-x^T\beta$}

= Proportional odds
{synonym}

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.