The proportional-odds (cumulative-link) model predicts an ordered categorical outcome, fitting one slope per predictor and k − 1 cumulative cutpoints.
When the outcome is ordered (Likert, severity grade, stage I–IV), ordinal logistic exploits the ordering by modelling P(Y ≤ j) for each cumulative split j. Each cut has its own intercept; the slopes β are shared across cuts under the proportional-odds (PO) assumption.
PO is the key assumption: the effect of each predictor on the log-odds is the same at every cut point. The Brant test checks this. If PO is violated, the marginal-by-marginal multinomial logistic is a fallback (more parameters, no ordering constraint), or a partial-proportional-odds model.
Treating ordered data as unordered (multinomial) loses information; treating it as continuous (linear regression of integer codes) imposes an even stronger assumption (equal spacing) that ordinal logistic avoids.
Ordered categorical outcome + predictors.
Slope coefficients (shared across cuts), k − 1 intercept cutpoints, OR + CI, Brant test of the PO assumption.
exp(β) is the cumulative OR: a one-unit increase in x_k multiplies the odds of being in category ≤ j vs > j by exp(β_k), for any cut j.
Brant p < 0.05 for any predictor ⇒ PO violated for that predictor. Consider relaxing PO for that predictor only (partial PO model) or switching to multinomial.