Ordinal Logistic Regression (Proportional Odds Model)

It is the assumption that each predictor has the same effect on the cumulative log-odds at every cut point — the relationship is 'parallel' across all category thresholds. This is what lets the model estimate just one coefficient per predictor. The Brant test (test of parallel lines) checks it; a p-value below 0.05 signals a violation.

Ordinal regression uses the ordering of the categories and fits a single slope per predictor across shared cut points, making it more parsimonious. Multinomial logistic regression ignores any ordering and estimates separate effects for each category. When the proportional odds assumption fails, the multinomial model is the recommended alternative because it allows category-specific effects.

OLS treats the outcome as continuous with equally spaced values, but ordered categories rarely have equal spacing, so the assumption is hard to justify. Ordinal regression respects the ranking without imposing fixed gaps, which is why it is preferred for genuinely ordinal responses.

Exponentiate a coefficient to get an odds ratio: it is the multiplicative change in the odds of being in a higher outcome category for a one-unit increase in that predictor, holding the others fixed. An odds ratio above one means the predictor pushes outcomes toward higher categories.