Which set of models are used to model ordinal data?

• A. Binary logistic regression
• B. Proportional hazards model
• C. Proportional odds, adjacent-category and continuation-ratio
• D. Linear regression

Answer: (C)

Ordinal outcomes have a natural order, but we can’t assume the distances between categories are equal. So we use models that respect that order and model thresholds or transitions between categories.

The proportional odds model handles the cumulative probabilities up to each category, estimating a single effect of predictors that applies across all thresholds, which captures the idea that shifting a predictor moves you across every cut point similarly.

The adjacent-category model looks at the odds of being in one category versus the next higher category, modeling the link between neighboring levels and allowing the data to inform how each adjacent step behaves.

The continuation-ratio model treats the process as sequential steps through the ordered categories, modeling the probability of advancing to higher categories given you’ve reached the current one.

Other approaches like binary logistic regression reduce the outcome to two levels, linear regression assumes equal spacing of a continuous outcome, and time-to-event models are for survival data, not ordinal responses. These three forms—proportional odds, adjacent-category, and continuation-ratio—are the standard ways to model ordinal data because they preserve the order information while providing interpretable, appropriate likelihoods.