Ordered Logistic Regression (Ordered Logit/Probit)
Also known as: ordinal logistic regression, proportional odds model, cumulative logit model, ordered probit, Sıralı Lojistik Regresyon (Ordered Logit/Probit)
Ordered logit is a cumulative regression model for an ordinal dependent variable, fitting a logit (or probit) link to the cumulative category probabilities. Developed in McCullagh's 1980 treatment of regression models for ordinal data, it is the standard tool for Likert-scale, rating, and ranked outcomes.
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When to use it
Use ordered logit when the dependent variable is an ordinal category — Likert items, ratings, or graded outcomes — and you want to relate it to predictors for prediction or to study relationships. It expects an ordered categorical outcome, the parallel-regression (equal-slopes) assumption checked with a Brant test, and enough observations in each category, with a recommended sample of at least about 100. It is best on cross-sectional data with ordinal or continuous predictors.
Strengths & limitations
- Respects the natural ordering of the outcome categories rather than treating them as unordered or as a continuous scale.
- A single set of coefficients summarises the effect of each predictor across all category thresholds, keeping the model parsimonious and interpretable.
- Accommodates both ordinal and continuous predictors and supports either a logit or a probit link.
- Relies on the parallel-regression (proportional odds) assumption; if it fails, the single-slope summary is misleading.
- Needs a reasonably large sample (about 100 or more) with enough observations in every category.
- Sparse or empty categories make the cut points and coefficients unstable.
Frequently asked
How is ordered logit different from ordinary logistic regression?
Ordinary logistic regression handles a binary outcome, while ordered logit handles an outcome with three or more ordered categories. It models the cumulative probability of being at or below each category and estimates separate cut points but a shared set of slopes.
What is the parallel-regression (proportional odds) assumption?
It assumes that a single coefficient vector describes the effect of the predictors at every category threshold — the slopes are parallel across cut points. You should test it, for example with a Brant test, before trusting the single-slope summary.
When should I use ordered probit instead of ordered logit?
Ordered logit and ordered probit differ only in the assumed link for the latent scale. Logit gives coefficients on the log-odds scale that are easy to read; probit assumes a normal latent error. The two usually agree closely, so the choice is mostly one of convention and interpretability.
Why not just run OLS on the rating?
Treating an ordinal rating as continuous assumes equal spacing between categories and can produce predictions outside the valid range. Ordered logit respects the ordering without imposing equal spacing, so it uses the information in the categories more faithfully.
Sources
- McCullagh, P. (1980). Regression Models for Ordinal Data. Journal of the Royal Statistical Society: Series B, 42(2), 109-142. DOI: 10.1111/j.2517-6161.1980.tb01109.x ↗
How to cite this page
ScholarGate. (2026, June 1). Ordered Logistic Regression (Ordered Logit/Probit). ScholarGate. https://scholargate.app/en/econometrics/ordered-logit
Which method?
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