---
title: "Ordinal logistic regression (proportional-odds model)"
method_id: SM.REL.REG.ORD.OLOGIT
family: Relationship
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/ordinal_regression.md
source: Clarus method library
---

# Ordinal logistic regression (proportional-odds model)

> A classical statistical method in the Clarus library (Relationship family).
> Clarus selects, assumption-checks and runs this method on your data with a
> deterministic rule engine and real numerical libraries (scipy / statsmodels);
> it never generates numbers, citations or results.

**Also known as:** proportional-odds model; cumulative logit model; PO model; ordered logit; ordinal logit regression.

## Hypotheses

- **Null (H0):** beta_j = 0 for predictor j (the predictor does not shift the cumulative log-odds of a higher category).
- **Alternative (H1):** beta_j != 0 (the predictor shifts the cumulative log-odds of a higher category).

## When to use it

Use this method when your goal is to:
- model ordinal outcome from predictors
- estimate predictor effects on ordered category
- predict probability of higher category

## Data it expects

- **dependent:** 1 ordinal (>= 3 ordered categories)
- **independent:** >= 1 predictor (continuous and/or categorical)
- **pairing:** independent (cross-sectional)

## Assumptions Clarus checks

- **proportional odds** (gate: brant_test; severity: critical; on violation: reroute)
- **no multicollinearity** (gate: vif; severity: warning; on violation: warn_only)
- **independence** (severity: critical; on violation: warn_only)
- **no complete separation** (gate: separation_check; severity: critical; on violation: warn_only)

## Effect size reported

- **odds ratio** (Agresti (2010), Ch.3)

## Honest limitations

- Odds ratios assume a CONSTANT effect across all category cut-points (proportional odds); always check Brant's test before trusting a single OR.
- McFadden pseudo-R^2 is not the OLS R^2 and is typically much lower; do not compare the two.
- An association is not causal unless the predictor was randomly assigned.
- Sparse outcome categories or few cases per predictor make threshold and coefficient estimates unstable.
- Complete or quasi-complete separation produces divergent coefficients that must not be interpreted.
- Results generalize only to the sampled population.

## Primary sources

- McCullagh, P. (1980). Regression models for ordinal data. Journal of the Royal Statistical Society: Series B, 42(2), 109-142. https://doi.org/10.1111/j.2517-6161.1980.tb01109.x
- Brant, R. (1990). Assessing proportionality in the proportional odds model for ordinal logistic regression. Biometrics, 46(4), 1171-1178. https://doi.org/10.2307/2532457
- Agresti, A. (2010). Analysis of Ordinal Categorical Data (2nd ed.). Wiley.
- McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics (pp. 105-142). Academic Press.
- Albert, A. & Anderson, J. A. (1984). On the existence of maximum likelihood estimates in logistic regression models. Biometrika, 71(1), 1-10. https://doi.org/10.1093/biomet/71.1.1

## How to cite this

To cite this Clarus method page (the page itself — for the method's own primary sources, see above):

**Plain text**

Clarus, "Ordinal logistic regression (proportional-odds model)", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/ordinal_regression.md

**APA**

Clarus. (2026). Ordinal logistic regression (proportional-odds model) (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/ordinal_regression.md

**BibTeX**

```bibtex
@misc{clarus-ordinal-regression,
  author       = {Clarus},
  title        = {Ordinal logistic regression (proportional-odds model)},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/ordinal_regression.md}
}
```

_No DOI is minted for Clarus method pages yet; this citation uses the canonical URL, version and date. Cite the primary sources above for the method's scientific provenance._

---

METHOD SM.REL.REG.ORD.OLOGIT · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library