---
title: "Multinomial logistic regression (baseline-category logit model)"
method_id: SM.REL.REG.NOM.MLOGIT
family: Relationship
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/multinomial_logistic_regression.md
source: Clarus method library
---

# Multinomial logistic regression (baseline-category logit 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:** baseline-category logit model; polytomous logistic regression; multinomial logit; softmax regression; generalized logit model.

## Hypotheses

- **Null (H0):** beta_jk = 0 for predictor j in the logit of category k versus the reference (the predictor does not change the relative log-odds of category k).
- **Alternative (H1):** beta_jk != 0 (the predictor shifts the log-odds of category k relative to the reference category).

## When to use it

Use this method when your goal is to:
- model unordered categorical outcome
- relate predictors to nominal outcome
- predict category membership from predictors

## Data it expects

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

## Assumptions Clarus checks

- **iia** (gate: iia_test; severity: warning; on violation: warn_only)
- **no multicollinearity** (gate: vif; severity: warning; on violation: warn_only)
- **events per variable** (gate: epv_check; severity: warning; on violation: warn_only)
- **independence of observations** (severity: critical; on violation: warn_only)
- **no complete separation** (gate: separation_check; severity: critical; on violation: warn_only)

## Effect size reported

- **odds ratio** (McFadden (1974); OR = exp(beta), relative-risk ratio of category k versus the reference per one-unit predictor change)

## Honest limitations

- Every coefficient and odds ratio is RELATIVE TO THE REFERENCE category — changing the reference changes the numbers, not the underlying fit.
- An odds ratio is a relative-risk ratio between categories, NOT a change in the outcome value, its mean, or an absolute probability.
- Cross-sectional / observational data permit no causal claim about the predictors.
- Sparse or rare outcome categories produce unstable coefficients and very wide confidence intervals.
- Complete or quasi-complete separation can make a category's coefficients diverge (appear extremely large) — treat such estimates with suspicion.
- If the IIA property is in doubt (close substitute categories), consider a nested logit or multinomial probit model.
- Pseudo-R2 values are not comparable to OLS R2 and tend to be lower by construction.
- Results generalize only to the sampled population.

## Primary sources

- McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in Econometrics (pp. 105-142). Academic Press.
- Hausman, J., & McFadden, D. (1984). Specification tests for the multinomial logit model. Econometrica, 52(5), 1219-1240. https://doi.org/10.2307/1910997
- Peduzzi, P., Concato, J., Kemper, E., Holford, T. R., & Feinstein, A. R. (1996). A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology, 49(12), 1373-1379. https://doi.org/10.1016/S0895-4356(96)00236-3
- 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
- Agresti, A. (2013). Categorical Data Analysis (3rd ed.). Wiley.
- Nagelkerke, N. J. D. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78(3), 691-692. https://doi.org/10.1093/biomet/78.3.691

## 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, "Multinomial logistic regression (baseline-category logit model)", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/multinomial_logistic_regression.md

**APA**

Clarus. (2026). Multinomial logistic regression (baseline-category logit model) (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/multinomial_logistic_regression.md

**BibTeX**

```bibtex
@misc{clarus-multinomial-logistic-regression,
  author       = {Clarus},
  title        = {Multinomial logistic regression (baseline-category logit model)},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/multinomial_logistic_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.NOM.MLOGIT · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library