---
title: "Binary logistic regression"
method_id: SM.REL.REG.BIN.LOGIT
family: Relationship
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/logistic_regression.md
source: Clarus method library
---

# Binary logistic regression

> 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:** logistic regression; binary logit model; logit regression; binomial logistic regression.

## Hypotheses

- **Null (H0):** beta_j = 0 for predictor j (the predictor does not change the log-odds of the event; odds ratio = 1).
- **Alternative (H1):** beta_j != 0 (the predictor changes the log-odds of the event; odds ratio != 1).

## When to use it

Use this method when your goal is to:
- model binary outcome from predictors
- estimate odds ratios
- predict probability of an event

## Data it expects

- **dependent:** 1 binary (dichotomous, 2 levels — event vs non-event)
- **independent:** >= 1 predictor (continuous and/or categorical)
- **pairing:** independent (cross-sectional)

## Assumptions Clarus checks

- **binary outcome** (severity: critical; on violation: reroute)
- **logit linearity** (gate: logit_linearity; severity: warning; on violation: warn_only)
- **no multicollinearity** (gate: vif; severity: warning; on violation: warn_only)
- **no influential points** (gate: cook_distance; severity: warning; on violation: warn_only)
- **events per variable** (gate: epv_check; severity: warning; on violation: warn_only)
- **no complete separation** (gate: separation_check; severity: critical; on violation: warn_only)

## Effect size reported

- **odds ratio** (Hosmer et al. (2013); OR = exp(beta), the multiplicative change in the odds of the event per one-unit increase in the predictor.)

## Honest limitations

- Coefficients are on the log-odds scale and exp(coefficient) is an odds ratio, NOT a probability or a change in the outcome's value — always state which outcome level is the event.
- An odds ratio is interpreted relative to the baseline event rate; the same OR means different absolute probability changes at different baselines.
- Cross-sectional / observational data permits no causal claim about the predictors.
- Complete or quasi-complete separation produces infinite or unstable coefficients; a penalized (Firth) fit is then required.
- Fewer than ~10 events per predictor (low EPV) biases the estimates — prefer fewer predictors or penalized estimation.
- Pseudo-R2 values are not OLS R2 and tend to be lower by construction; treat them as relative fit indices only.
- Results generalize only to the sampled population.

## Primary sources

- Cox, D. R. (1958). The regression analysis of binary sequences. Journal of the Royal Statistical Society B, 20(2), 215-242. https://doi.org/10.1111/j.2517-6161.1958.tb00292.x
- Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied Logistic Regression (3rd ed.). Wiley. https://doi.org/10.1002/9781118548387
- Box, G. E. P., & Tidwell, P. W. (1962). Transformation of the independent variables. Technometrics, 4(4), 531-550. https://doi.org/10.1080/00401706.1962.10490038
- 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
- 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
- McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in Econometrics. Academic Press.

## 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, "Binary logistic regression", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/logistic_regression.md

**APA**

Clarus. (2026). Binary logistic regression (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/logistic_regression.md

**BibTeX**

```bibtex
@misc{clarus-logistic-regression,
  author       = {Clarus},
  title        = {Binary logistic regression},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/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.BIN.LOGIT · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library