Firth penalised logistic regression
Shown in the app as firth_logistic. Part of the method reference, under Regression.
When to use
Model a binary outcome when ordinary logistic regression breaks down: a predictor that perfectly (or almost perfectly) separates the outcome, or very few events per predictor. Firth's penalised likelihood returns FINITE odds ratios with profile-likelihood confidence intervals where the ordinary fit runs off to infinity.
What you provide
- Outcome: one two-level column.
- Predictors: one or more columns.
Options
Missing data
- Complete case (listwise deletion)
- Mean imputation (single)
- Median imputation (single)
Multiple comparisons
- Not adjustable for this method. Where it makes post-hoc comparisons, the procedure applies its own correction.
Related methods
Other methods under Regression:
- Linear regression
- Logistic regression
- Poisson regression
- Negative-binomial regression
- Ordinal logistic regression
- Multinomial logistic regression
- Factors associated with outcome (continuous outcome)
- Factors associated with outcome (binary outcome)
Guides that discuss this method
Worked example
Celeus's result on a published or illustrative dataset, next to an independent computation and, where one exists, a published value. The data themselves are not reproduced here.
logistf::sex2
- Source: Published dataset distributed with an R package
- Licence: logistf (GPL)
- Reference: Heinze G, Schemper M (2002), Statistics in Medicine 21:2409-2419 (the worked example); data from Cytel Inc., LogXact 9 user manual. The dataset and the model are the paper's; the numbers below are this engine's, checked against logistf run independently - not against the paper's printed table.
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Estimate | 3.09601 | 3.09601 | - | Yes |
| p-value | 0.00495187 | 0.00495187 | - | Yes |
| Confidence interval | 0.774568, 8.030290 | 0.774568, 8.030290 | - | Yes |
| Number of observations | 239 | 239 | - | Yes |
References
- Firth, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika 80: 27-38. doi:10.1093/biomet/80.1.27 doi:10.1093/biomet/80.1.27
- Heinze, G., Schemper, M. (2002). A solution to the problem of separation in logistic regression. Statistics in Medicine 21: 2409-2419. doi:10.1002/sim.1047 doi:10.1002/sim.1047