Multinomial logistic regression
Shown in the app as multinomial_logistic. Part of the method reference, under Regression.
When to use
Model an UNORDERED categorical outcome with 3+ levels (e.g. treatment A/B/C, no natural order) from predictors, reporting an odds ratio per predictor for each outcome level vs a reference level.
What you provide
- Outcome: one categorical column.
- Predictors: one or more columns.
Options
Missing data
- Complete case (listwise deletion)
Multiple comparisons
- Not adjustable for this method. Where it makes post-hoc comparisons, the procedure applies its own correction.
Confidence level
Every interval in the result is reported at the level you choose:
- 90%
- 95%
- 99%
Related methods
Other methods under Regression:
- Linear regression
- Logistic regression
- Firth penalised logistic regression
- Poisson regression
- Negative-binomial regression
- Ordinal logistic regression
- Factors associated with outcome (continuous outcome)
- Factors associated with outcome (binary outcome)
Guides that discuss this method
How to read the output
Multinomial logistic regression analyses an outcome with three or more categories that have no order, for example a species or a preferred brand, from one or more predictors. One category is the reference (the first in the column’s category order, which you can change in the analysis settings), and the model compares every other category with it. Only rows with a value for the outcome and every predictor are used.
Coefficients and odds ratios. There is one set of coefficients per non-reference category. Exponentiated, each is an odds ratio for being in that category rather than the reference: per one-unit increase of a numeric predictor, or for a predictor category relative to its first category (an ordered predictor is compared category by category too, never fitted as a polynomial trend). Each describes only that one comparison, not an overall ordering. The headline result is the first predictor’s odds ratio for the first non-reference category. Its confidence interval is a Wald interval (the estimate plus or minus the normal quantile times its standard error), matching the Wald test beside it; you can choose a 90%, 95% or 99% level.
Testing a whole predictor. Because a predictor has one coefficient per comparison, each predictor is also tested as a whole with a likelihood-ratio test across all comparisons at once, and the whole model is tested against a model with no predictors. Read the whole-predictor test before any single odds ratio.
Sources: Agresti A (2013), Categorical Data Analysis, 3rd ed., Wiley.
Worked examples
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.
datasets::iris
- Source: Published dataset distributed with an R package
- Licence: base R (GPL)
- Reference: Fisher (1936), Ann. Eugenics 7(2)
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Estimate | -9.74099 | -9.74099 | - | Yes |
| p-value | 0.411011 | 0.411011 | - | Yes |
| Residual deviance | 23.8612 | 23.8612 | - | Yes |
datasets::iris
- Source: Published dataset distributed with an R package
- Licence: base R (GPL)
- Reference: Fisher (1936), Ann. Eugenics 7(2); independent computation
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Estimate | -9.74099 | -9.74099 | - | Yes |
| p-value | 0.411011 | 0.411011 | - | Yes |
| Confidence interval | -29.23030, 9.74834 | -29.23030, 9.74834 | - | Yes |
| Effect size | 5.88224e-05 | 5.88224e-05 | - | Yes |
| Effect size confidence interval | 2.02039e-13, 1.71258e+04 | 2.02039e-13, 1.71258e+04 | - | Yes |
| Test statistic for each model term | 9.62472, 158.20700 | 9.62472, 158.20700 | - | Yes |
| Residual deviance | 23.8612 | 23.8612 | - | Yes |
carData::WVS
- Source: Published dataset distributed with an R package
- Licence: carData (GPL)
- Reference: World Values Survey 1995-97, as shipped in carData; independent computation
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Estimate | 0.24345 | 0.24345 | - | Yes |
| p-value | 0.00231626 | 0.00231626 | - | Yes |
| Confidence interval | 0.0868198, 0.4000810 | 0.0868198, 0.4000810 | - | Yes |
| Effect size | 1.27564 | 1.27564 | - | Yes |
| Effect size confidence interval | 1.09070, 1.49195 | 1.09070, 1.49195 | - | Yes |
| Test statistic for each model term | 605.9050, 30.9372 | 605.9050, 30.9372 | - | Yes |
| Residual deviance | 13935.6 | 13935.6 | - | Yes |
References
- Venables, W. N., Ripley, B. D. (2002). Modern Applied Statistics with S. Springer, New York, 4th edition.