Multinomial logistic regression
Predicts an outcome with three or more unordered categories; each category is compared with a reference category.
Menu: Analyze → Regression → Multinomial Logistic…
When should I use it?
- Which transport mode (bus, car, bicycle) do commuters choose, given distance and income?
- Which programme do students enrol in?
What are the assumptions?
- Independent observations; categories that are not ordered.
- Independence of irrelevant alternatives (adding or removing a category would not change the odds between the others).
- Enough cases in every outcome category.
How do I run it in StatLab?
- Move the outcome to Dependent; choose the reference category.
- Add categorical predictors as Factors and numeric ones as Covariates.
How do I read the output?
| Output | Meaning |
|---|---|
| Model Fitting Information | Likelihood-ratio test of the final model against the intercept-only model. |
| Goodness-of-Fit | Pearson and deviance chi-square over covariate patterns (unreliable with many numeric predictors). |
| Pseudo R-Square | Cox and Snell, Nagelkerke, McFadden. |
| Likelihood Ratio Tests | Whether each predictor matters overall. |
| Parameter Estimates | One block per non-reference category: B, Wald, Sig., Exp(B) with CI. |
Worked example
On the practice survey dataset (File → Sample dataset), this command — which the dialog's Paste button also produces — runs the procedure:
PROC glmMultinomial /dep=group /factors=(gender) /covs=(age score) /ref=last /gof=YES /cls=YES /lrt=YES.
Output tables: Case Processing Summary · Model Fitting Information · Goodness-of-Fit · Pseudo R-Square · Likelihood Ratio Tests · Parameter Estimates · Classification.
How would I report it in APA style?
A multinomial logistic regression predicted Programme group (N = 150). The final model fitted better than the intercept-only model, χ²(6) = 18.62, p = .005; Nagelkerke R² = .133, McFadden R² = .059. age: χ²(2) = 8.09, p = .018; score: χ²(2) = 15.65, p < .001; gender: χ²(2) = 1.23, p = .541.
Computed by StatLab's validated procedure code when this page was built. The example only illustrates the steps; choose variables that fit your own research question.
What are common mistakes?
- Forgetting which category is the reference when reading the estimates.
- Using it for ordered categories, where ordinal regression is simpler and more powerful.