Multinomial Logistic Regression
Multinomial logistic regression online with reference category, log odds and pseudo R squared.
When to use it
Use when the outcome has three or more unordered categories (species identity, brand chosen, mode of transport, crop type chosen by a farmer) and you have one or more continuous or categorical predictors. The model fits a log-odds equation for each non-reference category against the reference, simultaneously.
When NOT to use it
Do not use when categories are ordered (low, medium, high); use ordinal logistic (proportional odds) instead, which is more parsimonious. Do not use for binary outcomes (use the Logistic Regression tool). With very small samples per category, the model is unstable; aim for at least 10 events per predictor per category. The independence of irrelevant alternatives (IIA) assumption may fail; check by removing one category and refitting.
What you get
Coefficient table per non-reference category: log-odds estimates, standard errors, Wald z, two-sided p, 95 percent CIs; relative-risk ratios (exp(b)) with their CIs (the more interpretable scale); McFadden's pseudo R-squared; null and residual deviance with the model likelihood-ratio chi-square; classification accuracy table.
How to interpret the output
A relative-risk ratio above 1 means the predictor increases the odds of that category relative to the reference; below 1 decreases. Each non-reference category gives its own equation; coefficients can differ in sign across categories. The reference category is arbitrary in interpretation but changes the displayed coefficients; pick a baseline that is meaningful (e.g. most common category, or 'no choice'). McFadden between 0.2 and 0.4 is excellent (Hensher and Stopher 1979).
Common pitfalls
- Reporting log-odds without the relative-risk ratios (less interpretable).
- Choosing an unstable reference category (e.g. one with few observations).
- Ignoring the IIA assumption when adding or removing categories.
- Forcing an ordered outcome (e.g. severity grades) into multinomial when ordinal would be more powerful.
Try it in StatVeda
The Multinomial Logistic Regression (3+ categories) engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.
Open Multinomial Logistic Regression (3+ categories)References
- Agresti, A. (2013). Categorical Data Analysis, 3rd edition. John Wiley and Sons, Hoboken. Chapter 8.
- Hosmer, D. W., Lemeshow, S. and Sturdivant, R. X. (2013). Applied Logistic Regression, 3rd edition. John Wiley and Sons, Hoboken. Chapter 8.
- McFadden, D. (1973). Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics. Academic Press, New York.