Predict which of three or more unordered categories a case falls into.
Multinomial logistic regression predicts a categorical outcome with three or more categories that have no natural order: mode of transport (bike, bus, car), chosen field of study, type of employment. Binary logistic regression handles only two categories, and ordinal regression assumes an order that does not exist here.
The model picks one outcome category as the reference and estimates a separate set of coefficients for every other category against it. With bike as the reference, one equation describes bus versus bike and another car versus bike. Each coefficient is reported as a relative-risk ratio (RRR): the factor by which the odds of that category, relative to the reference, change for a one-unit increase in the predictor.
StatRyx reports, for every non-reference category, each predictor's B, SE, z, p, relative-risk ratio and 95% confidence interval, along with the number of cases in each outcome category. Model fit is given by the likelihood-ratio χ² test against the intercept-only model and by McFadden's and Nagelkerke's pseudo-R². You can choose the reference category in your request.
The model needs enough cases in every outcome category — a category with very few cases gives unstable estimates. Predictors can be numeric or categorical.
| Outcome vs Bike | Predictor | RRR | 95% CI | p |
|---|---|---|---|---|
| Bus | Age | 0.97 | [0.94, 1.00] | .035 |
| Bus | Distance (km) | 1.04 | [0.97, 1.12] | .300 |
| Car | Age | 1.04 | [1.01, 1.07] | .008 |
| Car | Distance (km) | 1.12 | [1.04, 1.21] | .003 |
A multinomial logistic regression (reference: bike) predicted mode of transport from age and distance, χ²(4) = 47.42, p < .001, McFadden R² = .10, N = 240. Each additional kilometre raised the odds of driving rather than cycling, RRR = 1.12, 95% CI [1.04, 1.21], p = .003, and older commuters were more likely to drive, RRR = 1.04, 95% CI [1.01, 1.07], p = .008.
Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.
Name the reference category, give the overall model test (χ², df, p) and a pseudo-R², then report each relevant predictor's relative-risk ratio with its 95% CI and p for each comparison: "RRR = 1.12, 95% CI [1.04, 1.21], p = .003."
The exponentiated coefficient. It is the factor by which the odds of an outcome category, relative to the reference category, change for a one-unit increase in the predictor. Values above 1 make that category more likely relative to the reference.
Pick the category that makes the comparisons most meaningful — often the most common one or a natural baseline. Name it in your request; otherwise StatRyx uses the first category.
Use multinomial when the outcome categories have no order. If they are ordered, ordinal regression uses that information and gives a single, simpler odds ratio per predictor.
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