Ordinal regression (proportional odds)
Predicts an ordered categorical outcome (e.g. a 1–5 rating) with a cumulative logit model: one set of predictor effects and a threshold between each pair of adjacent categories.
Menu: Analyze → Regression → Ordinal…
When should I use it?
- What predicts satisfaction rated very low … very high?
- Does treatment shift the distribution of symptom severity (none, mild, moderate, severe)?
What are the assumptions?
- Ordered outcome categories.
- Proportional odds: each predictor has the same effect at every threshold (test of parallel lines, Sig. > .05).
- Enough cases in each outcome category.
How do I run it in StatLab?
- Move the outcome to Dependent, categorical predictors to Factor(s) and numeric predictors to Covariate(s).
- Keep the test of parallel lines.
- Choose the link: logit (default; odds ratios), probit (latent normal), complementary log-log (higher categories more likely), negative log-log (lower categories more likely), cauchit (extreme latent values).
How do I read the output?
| Output | Meaning |
|---|---|
| Model Fitting Information | Chi-square test of the model. |
| Goodness-of-Fit | Pearson and deviance statistics. |
| Pseudo R-Square | Cox and Snell, Nagelkerke, McFadden. |
| Parameter Estimates | Thresholds and location (predictor) estimates; positive estimates mean higher categories are more likely. |
| Test of Parallel Lines | Sig. < .05 means the proportional-odds assumption is doubtful. |
Worked example
On the practice survey dataset (File → Sample dataset), this command — which the dialog's Paste button also produces — runs the procedure:
PROC glmOrdinal /dep=educ /factors=(gender) /covs=(age) /link=logit /gof=YES /parallel=YES.
Output tables: Case Processing Summary · Model Fitting Information · Goodness-of-Fit · Pseudo R-Square · Parameter Estimates · Test of Parallel Linesᵃ.
How would I report it in APA style?
An ordinal (cumulative logit link) regression predicted Highest education (N = 150): model χ²(2) = 0.81, p = .668, Nagelkerke R² = .006; test of parallel lines χ²(4) = 5.76, p = .218. age: b = −0.01, OR = 0.99, Wald χ²(1) = 0.80, p = .372; [gender=Male]: b = 0.07, OR = 1.07, Wald χ²(1) = 0.06, p = .813.
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?
- Reading the threshold estimates as effects.
- Ignoring a significant test of parallel lines.