Proportional Odds Assumption
π― Purpose¶
Use this card to decide whether Ordinal Logistic Regression is appropriate by evaluating the Proportional Odds (PO) assumption. PO assumes that predictor effects are constant across all cumulative logit thresholds.
π 1. What is the PO Assumption?¶
The effect of each predictor is assumed to be equal across all splits in the ordinal target.
$$ \log \left( \frac{P(Y \leq j)}{P(Y > j)} \right) = \theta_j - X \cdot \beta $$
βοΈ If this assumption holds, a single slope vector Ξ² applies to all logit splits.
π§ͺ 2. When to Suspect Violation¶
| Symptom | Action |
|---|---|
| Different predictors affect different thresholds | PO may be violated |
| Residuals or marginal effects vary by class group | Suspect PO violation |
| Strong nonlinearity in feature vs threshold plots | Consider relaxing PO |
π οΈ 3. How to Check the Assumption¶
| Tool | Approach |
|---|---|
brant() in R |
Formal test of PO assumption for each variable |
| Compare slope plots across class splits | Visual inconsistency suggests PO failure |
| Fit parallel binary logistic models | Test for consistent slopes manually |
π 4. Alternatives if PO Fails¶
| Option | Description |
|---|---|
| Partial Proportional Odds Model | Allows some slopes to vary, others stay constant |
| Adjacent-Category Logit | Models odds between neighboring categories |
| Nonparametric or Tree-Based Ordinal | Use ordinal classification trees |
β PO Evaluation Checklist¶
- [ ] Target verified as ordinal
- [ ] Assumption formally tested or visualized
- [ ] Predictor effects reviewed across logit splits
- [ ] Alternate model considered if PO violated
- [ ] Business interpretation updated for model structure
π‘ Tip¶
βOrdinal logistic regression is powerful β but only when its threshold logic speaks with one voice.β