IRT — Polytomous
Coming soonPsychometrics (legacy hub)
This test is implemented and is currently going through StatMinds’ production verification: every statistic is independently checked against a trusted reference (scipy / R), locked with regression tests, and the screen is exercised across assumption-met/violated and significant/non-significant scenarios before it opens up.
See what’s live nowItem Response Theory calibration for ordered polytomous items (Likert scales, partial-credit scoring).
Three models: GRM (Graded Response Model — Samejima 1969, the standard for Likert), PCM (Partial Credit Model — Masters 1982, Rasch family with item-specific category thresholds), RSM (Rating Scale Model — Andrich 1978, common rating-scale structure across all items). Reports per-item discrimination (a) + category thresholds (b_k) + category characteristic curves + test information function + person θ. Engine auto-picks model by IC + theoretical fit.
Worked example
How do Likert items function across the trait continuum?
A graded-response IRT model was fit to 15 five-point items, estimating discrimination and ordered thresholds per item.
Discriminations were strong (1.2–2.4) and category thresholds were correctly ordered for all items, indicating well-functioning categories.
A graded-response model showed strong discriminations (1.2–2.4) with correctly ordered thresholds across items.
When to use it
- Likert questionnaire calibration (GRM default)20-item depression scale (5-point Likert: not at all → extremely) on n=800.
- Partial Credit / Rating Scale Model (Rasch family)10-item motor-functioning rating scale (0-3 partial credit per item) on n=400 patients.
When NOT to — use instead
- Binary (0/1) itemsUse 1PL/2PL/3PL for dichotomous items. → IRT \u2014 Dichotomous
- Continuous outcome (not ordered categorical)Polytomous IRT is for ordered categories. → Exploratory FA
- Sample too small (n < 300 for GRM, < 200 for PCM)Polytomous IRT calibration is sample-hungry. → CTT Item Analysis
- DIF analysis across groupsDIF is a separate analysis comparing per-item parameters across groups. → Differential Item Func.
Assumptions (and what to do if they fail)
Check: See the assumption diagnostics in the workspace.
If violated: The workspace flags this and suggests a robust or nonparametric alternative.
Check: See the assumption diagnostics in the workspace.
If violated: The workspace flags this and suggests a robust or nonparametric alternative.
Check: See the assumption diagnostics in the workspace.
If violated: The workspace flags this and suggests a robust or nonparametric alternative.
Check: See the assumption diagnostics in the workspace.
If violated: The workspace flags this and suggests a robust or nonparametric alternative.
Ready to run a IRT — Polytomous on your own data?
Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.
Run this test →