Ordinal Rasch Model (Rating Scale and Partial Credit Models)
Also known as: Rating Scale Model, Partial Credit Model, RSM, PCM
The ordinal Rasch model extends the dichotomous Rasch framework to items with ordered response categories such as Likert-type scales. It places both persons and items on a shared interval-level metric, enabling principled measurement from ordinal data while checking whether items function consistently across all response thresholds.
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When to use it
Use the ordinal Rasch model when your items have ordered response categories and you need interval-level person measures (e.g., for parametric downstream analyses or for comparing change across time). It is particularly appropriate during scale development to check threshold ordering, item fit, and unidimensionality before finalising the instrument. Choose the RSM when every item shares the same response format and a uniform threshold structure is defensible; choose the PCM when items plausibly have idiosyncratic threshold spacings. Do not use ordinal Rasch models when the data are purely binary (use the dichotomous Rasch model instead), when sample sizes are very small (fewer than roughly 150–200 respondents risk unstable calibrations), or when the construct is clearly multidimensional and you are not willing to develop separate unidimensional scales for each dimension.
Strengths & limitations
- Converts ordinal ratings into interval-level logit scores, enabling parametric downstream analyses.
- Provides explicit, testable quality indicators — threshold ordering, item fit, person fit — that flag problematic items or respondents.
- The Wright map offers an intuitive visual alignment of item difficulties and person abilities on a shared scale.
- Item and person parameters are theoretically separable (specific objectivity), supporting sample-independent item calibration when fit is adequate.
- Detects disordered thresholds early, prompting defensible collapsing of underused categories.
- Strict unidimensionality is required; fitting a single Rasch model to a multidimensional instrument will produce poor fit and misleading measures.
- Calibration requires adequate sample sizes — commonly cited minima range from 100 to 250 respondents depending on the number of items and categories.
- The assumption that all items are equally discriminating (fixed discrimination = 1) is a constraint that real data sometimes violate; the 2PL-based Generalized Partial Credit Model relaxes this.
Frequently asked
How do I choose between the Rating Scale Model and the Partial Credit Model?
Start by asking whether all items share the same response format and whether the category spacings are likely to be similar across items. If yes, the RSM is more parsimonious and should be tried first. If items differ substantively in content or wording, the PCM's item-specific thresholds are more appropriate. A formal likelihood-ratio test between the two nested models can guide the decision when sample size permits.
What does a disordered threshold mean and what should I do about it?
A disordered threshold occurs when, for example, category 3 is never the most probable response for any trait level — respondents effectively skip it, jumping from category 2 to category 4. This usually means the category is redundant or ambiguously worded. The standard remedy is to collapse adjacent categories (e.g., merge 3 and 4) and refit the model, then reassess threshold ordering.
What sample size do I need for stable Rasch calibration?
Common guidance for the RSM and PCM suggests a minimum of about 150–250 respondents for stable item parameter estimates, with larger samples needed when the number of categories is high or item fit is borderline. Simulation studies by Linacre (1994) suggest 150–250 persons for ±0.5 logit accuracy at the 99% confidence level.
Can the ordinal Rasch model handle multidimensional data?
No — a single Rasch analysis assumes a single dominant latent dimension. If your scale is intended to measure multiple distinct constructs, you should fit separate unidimensional Rasch models for each subscale, or consider multidimensional IRT models. Principal component analysis of residuals is a common diagnostic to check whether significant secondary dimensions remain after Rasch calibration.
How is the ordinal Rasch model different from a graded response model?
Both model ordered polytomous responses, but they parameterise the response process differently. The ordinal Rasch model (RSM/PCM) models the log-odds of being in category k versus k-1, with fixed item discrimination equal to 1. The Graded Response Model (Samejima, 1969) models the cumulative probability of responding at or above each category and allows discrimination to vary. The Rasch family prioritises the specific objectivity property; the GRM is more flexible but loses that property.
Sources
- Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561–573. DOI: 10.1007/BF02293814 ↗
- Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149–174. DOI: 10.1007/BF02296272 ↗
How to cite this page
ScholarGate. (2026, June 3). Ordinal Rasch Model (Rating Scale and Partial Credit Models). ScholarGate. https://scholargate.app/en/psychometrics/ordinal-rasch-model
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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