A Rasch model for partial credit scoring
Abstract
A unidimensional latent trait model for responses scored in two or more ordered categories is developed. This “Partial Credit” model is a member of the family of latent trait models which share the property of parameter separability and so permit “specifically objective” comparisons of persons and items. The model can be viewed as an extension of Andrich's Rating Scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item. The difference between the parameters in this model and the “category boundaries” in Samejima's Graded Response model is demonstrated. An unconditional maximum likelihood procedure for estimating the model parameters is developed.
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Due to the low sample size in the 2019 sample, only difficulty parameters were examined, with the discrimination parameter fixed to 1; the one-parameter logistic model was used for items scored 0-1, and the partial credit model for items scored 0-1-2.
“Due to the low sample size in the 2019 sample, we only examined difficulty parameters, with the discrimination parameter fixed to 1: the one-parameter logistic model (1-PL; see Birnbaum, 1968;Rasch, 1960) was used for items scored 0-1, and the partial credit model (PCM with a slope fixed to 1; Masters, 1982) was used for items scored 0-1-2.”
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- Authors
- Masters, G. N.
- Affiliations
- University of Chicago (US)
- Corresponding author
- Masters, Geoff N.
- ORCID
- Masters, Geoff N.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1982-06
- Volume
- 47
- Issue
- 2
- Pages
- 149-174
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W1966576448
- Cited by
- 3,782
- References
- 0
- Citations by year
- 2026: 142 · 2025: 160 · 2024: 158 · 2023: 154 · 2022: 198 · 2021: 178 · 2020: 222 · 2019: 203 · 2018: 168 · 2017: 209 · 2016: 179 · 2015: 175 · 2014: 184 · 2013: 150 · 2012: 140
- FWCI
- 11.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychometrika (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Education › Educational Assessment and Pedagogy
- Physical Sciences › Computer Science › Information Systems › Educational Technology and Assessment
- Keywords
- partial credit model, Rasch model, latent trait models, ordered categorical responses, graded response model, category boundaries, item response theory, maximum likelihood estimation, unidimensional model
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