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A Rasch Model for Partial Credit Scoring

Published online by Cambridge University Press:  01 January 2025

Geoff N. Masters
Geoff N. Masters*
Affiliation:
University of Chicago
*
Requests for reprints should be sent to Geoff Masters, Department of Education, University of Chicago, 5835 S. Kimbark, Chicago, 60637.
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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.

Keywords

latent traitRasch modelordered categoriespartial credit

Information

Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 2 , June 1982 , pp. 149 - 174
Copyright
Copyright © 1982 The Psychometric Society

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Footnotes

Preparation of this paper was supported by grants from the Spencer Foundation and the National Institute for Justice. I would like to thank Professor Benjamin D. Wright of the University of Chicago for his very kind help with the various drafts of this paper.

References

Reference Notes

Rasch, G. Objektivitet i samfundsvidenskaberne et metodeproblem. Paper presented at the University of Copenhagen, 1972 (mimeo).Google Scholar
Masters, G. N. A Rasch model for rating scales. Doctoral dissertation, University of Chicago, 1980.Google Scholar
Wright, B. D. & Masters, G. N. The measurement of knowledge and attitude. Research Memorandum No. 30, MESA Psychometric Laboratory, Department of Education, University of Chicago, 1981.Google Scholar
Masters, G. N. & Wright, B. D. A model for partial credit scoring. Research Memorandum No. 31, MESA Psychometric Laboratory, Department of Education, University of Chicago, 1981.Google Scholar

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