Hostname: page-component-f554764f5-44mx8 Total loading time: 0 Render date: 2025-04-08T22:07:16.093Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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

References

Andersen, E. B. Conditional inference and models for measuring, 1973, Copenhagen: Mentalhygiejnisk Forlag.Google Scholar
Andersen, E. B. Conditional inference and multiple choice questionnaires. British Journal of Mathematical and Statistical Psychology, 1973, 26, 31–44.CrossRefGoogle Scholar
Andersen, E. B. Sufficient statistics and latent trait models. Psychometrika, 1977, 42, 69–81.CrossRefGoogle Scholar
Andersen, E. B. Discrete statistical models with social science applications, 1980, Amsterdam: North-Holland Publishing Company.Google Scholar
Andrich, D. A binomial latent trait model for the study of Likert-style attitude questionnaires. British Journal of Mathematical and Statistical Psychology, 1978, 31, 84–98.CrossRefGoogle Scholar
Andrich, D. A rating formulation for ordered response categories. Psychometrika, 1978, 43, 561–573.CrossRefGoogle Scholar
Andrich, D. Scaling attitude items constructed and scored in the Likert tradition. Educational and Psychological Measurement, 1978, 38, 665–680.CrossRefGoogle Scholar
Andrich, D. Application of a psychometric rating model to ordered categories which are scored with successive integers. Applied Psychological Measurement, 1978, 2, 581–594.CrossRefGoogle Scholar
Andrich, D. A model for contingency tables having an ordered response classification. Biometrics, 1979, 35, 403–415.CrossRefGoogle Scholar
Edwards, A. L. & Thurstone, L. L. An internal consistency check for scale values determined by the method of successive intervals. Psychometrika, 1952, 17, 169–180.CrossRefGoogle Scholar
Fischer, G. H. A measurement model for the effect of mass-media. Acta Psychologica, 1972, 36, 207–220.CrossRefGoogle Scholar
Fischer, G. H. Some probabilistic models for the description of attitudinal and behavioral changes under the influence of mass communication. In Kempf, W. F., Repp, B. H. (Eds.), Mathematical models for social psychology, 1977, Vienna: Hans Huber.Google Scholar
Mardell, C. & Goldenberg, D. S. DIAL: Developmental Indicators for the assessment of learning, 1972, Highland Park, Ill.: DIAL Inc..Google Scholar
Mardell, C. & Goldenberg, D. S. For prekindergarten screening information: DIAL. Journal of Learning Disabilities, 1975, 8, 140–147.CrossRefGoogle Scholar
Rasch, G. Probabilistic Models for Some Intelligence and Attainment Tests, 1960, Copenhagen, Denmark: Danmarks Paedogogiske Institut.Google Scholar
Rasch, G. On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1961, 321–333.Google Scholar
Rasch, G. On specific objectivity: An attempt at formalizing the request for generality and validity of scientific statements. Danish Yearbook of Philosophy, 1977, 14, 58–94.CrossRefGoogle Scholar
Samejima, F. Estimation of latent ability using a response pattern of graded scores. Psychometrika, Monograph Supplement No. 17, 1969.Google Scholar
Thurstone, L. L. The measurement of opinion. Journal of Abnormal and Social Psychology, 1928, 22, 415–430.CrossRefGoogle Scholar
Wright, B. D. & Douglas, G. A. Conditional versus unconditional procedures for sample-free item analysis. Educational and Psychological Measurement, 1977, 37, 47–60.CrossRefGoogle Scholar
Wright, B. D. & Masters, G. N. Rating scale analysis, 1982, Chicago: MESA Press.Google Scholar
Wright, B. D. & Panchapakesan, N. A procedure for sample-free item analysis. Educational and Psychological Measurement, 1969, 29, 23–48.CrossRefGoogle Scholar