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.

This is a preview of subscription content, log in to check access.

Reference notes

  1. Rasch, G. Objektivitet i samfundsvidenskaberne et metodeproblem. Paper presented at the University of Copenhagen, 1972 (mimeo).

  2. Masters, G. N. A Rasch model for rating scales. Doctoral dissertation, University of Chicago, 1980.

  3. 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.

  4. 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.

References

  1. Andersen, E. B.Conditional inference and models for measuring, Copenhagen: Mentalhygiejnisk Forlag, 1973a.

    Google Scholar 

  2. Andersen, E. B. Conditional inference and multiple choice questionnaires.British Journal of Mathematical and Statistical Psychology, 1973b,26, 31–44.

    Google Scholar 

  3. Andersen, E. B. Sufficient statistics and latent trait models.Psychometrika, 1977,42, 69–81.

    Google Scholar 

  4. Andersen, E. B.Discrete statistical models with social science applications. Amsterdam: North-Holland Publishing Company, 1980.

    Google Scholar 

  5. Andrich, D. A binomial latent trait model for the study of Likert-style attitude questionnaires.British Journal of Mathematical and Statistical Psychology, 1978a,31, 84–98.

    Google Scholar 

  6. Andrich, D. A rating formulation for ordered response categories.Psychometrika, 1978b,43, 561–573.

    Article  Google Scholar 

  7. Andrich, D. Scaling attitude items constructed and scored in the Likert tradition.Educational and Psychological Measurement, 1978c,38, 665–680.

    Google Scholar 

  8. Andrich, D. Application of a psychometric rating model to ordered categories which are scored with successive integers.Applied Psychological Measurement, 1978d,2, 581–594.

    Google Scholar 

  9. Andrich, D. A model for contingency tables having an ordered response classification.Biometrics, 1979,35, 403–415.

    Google Scholar 

  10. 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.

    Article  Google Scholar 

  11. Fischer, G. H. A measurement model for the effect of mass-media.Acta Psychologica, 1972,36, 207–220.

    Article  Google Scholar 

  12. Fischer, G. H. Some probabilistic models for the description of attitudinal and behavioral changes under the influence of mass communication. In W. F. Kempf and B. H. Repp,Mathematical models for social psychology. Vienna: Hans Huber, 1977.

    Google Scholar 

  13. Mardell, C. & Goldenberg, D. S.DIAL: Developmental Indicators for the assessment of learning. Highland Park, Ill.: DIAL Inc., 1972.

    Google Scholar 

  14. Mardell, C. & Goldenberg, D. S. For prekindergarten screening information: DIAL.Journal of Learning Disabilities, 1975,8, 140–147.

    Google Scholar 

  15. Rasch, G.Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen, Denmark: Danmarks Paedogogiske Institut, 1960 (Chicago: University of Chicago Press, 1980).

    Google Scholar 

  16. 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.

  17. 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.

    Google Scholar 

  18. Samejima, F. Estimation of latent ability using a response pattern of graded scores.Psychometrika, Monograph Supplement No. 17, 1969.

  19. Thurstone, L. L. The measurement of opinion.Journal of Abnormal and Social Psychology, 1928,22, 415–430.

    Google Scholar 

  20. Wright, B. D. & Douglas, G. A. Conditional versus unconditional procedures for sample-free item analysis.Educational and Psychological Measurement, 1977,37, 47–60.

    Google Scholar 

  21. Wright, B. D. & Masters, G. N.Rating scale analysis. Chicago: MESA Press, 1982.

    Google Scholar 

  22. Wright, B. D. & Panchapakesan, N. A procedure for sample-free item analysis.Educational and Psychological Measurement, 1969,29, 23–48.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Geoff N. Masters.

Additional information

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.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Masters, G.N. A rasch model for partial credit scoring. Psychometrika 47, 149–174 (1982). https://doi.org/10.1007/BF02296272

Download citation

Key words

  • latent trait
  • Rasch model
  • ordered categories
  • partial credit