Graded Response Model

  • Fumiko Samejima


The graded response model represents a family of mathematical models that deals with ordered polytomous categories. These ordered categories include rating such as letter grading, A, B, C, D, and F, used in the evaluation of students’ performance; strongly disagree, disagree, agree, and strongly agree, used in attitude surveys; or partial credit given in accordance with an examinee’s degree of attainment in solving a problem.


Latent Trait Item Parameter Homogeneous Case Partial Credit Grade Response Model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bock, R.D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika 37, 29–51.MathSciNetMATHCrossRefGoogle Scholar
  2. Bock, R.D. and Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika 46, 443–459.MathSciNetCrossRefGoogle Scholar
  3. Kolakowski, D. and Bock, R.D. (1973). Maximum Likelihood Item Analysis and Test Scoring: Logistic Model for Multiple Item Responses. Ann Arbor, MI: National Educational Resources.Google Scholar
  4. Koch, W.R. (1983). Likert scaling using the graded response latent trait model. Applied Psychological Measurement 7, 15–32.CrossRefGoogle Scholar
  5. Levine, M. (1984). An Introduction to Multilinear Formula Scoring Theory (Office of Naval Research Report, 84–4 ). Champaign, IL: Model-Based Measurement Laboratory, Education Building, University of Illinois.Google Scholar
  6. Lord, F.M. (1952). A theory of mental test scores. Psychometric Monograph, No. 7.Google Scholar
  7. Lord, F.M. and Novick, M.R. (1968). Statistical Theories of Mental Test Scores. Reading, MA: Addison Wesley.MATHGoogle Scholar
  8. Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika 47, 149–174.MATHCrossRefGoogle Scholar
  9. Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement 16, 159–176.CrossRefGoogle Scholar
  10. Muraki, E. and Bock, R.D. (1993). Parscale. Chicago, IL: Scientific Software.Google Scholar
  11. Ramsay, J.O. and Wang, X. (1993). Hybrid IRT Models. Paper presented at the Meeting of the Psychometric Society, Berkeley, CA.Google Scholar
  12. Roche, A.F., Wainer, H., and Thissen, D. (1975). Skeletal Maturity: The Knee Joint As a Biological Indicator. New York, NY: Plenum Medical Book.Google Scholar
  13. Samejima, F. (1969). Estimation of ability using a response pattern of graded scores. Psychometrika Monograph, No. 17.Google Scholar
  14. Samejima, F. (1972). A general model for free-response data. Psychometrika Monograph, No. 18.Google Scholar
  15. Samejima, F. (1973). Homogeneous case of the continuous response model. Psychometrika 38, 203–219.MATHCrossRefGoogle Scholar
  16. Samejima, F. (1983). Some methods and approaches of estimating the operating characteristics of discrete item responses. In H. Wainer and S. Messick (Eds.), Principles of Modern Psychological Measurement: A Festschrift for Frederic M. Lord (pp. 159–182 ). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  17. Samejima, F. (1993). Roles of Fisher type information in latent trait models. In H. Bozdogan (Ed.), Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach (pp. 347–378 ). Netherlands: Kluwer Academic Publishers.Google Scholar
  18. Samejima, F. (1994). Nonparametric estimation of the plausibility functions of the distractors of vocabulary test items. Applied Psychological Measurement 18, 35–51.CrossRefGoogle Scholar
  19. Samejima, F. (1995). Acceleration model in the heterogeneous case of the general graded response model. Psychometrika 60, 549–572.MathSciNetMATHCrossRefGoogle Scholar
  20. Samejima, F. (1996). Rationale and actual procedures of efficient nonparametric approaches for estimating the operating characteristics of discrete item responses. (In press.)Google Scholar
  21. Thissen, D. (1991). Multilog User’s Guide Version 6. Chicago, IL: Scientific Software.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Fumiko Samejima

There are no affiliations available

Personalised recommendations