A Response Model for Multiple-Choice Items

  • David Thissen
  • Lynne Steinberg


In the mid-1960s, Samejima initiated the development of item response models that involve separate response functions for all of the alternatives in the multiple choice and Likert-type formats. Her work in this area began at the Educational Testing Service and continued during a visit to the L.L. Thurstone Psychometric Laboratory at the University of North Carolina. Both Samejima’s (1969; this volume) original model for graded item responses and Bock’s (1972; this volume) model for nominal responses were originally intended to produce response functions for all of the alternatives of multiple-choice items. For various reasons, neither model has proved entirely satisfactory for that purpose, although both have been applied in other contexts. Using a combination of ideas suggested by Bock (1972) and Samejima (1968, 1979), a multiple-choice model was developed that produces response functions that fit unidimensional multiple-choice tests better (Thissen and Steinberg, 1984); that model is the subject of this chapter.


Response Function Differential Item Functioning Item Response Theory Item Analysis Item Parameter 
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  1. Abrahamowicz, M. and Ramsay, J.O. (1992). Multicategorical spline model for item response theory. Psychometrika 57, 5–27.CrossRefGoogle Scholar
  2. Bock, R.D. (1972). Estimating item parameters and latent ability when responses are scored in two or more latent categories. Psychometrika 37, 29–51.MathSciNetMATHCrossRefGoogle Scholar
  3. Bock, R.D. (1975). Multivariate Statistical Methods in Behavioral Research. New York: McGraw-Hill.MATHGoogle Scholar
  4. Bock, R.D. and Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of the EM algorithm. Psychometrika 46, 443–449.MathSciNetCrossRefGoogle Scholar
  5. Bock, R.D. and Lieberman, M. (1970). Fitting a response model for n dichotomously scored items. Psychometrika 35, 179–197.CrossRefGoogle Scholar
  6. Bock, R.D. and Mislevy, R.J. (1982). Adaptive EAP estimation of ability in a microcomputer environment. Applied Psychological Measurement 6, 431–444.CrossRefGoogle Scholar
  7. Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 39, 1–38.MathSciNetMATHGoogle Scholar
  8. Glas, C.A.W. (1988). The derivation of some tests for the Rasch model from the multinomial distribution. Psychometrika 53, 525–546.MathSciNetMATHCrossRefGoogle Scholar
  9. Green, B.F., Crone, C.R., and Folk, V.G. (1989). A method for studying differential distractor functioning. Journal of Educational Measurement 26, 147–160.CrossRefGoogle Scholar
  10. Lazarsfeld, P.F. (1950). The logical and mathematical foundation of latent structure analysis. In S.A. Stouffer, L. Guttman, E.A. Suchman, P.F. Lazarsfeld, S.A. Star, and J.A. Clausen, Measurement and Prediction (pp. 362–412 ). New York: Wiley.Google Scholar
  11. Levine, M.V. and Drasgow, F. (1983). The relation between incorrect option choice and estimated proficiency. Educational and Psychological Measurement 43, 675–685.CrossRefGoogle Scholar
  12. Ramsay, J.O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika 56, 611–630.MathSciNetMATHCrossRefGoogle Scholar
  13. Ramsay, J.O. (1992). TESTGRAF: A Program for the Graphical Analysis of Multiple Choice Test and Questionnaire Data (Technical Report). Montreal, Quebec: McGill University.Google Scholar
  14. Samejima, F. (1968). Application of the Graded Response Model to the Nominal Response and Multiple Choice Situations (Research Report #63). Chapel Hill, N.C.: University of North Carolina, L.L. Thurstone Psychometric Laboratory.Google Scholar
  15. Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometric Monograph, No. 17.Google Scholar
  16. Samejima, F. (1979). A New Family of Models for the Multiple Choice Item (Research Report #79–4). Knoxville, TN: University of Tennessee, Department of Psychology.Google Scholar
  17. Steinberg, L. and Thissen, D. ( 1984, June). Some Consequences of Non-Monotonic Trace Lines in Item Response Theory. Paper presented at the meeting of the Psychometric Society, Santa Barbara, CA.Google Scholar
  18. Sympson, J.B. (1983, June). A New IRT Model for Calibrating Multiple Choice Items. Paper presented at the meeting of the Psychometric Society, Los Angeles, CA.Google Scholar
  19. Thissen, D. (1976). Information in wrong responses to the Raven Progressive Matrices. Journal of Educational Measurement 13, 201–214.CrossRefGoogle Scholar
  20. Thissen, D. (1991). MULTILOG User’s Guide-Version 6. Chicago, IL: Scientific Software.Google Scholar
  21. Thissen, D. and Steinberg, L. (1984). A response model for multiple choice items. Psychometrika 49, 501–519.Google Scholar
  22. Thissen, D., Steinberg, L., and Fitzpatrick, A.R. (1989). Multiple choice models: The distractors are also part of the item. Journal of Educational Measurement 26, 161–176.CrossRefGoogle Scholar
  23. Thissen, D., Steinberg, L., and Wainer, H. (1993). Detection of differential item functioning using the parameters of item response models. In P.W. Holland and H. Wainer (Eds.), Differential Item Functioning (pp. 67113 ). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  24. Wainer, H. (1989). The future of item analysis. Journal of Educational Measurement 26, 191–208.Google Scholar
  25. Wainer, H. and Thissen, D. (1987). Estimating ability with the wrong model. Journal of Educational Statistics 12, 339–368.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • David Thissen
  • Lynne Steinberg

There are no affiliations available

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