, Volume 49, Issue 4, pp 501–519 | Cite as

A response model for multiple choice items

  • David Thissen
  • Lynne Steinberg


We introduce an extended multivariate logistic response model for multiple choice items; this model includes several earlier proposals as special cases. The discussion includes a theoretical development of the model, a description of the relationship between the model and data, and a marginal maximum likelihood estimation scheme for the item parameters. Comparisons of the performance of different versions of the full model with more constrained forms corresponding to previous proposals are included, using likelihood ratio statistics and empirical data.

Key words

item response theory multiple choice items marginal maximum likelihood 


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  1. Bock, R. D. (1972). Estimating item parameters and latent ability when the responses are scored in two or more nominal categories.Psychometrika, 37, 29–51.Google Scholar
  2. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of anEM algorithm.Psychometrika, 46, 443–459.CrossRefGoogle Scholar
  3. Bock, R. D., & Lieberman, M. (1970). Fitting a response model forn dichotomously scored items.Psychometrika, 35, 179–197.Google Scholar
  4. Bock, R. D., & Mislevy, R. G. (1982, August) Applications of EAP estimation in computerized adaptive testing. Paper presented at the annual meeting of the Psychometric Society, Montreal, Canada.Google Scholar
  5. Choppin, B. (1983).A two-parameter latent trait model. (CSE Report No. 197). Los Angeles: University of California, Center for the Study of Evaluation, Graduate School of Education.Google Scholar
  6. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via theEM algorithm (with Discussion).Journal of the Royal Statistical Society, 39, (Series B) 1–38.Google Scholar
  7. Haberman, S. (1974).Subroutine MINIM [Computer program]. In R. D. Bock & Bruno Repp (Eds.)MATCAL: Double precision matrix operations subroutines for the IBM System 360/370 computers. Chicago: National Educational Resources.Google Scholar
  8. Levine, M. V., & Drasgow, F. (1983). The relation between incorrect option choice and estimated ability.Educational and Psychological Measurement, 43, 675–685.Google Scholar
  9. Lord, F. M. (1983). Maximum likelihood estimation of item response parameters when some responses are omitted.Psychometrika, 48, 477–482.Google Scholar
  10. Samejima, F. (1979).A new family of models for the multiple choice item. (Research Report No. 79-4) Knoxville: University of Tennessee, Department of Psychology.Google Scholar
  11. Sympson, J. B. (1983, June).A new IRT model for calibrating multiple choice items. Paper presented at the annual meeting of the Psychometric Society, Los Angeles, CA.Google Scholar
  12. Thissen, D. (1976). Information in wrong responses to the Raven Progressive Matrices.Journal of Educational Measurement, 13, 201–214.CrossRefGoogle Scholar
  13. Thissen, D. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model.Psychometrika, 47, 175–186.Google Scholar

Copyright information

© The Psychometric Society 1984

Authors and Affiliations

  • David Thissen
    • 1
  • Lynne Steinberg
    • 1
  1. 1.Department of PsychologyUniversity of KansasLawrence

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