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A Response Model for Multiple Choice Items

Published online by Cambridge University Press:  01 January 2025

David Thissen  and
Lynne Steinberg
David Thissen*
Affiliation:
University of Kansas
Lynne Steinberg
Affiliation:
University of Kansas
*
Requests for reprints should be sent to David Thissen, Department of Psychology, University of Kansas, Lawrence, KS, 66045, (913)864-4131.
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Abstract

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.

Keywords

item response theorymultiple choice itemsmarginal maximum likelihood
Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 4 , December 1984 , pp. 501 - 519
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

This research was supported in part by ONR contract N00014-83-C-0283 to the University of Chicago, R, Darrell Bock, Principal Investigator, and AFHRL contract F41689-82-C-00020 to the Educational Testing Service, Howard Wainer, Principal Investigator. This project was facilitated by a sabbatical leave provided David Thissen by the University of Kansas, during which time some of this work was done with the Research Statistics Group of the Educational Testing Service. Conversations with Darrell Bock, Howard Wainer, Paul Holland, Frederic Lord, Donald Rubin, James Ramsay and Malcolm Ree have also been important and useful in shaping the research and its presentation here. While all those mentioned have helped us gain wisdom in these matters, any error that remains is, of course, our own.

References

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.CrossRefGoogle Scholar
Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of anEM algorithm. Psychometrika, 46, 443–459.CrossRefGoogle Scholar
Bock, R. D., & Lieberman, M. (1970). Fitting a response model forn dichotomously scored items. Psychometrika, 35, 179–197.CrossRefGoogle Scholar
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
Choppin, B. (1983). A two-parameter latent trait model, Los Angeles: University of California, Center for the Study of Evaluation, Graduate School of Education.Google Scholar
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, 1–38.CrossRefGoogle Scholar
Haberman, S. (1974). Subroutine MINIM [Computer program]. In Bock, R. D., Repp, Bruno (Eds.), MATCAL: Double precision matrix operations subroutines for the IBM System 360/370 computers, Chicago: National Educational Resources.Google Scholar
Levine, M. V., & Drasgow, F. (1983). The relation between incorrect option choice and estimated ability. Educational and Psychological Measurement, 43, 675–685.CrossRefGoogle Scholar
Lord, F. M. (1983). Maximum likelihood estimation of item response parameters when some responses are omitted. Psychometrika, 48, 477–482.CrossRefGoogle Scholar
Samejima, F. (1979). A new family of models for the multiple choice item, Knoxville: University of Tennessee, Department of Psychology.CrossRefGoogle Scholar
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
Thissen, D. (1976). Information in wrong responses to the Raven Progressive Matrices. Journal of Educational Measurement, 13, 201–214.CrossRefGoogle Scholar
Thissen, D. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 175–186.CrossRefGoogle Scholar