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Bayesian Estimation of Item Response Curves

Published online by Cambridge University Press:  01 January 2025

Robert K. Tsutakawa and
Hsin Ying Lin
Robert K. Tsutakawa*
Affiliation:
University of Missouri-Columbia
Hsin Ying Lin
Affiliation:
University of Missouri-Columbia
*
Requests for reprints should be sent to Robert K. Tsutakawa, Department of Statistics, University of Missouri, Columbia, MO 65211.
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Abstract

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data from a mathematics test.

Keywords

item responsesBayesian estimationEM algorithm

Information

Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 2 , June 1986, pp. 251 - 267
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

This work was supported under Contract No. N00014-85-K-0113, NR 150-535, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank Mark D. Reckase for providing the ACT data used in the illustration and Michael J. Soltys for computational assistance. They also wish to thank the editor and four anonymous reviewers for many valuable suggestions.

References

Bock, R. D., Aitkin, M. (1981). Marginal maximum likelihood estimator of item parameters: An application of an EM algorithm. Psychometrika, 46, 443–459.CrossRefGoogle Scholar
Dempster, A. P., Laird, N. M., Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, 39, 1–38.CrossRefGoogle Scholar
Leonard, T. (1975). Bayesian estimation methods for two-way contingency tables. Journal of the Royal Statistical Society, 37, 23–37.CrossRefGoogle Scholar
Lindley, D. V., Smith, A. F. M. (1972). Bayes estimates for the linear model (with discussion). Journal of the Royal Statistical Society, 34, 1–41.CrossRefGoogle Scholar
Lord, F. M. (1980). Applications of item response theory to practical testing problems, Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal for the Society of Applied Mathematics, 11, 431–441.Google Scholar
Mislevy, R. J., Bock, R. D. (1981). BILOG—Maximum Likelihood item analysis and test scoring: LOGISTIC model, Chicago: International Educational Services.Google Scholar
Novick, M. R., Jackson, P. H., Thayer, D. T., Cole, N. S. (1972). Estimating multiple regressions inm groups: A cross-validation study. British Journal of Mathematical & Statistical Psychology, 25, 33–50.CrossRefGoogle Scholar
O'Hagan, A. (1976). On posterior joint and marginal modes. Biometrika, 63, 329–333.CrossRefGoogle Scholar
Raiffa, H., Schlaifer, R. (1961). Applied statistical decision theory, Boston: Harvard University, Division of Research, Graduate School of Business Administration.Google Scholar
Rigdon, S. E., Tsutakawa, R. K. (1983). Estimation in latent trait models. Psychometrika, 48, 567–574.CrossRefGoogle Scholar
Swaminathan, H. (1981). Bayesian estimation in the two-parameter logistic model, Boston: University of Massachusetts, School of Education.Google Scholar
Swaminathan, H., Gifford, J. A. (1982). Bayesian estimation in the Rasch model. Journal of Educational Statistics, 7, 175–191.CrossRefGoogle Scholar
Tsutakawa, R. K. (1984). Estimation of two-parameter logistic item response curves. Journal of Educational Statistics, 9, 263–276.CrossRefGoogle Scholar
Tsutakawa, R. K. (1985). Estimation of item parameters and theGEM algorithm. In Weiss, D. J. (Eds.), Proceedings of the 1982 Item Response Theory and Computerized Adaptive Testing Conference (pp. 180–188). Minneapolis: University of Minnesota, Department of Psychology.Google Scholar
Wingersky, M. S., Barton, M. A., Lord, F. M. (1982). LOGIST user's guide, Princeton, NJ: Educational Testing Services.Google Scholar