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Bayesian Estimation in the Three-Parameter Logistic Model

Published online by Cambridge University Press:  01 January 2025

Hariharan Swaminathan  and
Janice A. Gifford
Hariharan Swaminathan*
Affiliation:
University of Massachusetts
Janice A. Gifford
Affiliation:
Mount Holyoke College
*
Requests for reprints should be sent to H. Swaminathan, School of Education, University of Massachusetts, Amherst, MA 01003.
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Abstract

A joint Bayesian estimation procedure for the estimation of parameters in the three-parameter logistic model is developed in this paper. Procedures for specifying prior beliefs for the parameters are given. It is shown through simulation studies that the Bayesian procedure (i) ensures that the estimates stay in the parameter space, and (ii) produces better estimates than the joint maximum likelihood procedure as judged by such criteria as mean squared differences between estimates and true values.

Keywords

Bayes estimationthree-parameter logistic modelitem response theory
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 4 , December 1986 , pp. 589 - 601
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

The research reported here was performed pursuant to Grant No. N0014-79-C-0039 with the Office of Naval Research.

A related article by Robert J. Mislevy (1986) appeared when the present paper was in the printing stage.

References

Bock, R. D., Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of the EM algorithm. Psychometrika, 46, 443–460.CrossRefGoogle Scholar
Hambleton, R. K., Rovinelli, R. (1973). A FORTRAN IV program for generating examinees response data from logistic test models. Behavioral Science, 18, 74–74.Google Scholar
Hambleton, R. K., Swaminathan, H., Cook, L. L., Eignor, D. R., Gifford, J. A. (1978). Developments in latent train theory: Models, technical issues, and applications. Review of Educational Research, 48, 467–510.CrossRefGoogle Scholar
Lindley, D. V., Smith, A. F. (1972). Bayesian estimates for the linear model. Journal of the Royal Statistical Society, 34 (Series B), 1–41.CrossRefGoogle Scholar
Lord, F. M. (1980). Applications of item response theory to practical testing problems, Hillsdale: Lawrence Erlebaum.Google Scholar
Loyd, B. H., Hoover, H. D. (1980). Vertical equating using the Rasch model. Journal of Educational Measurement, 17, 179–193.CrossRefGoogle Scholar
Mislevy, R. J. (1986). Bayes Modal Estimation in Item Response Models. Psychometrika, 51, 177–195.CrossRefGoogle Scholar
Novick, M. R., Jackson, P. H. (1974). Statistical methods for educational and psychological research, New York: McGraw-Hill.Google Scholar
Novick, M. R., Lewis, C., Jackson, P. H. (1973). The estimation of proportions inm groups. Psychometrika, 38, 19–46.CrossRefGoogle Scholar
Slinde, J. A., Linn, R. L. (1979). A note on vertical equating via the Rasch model for groups of quite different ability and tests of quite different difficulty. Journal of Educational Measurement, 16, 159–165.CrossRefGoogle Scholar
Swaminathan, H., Gifford, J. A. (1982). Bayesian estimation in the Rasch model. Journal of Educational Statistics, 7, 175–192.CrossRefGoogle Scholar
Swaminathan, H., Gifford, J. A. (1985). Bayesian estimation in the two-parameter logistic model. Psychometrika, 50, 349–364.CrossRefGoogle Scholar
Urry, V. W. (1976). Ancilliary estimators for the item parameters of mental tests. In Gorham, W. A. (Eds.), Computerized testing: Steps toward the inevitable conquest (PS-76-1), Washington, DC: US Civil Service Commission, Personnel Research and Development Center.Google Scholar
Wood, R. L., Wingersky, M. S., Lord, F. M. (1978). LOGIST: A computer program for estimating ability and item characteristic curve parameters, Princeton, NJ: Educational Testing Service.Google Scholar