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Some Standard Errors in Item Response Theory

Published online by Cambridge University Press:  01 January 2025

David Thissen  and
Howard Wainer
David Thissen
Affiliation:
University of Kansas
Howard Wainer*
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Howard Wainer, Educational Testing Service, Princeton, New Jersey, 08541.
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Abstract

The mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for some common situations. It is shown that the maximum likelihood estimation of a lower asymptote can wreak havoc with the accuracy of estimation of a location parameter, indicating that if one needs to have accurate estimates of location parameters (say for purposes of test linking/equating or computerized adaptive testing) the sample sizes required for acceptable accuracy may be unattainable in most applications. It is suggested that other estimation methods be used if the three parameter model is applied in these situations.

Keywords

asymptotic standard errorsitem response theory
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 4 , December 1982 , pp. 397 - 412
Copyright
Copyright © 1982 The Psychometric Society

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Footnotes

The research reported here was supported, in part, by contract #F41689-81-6-0012 from the Air Force Human Resources Laboratory to McFann-Gray & Associates, Benjamin A. Fairbank, Jr., Principal Investigator. Further support of Wainer’s effort was supplied by the Educational Testing Service, Program Statistics Research Project.

We would like to thank Henry Braun, Benjamin Fairbank, Paul Holland, Janos Koplyay, Frederic Lord, Malcolm Ree, and two anonymous referees for their careful reading of, and helpful comments on this paper. Our gratitude also to Linda DeLauro who cheerfully coordinated the preparation and many reorganizations and revisions of this manuscript.

References

Reference Notes

Swaminathan, H. & Gifford, J. A. Bayesian estimation in item response models. A talk given at the annual meeting of the Psychometric Society, Chapel Hill, North Carolina, 1981.Google Scholar
Wood, R. L., Wingersky, M. S. & Lord, F. M. LOGIST: A computer program for estimating examinee ability on item characteristic curve parameters, 1976, Princeton, N.J.: Educational Testing Service.Google Scholar

References

Andersen, E. B. A goodness-of-fit test for the Rasch model. Psychometrica, 1973, 38, 123–140.CrossRefGoogle Scholar
Bock, R. D. & Aitkin, M. Marginal maximum likelihood estimation of item parameters: application of an EM algorithm. Psychometrika, 1981, 46, 443–459.CrossRefGoogle Scholar
Kendall, M. G. & Stuart, A. The advanced theory of statistics, Volume II, Third edition, London: Griffin & Co., 1960.Google Scholar
Lord, F. M. Applications of item response theory to practical testing problems, 1980, Hillsdale, N.J.: Lawrence Erlbaum Associates.Google Scholar
Thissen, D. Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 1982, 47, 175–186.CrossRefGoogle Scholar
Wainer, H., Morgan, A., & Gustafsson, J. E. A review of estimation procedures for the Rasch Model with an eye toward longish tests. Journal of Educational Statistics, 1980, 5, 35–64.CrossRefGoogle Scholar