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Statistical Bias in Maximum Likelihood Estimators of Item Parameters

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord
Frederic M. Lord*
Affiliation:
Educational Testing Service
*
Reprint requests should be addressed to Frederic M. Lord, Educational Testing Service, Princeton, New Jersey 08541.
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Abstract

Asymptotic formulas are derived for the bias in the maximum likelihood estimators of the item parameters in the logistic item response model when examinee abilities are known. Numerical results are given for a typical verbal test for college admission.

Keywords

item response theoryitem parametersstatistical biasmaximum likelihood
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 3 , September 1983 , pp. 425 - 435
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

This work was supported in part by contract N00014-80-C-0402, project designation NR 150-453 between the Office of Naval Research and Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.

References

Lord, F. M. Applications of item response theory to practical testing problems, Hillsdale, N.J.: Lawrence Erlbaum Associates, 1980.Google Scholar
Lord, F. M. Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability. Psychometrika, in press.Google Scholar
Lord, F. M. & Wingersky, M. S. Sampling variances and covariances of parameter estimates in item response theory. In Weiss, D. J. (Eds.), Proceedings of the 1982 Item Response Theory/Computerized Adaptive Testing Conference, Minneapolis, Minn.: University of Minnesota, Department of Psychology, Computerized Adaptive Testing Laboratory, 1983, in press.Google Scholar