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Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm

Published online by Cambridge University Press:  01 January 2025

R. Darrell Bock  and
Murray Aitkin
R. Darrell Bock*
Affiliation:
University of Chicago
Murray Aitkin
Affiliation:
University of Lancaster
*
Requests for reprints should be addressed to R. Darrell Bock, Department of Behavioral Sciences, The University of Chicago, 5848 South University Avenue, Chicago, Illinois, 60637.
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Abstract

Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The Em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.

Keywords

estimation of item parametersEM algorithmitem analysislatent traitdichotomous factor analysisLaw School Aptitude Test (LSAT)
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 4 , December 1981 , pp. 443 - 459
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

Supported in part by NSF grant BNS 7912417 to the University of Chicago and by SSRC (UK) grant HR6132 to the University of Lancaster.

We are indebted to Mark Reiser and Robert Gibbons for computer programming. David Thissen clarified a number of points in an earlier draft.

References

Reference Notes

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A correction has been issued for this article:

Errata

R. D. Bock  and M. Aitkin