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The Asymptotic Posterior Normality of the Latent Trait in an IRT Model

Published online by Cambridge University Press:  01 January 2025

Hua-Hua Chang  and
William Stout
Hua-Hua Chang*
Affiliation:
Educational Testing Service
William Stout*
Affiliation:
Department of Statistics, University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Hua-Hua Chang, Educational Testing Service, Rosedale Road, Princeton, NJ 08541, or
William Stout, Department of Statistics, University of Illinois, 101 Illini Hall, 725 South Wright Street, Champaign, IL 61820.
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Abstract

It has long been part of the item response theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general and nonrestrictive nonparametric assumptions, we make this claim rigorous for a broad class of latent models.

Keywords

item response theoryempirical Bayesposterior distributionability estimationconfidence intervalmanifest probablyDutch Identity
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 1 , March 1993 , pp. 37 - 52
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

This research was partially supported by Office of Naval Research Cognitive and Neural Sciences Grant N0014-J-90-1940, 442-1548, National Science Foundation Mathematics Grant NSF-DMS-91-01436, and the National Center for Supercomputing Applications. We wish to thank Kumar Joag-dev and Zhiliang Ying for enlightening suggestions concerning the proof of the basic result.

The authors wish to thank Kumar Joag-Dev, Brian Junker, Bert Green, Paul Holland, Robert Mislevy, and especially Zhiliang Ying for their useful comments and discussions.

References

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