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Methods for Evaluating Empirical Bayes Point Estimates of Latent Trait Scores

Published online by Cambridge University Press:  01 January 2025

Jack Kearns  and
William Meredith
Jack Kearns
Affiliation:
Educational Testing Service
William Meredith
Affiliation:
University of California, Berkeley
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Abstract

Empirical Bayes point estimates of latent trait scores, derived under the assumptions of one of several test theory models, display a certain degree of instability unless the sample size is sufficiently large. A measure of this instability over repeated sampling is the distribution of the overall expected squared error loss which converges, both in probability and in the mean, to the minimum (Bayes) overall expected loss as sample size increases. An asymptotic distribution theory is developed, and the resulting large sample approximation is compared with results obtained from simulated data. Attention is also given to the effects of using a smoothing procedure.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 3 , September 1975 , pp. 373 - 394
Copyright
Copyright © 1975 The Psychometric Society

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Footnotes

†

Research leading to this paper was partially supported by the National Science Foundation, Division of Biological and Medical Sciences, Program in Psychobiology, Grant No. NSF-GB-30779.

*

The authors are indebted to Thomas W. F. Stroud and Noel Cressie for their reviews of an earlier version of this paper and to Frederic M. Lord for helpful comments and suggestions.

*

The authors wish to thank Dr. John Bianchiai and Dr. John Helmick of Educational Testing Service for making these data available.

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