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Shrinkage Estimation of Linear Combinations of True Scores

Published online by Cambridge University Press:  01 January 2025

Nicholas T. Longford
Nicholas T. Longford*
Affiliation:
De Montfort University, Leicester, England
*
Requests for reprints should be sent to Nicholas T. Longford, Department of Medical Statistics, De Montfort University, Leicester LE1 9BH, ENGLAND.
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Abstract

This paper is concerned with combining observed scores from sections of tests. It is demonstrated that in the presence of population information a linear combination of true scores can be estimated more efficiently than by the same linear combination of the observed scores. Three criteria for optimality are discussed, but they yield the same solution which can be described and motivated as a multivariate shrinkage estimator.

Keywords

mean squared errormeasurement errorobserved and true scoresshrinkage estimation
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 2 , June 1997 , pp. 237 - 244
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

Input from Eric Bradlow, Charles Lewis, and Linda Zeger is acknowledged. Research for this paper was funded by the Program Research Council (ETS). Suggestions of the Editor and of anonymous referees were instrumental in several improvements of the paper.

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