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Lower Bounds to the Reliabilities of Factor Score Estimators

Published online by Cambridge University Press:  01 January 2025

David J. Hessen
David J. Hessen*
Affiliation:
Utrecht University
*
Correspondence should be made to David J. Hessen, Department of Methodology and Statistics, Utrecht University, Padualaan 14, PO Box 80.140, 3508 TC Utrecht, The Netherlands. Email: [email protected]
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Abstract

Under the general common factor model, the reliabilities of factor score estimators might be of more interest than the reliability of the total score (the unweighted sum of item scores). In this paper, lower bounds to the reliabilities of Thurstone’s factor score estimators, Bartlett’s factor score estimators, and McDonald’s factor score estimators are derived and conditions are given under which these lower bounds are equal. The relative performance of the derived lower bounds is studied using classic example data sets. The results show that estimates of the lower bounds to the reliabilities of Thurstone’s factor score estimators are greater than or equal to the estimates of the lower bounds to the reliabilities of Bartlett’s and McDonald’s factor score estimators.

Keywords

reliabilityclassical test theorycommon factor modelfactor scores
Type
Original paper
Information
Psychometrika , Volume 82 , Issue 3 , September 2017 , pp. 648 - 659
Copyright
Copyright © 2016 The Psychometric Society

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