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In Spite of Indeterminacy Many Common Factor Score Estimates Yield an Identical Reproduced Covariance Matrix

Published online by Cambridge University Press:  01 January 2025

André Beauducel
André Beauducel*
Affiliation:
Helmut-Schmidt University, Educational Department
*
Requests for reprints should be sent to André Beauducel, Helmut-Schmidt University, Educational Department, Postbox 700822, 22008 Hamburg, Germany. E-mail: [email protected]
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Abstract

It was investigated whether commonly used factor score estimates lead to the same reproduced covariance matrix of observed variables. This was achieved by means of Schönemann and Steiger’s (1976) regression component analysis, since it is possible to compute the reproduced covariance matrices of the regression components corresponding to different factor score estimates. It was shown that Thurstone’s, Ledermann’s, Bartlett’s, Anderson-Rubin’s, McDonald’s, Krijnen, Wansbeek, and Ten Berge’s, as well as Takeuchi, Yanai, and Mukherjee’s score estimates reproduce the same covariance matrix. In contrast, Harman’s ideal variables score estimates lead to a different reproduced covariance matrix.

Keywords

factor score estimatesregression component analysisindeterminacy
Type
Original Paper
Information
Psychometrika , Volume 72 , Issue 3 , September 2007 , pp. 437 - 441
Copyright
Copyright © 2007 The Psychometric Society

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