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Concise Formulas for the Standard Errors of Component Loading Estimates

Published online by Cambridge University Press:  01 January 2025

Haruhiko Ogasawara
Haruhiko Ogasawara*
Affiliation:
Otaru University of Commerce
*
Request for reprints should be sent to Haxuhiko Ogasawara, Department of Information and Management Science, Otaru University of Commerce, 3-5-21, Midori, Otaxu 047-8501 JAPAN. Email: hogasa@res.otaru-uc.ac.jp
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Abstract

Concise formulas for the asymptotic standard errors of component loading estimates were derived. The formulas cover the cases of principal component analysis for unstandardized and standardized variables with orthogonal and oblique rotations. The formulas can be used under any distributions for observed variables as long as the asymptotic covariance matrix for sample covariances/correlations is available. The estimated standard errors in numerical examples were shown to be equivalent to those by the methods using information matrices.

Keywords

asymptotic standard errorsprincipal component analysiscomponent loadingsrotationinformation matrixleast squares

Information

Type
Articles
Information
Psychometrika , Volume 67 , Issue 2 , June 2002 , pp. 289 - 297
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

The author is indebted to anonymous reviewers for the corrections and suggestions on this study, which have led to improvements of earlier versions of this article.

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