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Standard Errors for the Class of Orthomax-Rotated Factor Loadings: Some Matrix Results

Published online by Cambridge University Press:  01 January 2025

Kentaro Hayashi  and
Yiu-Fai Yung
Kentaro Hayashi
Affiliation:
L. L. Thurstone Psychometric Laboratory, University of North Carolina, Chapel Hill
Yiu-Fai Yung*
Affiliation:
L. L. Thurstone Psychometric Laboratory, University of North Carolina, Chapel Hill
*
Requests for reprints should be sent to Yiu-Fai Yung, SAS Institute, Inc., R51, Multivariate and Numerical R&D, SAS Campus Drive, Cary, NC 27513.
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Abstract

The partial derivative matrices of the class of orthomax-rotated factor loadings with respect to the unrotated maximum likelihood factor loadings are derived. The reported results are useful for obtaining standard errors of the orthomax-rotated factor loadings, with or without row normalization (standardization) of the initial factor loading matrix for rotation. Using a numerical example, we verify our analytic formulas by comparing the obtained standard error estimates with that from some existing methods. Some advantages of the current approach are discussed.

Keywords

factor analysisorthomax rotationstandard errors
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 4 , December 1999 , pp. 451 - 460
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

Authorship is determined by alphabetical order. The authors contributed equally to the research. Kentaro Hayashi is now at the Department of Mathematics, Bucknell University, Lewisburg, PA 17837 (email: [email protected]). Yiu-Fai Yung is now at the SAS Institute, Inc., SAS Campus Drive, Cary, NC 27513 (email: [email protected]).

Part of the research was completed while Yiu-Fai Yung was a visiting scholar at the Department of Psychology, the Ohio State University. The visit was supported in part by grant N4856118101 from the NIMH and the Mason and Linda Stephenson Travel Award from the Department of Psychology, University of North Carolina at Chapel Hill. The authors are grateful to Michael Browne who suggested some relevant references and provided valuable comments on the research, and to Robert Cudeck who provided the FAS program for the numerical comparison. The expert comments by the reviewers are deeply appreciated.

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