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Standard Errors for Obliquely Rotated Factor Loadings

Published online by Cambridge University Press:  01 January 2025

Robert I. Jennrich
Robert I. Jennrich*
Affiliation:
University of California at Los Angeles Educational Testing Service
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Abstract

In a manner similar to that used in the orthogonal case, formulas for the aymptotic standard errors of analytically rotated oblique factor loading estimates are obtained. This is done by finding expressions for the partial derivatives of an oblique rotation algorithm and using previously derived results for unrotated loadings. These include the results of Lawley for maximum likelihood factor analysis and those of Girshick for principal components analysis. Details are given in cases including direct oblimin and direct Crawford-Ferguson rotation. Numerical results for an example involving maximum likelihood estimation with direct quartimin rotation are presented. They include simultaneous tests for significant loading estimates.

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 4 , December 1973 , pp. 593 - 604
Copyright
Copyright © 1973 The Psychometric Society

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Footnotes

*

This research was supported in part by NIH Grant RR-3. The author is indebted to Dorothy Thayer who implemented the algorithms required for the example and to Gunnar Gruvaeus and Allen Yates for reviewing an earlier version of this paper. Special thanks are extended to Michael Browne for many conversations devoted to clarifying the thoughts of the author.

References

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