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A Look, by Simulation, at the Validity of Some Asymptotic Distribution Results for Rotated Loadings

Published online by Cambridge University Press:  01 January 2025

Claude O. Archer  and
Robert I. Jennrich
Claude O. Archer*
Affiliation:
Veterans Administration Hospital, Brentwood Los Angeles, California University of California at Los Angeles
Robert I. Jennrich
Affiliation:
University of California at Los Angeles
*
Requests for reprints should be sent to Claude O. Archer (530/153A), Veterans Administration Hospital, Brentwood, Wilshire and Sawtelle Blvds., Los Angeles, California 90073.
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Abstract

In the last few years, a number of asymptotic results for the distribution of unrotated and rotated factor loadings have been given. This paper investigates the validity of some of these results based on simulation techniques. In particular, it looks at principal component extraction and quartimax rotation on a problem with 13 variables. The indication is that the asymptotic results are quite good.

Keywords

factor analysisquartimax rotationstandard errors
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 4 , December 1976 , pp. 537 - 541
Copyright
Copyright © 1976 The Psychometric Society

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References

Archer, C. O. and Jennrich, R. I. Standard errors for rotated factor loadings. Psychometrika, 1973, 38, 581–592.CrossRefGoogle Scholar
Girshick, M. A. On the sampling theory of roots of determinantal equations. Annals of Mathematical Statistics, 1939, 10, 203–224.CrossRefGoogle Scholar
Harman, H. H. Modern factor analysis, 1967, Chicago: University of Chicago Press.Google Scholar
Kshirsagar, A. M. Bartlett decomposition and Wishart distribution. Annals of Mathematical Statistics, 1959, 30, 239–241.CrossRefGoogle Scholar
Tukey, J. W. Exploratory data analysis, Vol. 1, 1970, Reading: Addison-Wesley.Google Scholar