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Some Relationships between Factors and Components

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 Haruhiko Ogasawara, Department of Information and Management Science, Otaru University of Commerce, 3-5-21, Midori, Otaru 047-8501 JAPAN. E-mail address: hogasa@res.otaru-uc.ac.jp
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Abstract

The asymptotic correlations between the estimates of factor and component loadings are obtained for the exploratory factor analysis model with the assumption of a multivariate normal distribution for manifest variables. The asymptotic correlations are derived for the cases of unstandardized and standardized manifest variables with orthogonal and oblique rotations. Based on the above results, the asymptotic standard errors for estimated correlations between factors and components are derived. Further, the asymptotic standard error of the mean squared canonical correlation for factors and components, which is an overall index for the closeness of factors and components, is derived. The results of a Monte Carlo simulation are presented to show the usefulness of the asymptotic results in the data with a finite sample size.

Keywords

component loadingsfactor loadingsstandardized variablesfactor rotationasymptotic correlationsstandard errors
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 2 , June 2000 , pp. 167 - 185
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

The author is indebted to anonymous referees for their comments, corrections and suggestions which have led to the improvement of this article.

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