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Oblique Factors and Components with Independent Clusters

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: hogasa@res.otaru-uc.ac.jp
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Abstract

Relationships between the results of factor analysis and component analysis are derived when oblique factors have independent clusters with equal variances of unique factors. The factor loadings are analytically shown to be smaller than the corresponding component loadings while the factor correlations are shown to be greater than the corresponding component correlations. The condition for the inequality of the factor/component contributions is derived in the case with different variances for unique factors. Further, the asymptotic standard errors of parameter estimates are obtained for a simplified model with the assumption of multivariate normality, which shows that the component loading estimate is more stable than the corresponding factor loading estimate.

Keywords

oblique factorscomponent loadingsorthoblique rotationstandard errorsindependent clusterssphericity
Type
Articles
Information
Psychometrika , Volume 68 , Issue 2 , June 2003 , pp. 299 - 321
Copyright
Copyright © 2003 The Psychometric Society

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