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Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric

Published online by Cambridge University Press:  01 January 2025

Carel F. W. Peeters*
Affiliation:
VU University Medical Center
*
Requests for reprints should be sent to Carel F.W. Peeters, Department of Epidemiology & Biostatistics, VU University medical center, P.O. Box 7057, 1007 MB, Amsterdam, The Netherlands. E-mail: cf.peeters@vumc.nl

Abstract

In an addendum to his seminal 1969 article Jöreskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix (Jöreskog in Advances in factor analysis and structural equation models, pp. 40–43, 1979). These condition sets, formulated under factor correlation and factor covariance metrics, respectively, were claimed to be equivalent and to lead to global rotational uniqueness of the factor solution. It is shown here that the conditions for the oblique factor correlation structure need to be amended for global rotational uniqueness, and, hence, that the condition sets are not equivalent in terms of unicity of the solution.

Type
Original Paper
Copyright
Copyright © 2012 The Psychometric Society

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Footnotes

Written while a Ph.D. candidate at the Department of Methodology and Statistics, Utrecht University, Utrecht, the Netherlands. Starting February 1, the author will be at the Department of Epidemiology & Biostatistics, VU University medical center, Amsterdam, the Netherlands.

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