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The Weighted Oblimin Rotation

Published online by Cambridge University Press:  01 January 2025

Urbano Lorenzo-Seva
Urbano Lorenzo-Seva*
Affiliation:
Universitat Rovira i Virgili
*
Requests for reprints should be sent to Urbano Lorenzo-Seva, Department of Psychology, Universitat Rovira i Virgili, Ctra de Vails s/n, 43007—Tarragona Spain. E-Mail: uls@fcep.urv.es
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Abstract

Cureton & Mulaik (1975) proposed the Weighted Varimax rotation so that Varimax (Kaiser, 1958) could reach simple solutions when the complexities of the variables in the solution are larger than one. In the present paper the weighting procedure proposed by Cureton & Mulaik (1975) is applied to Direct Oblimin (Clarkson & Jennrich, 1988), and the rotation method obtained is called Weighted Oblimin. It has been tested on artificial complex data and real data, and the results seem to indicate that, even though Direct Oblimin rotation fails when applied to complex data, Weighted Oblimin gives good results if a variable with complexity one can be found for each factor in the pattern. Although the weighting procedure proposed by Cureton & Mulaik is based on Landahl's (1938) expression for orthogonal factors, Weighted Oblimin seems to be adequate even with highly oblique factors. The new rotation method was compared to other rotation methods based on the same weighting procedure and, whenever a variable with complexity one could be found for each factor in the pattern, Weighted Oblimin gave the best results. When rotating a simple empirical loading matrix, Weighted Oblimin seemed to slightly increase the performance of Direct Oblimin.

Keywords

component analysisfactor analysisoblique rotationweighted rotationDirect ObliminPromaxVarimax
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 3 , September 2000 , pp. 301 - 318
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

The author is obliged to Henk A. L. Kiers and three anonymous reviewers for helpful comments on an earlier version of this paper.

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