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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

Information

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.

References

Bentler, P.M. (1977). Factor simplicity index and transformations. Psychometrika, 42, 277–295CrossRefGoogle Scholar
Browne, M.W. (1972). Oblique rotation to a partially specified target. British Journal of Mathematical and Statistical Psychology, 25, 207–212CrossRefGoogle Scholar
Browne, M.W., Du Toit, S.H.C. (1992). Automated fitting of nonstandard models. Multivariate Behavioral Research, 27, 269–300CrossRefGoogle ScholarPubMed
Clarkson, D.B., Jennrich, R.I. (1988). Quartic rotation criteria and algorithms. Psychometrika, 53, 251–259CrossRefGoogle Scholar
Crawford, C. (1975). A comparison of the direct oblimin and primary parsimony methods of oblique rotation. British Journal of Mathematical and Statistical Psychology, 28, 201–213CrossRefGoogle Scholar
Cureton, E.E., Mulaik, S. (1975). The weighted varimax rotation and the promax rotation. Psychometrika, 40, 183–195CrossRefGoogle Scholar
Harris, C.W., Kaiser, H.F. (1964). Oblique factor analytic solutions by orthogonal transformations. Psychometrika, 29, 347–362CrossRefGoogle Scholar
Hendrickson, A.E., White, P.O. (1964). PROMAX: a quick method for rotation to oblique simple structure. British Journal of Statistical Psychology, 17, 65–70CrossRefGoogle Scholar
Jennrich, R.I. (1979). Admissible values of gamma in direct oblimin rotation. Psychometrika, 44, 173–177CrossRefGoogle Scholar
Kaiser, H.F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200CrossRefGoogle Scholar
Kiers, H.A.L. (1994). Simplimax: oblique rotation to an optimal target with simple structure. Psychometrika, 59, 567–579CrossRefGoogle Scholar
Landahl, H.D. (1938). Centroid orthogonal transformations. Psychometrika, 3, 219–223CrossRefGoogle Scholar
Lorenzo-Seva, U. (1999). Promin: a method for oblique factor rotation. Multivariate Behavioral Research, 34, 347–356CrossRefGoogle Scholar
The MathWorks (1984). Matlab. Natick. MA: AuthorGoogle Scholar
Meredith, W. (1977). On weighted Procrustes and hyperplane fitting in factor analytic rotation. Psychometrika, 42, 491–522CrossRefGoogle Scholar
Stankov, L., Roberts, R., Spilsbury, G. (1994). Attention and speed of test-taking in intelligence and aging. Personality and Individual Differences, 27, 273–284CrossRefGoogle Scholar
ten Berge, J.M.F.T. (1995). Suppressing permutations or rigid planar rotations: A remedy against nonoptimal varimax rotations. Psychometrika, 60, 437–446CrossRefGoogle Scholar
Thurstone, L.L. (1947). Multiple factor analysis. Chicago: University of Chicago PressGoogle Scholar
Trendafilov, N. (1994). A simple method for procrustean rotation in factor analysis using majorization theory. Multivariate Behavioral Research, 29, 385–408CrossRefGoogle ScholarPubMed
Tucker, L.R. (1951). Common factor analysis versus principal components analysis: Differential bias in representing model parameters. Multivariate Behavioral Research, 28, 263–311Google Scholar