Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-02-04T18:55:54.109Z Has data issue: false hasContentIssue false
  • English
  • Français

The Weighted Varimax Rotation and the Promax Rotation

Published online by Cambridge University Press:  01 January 2025

Edward E. Cureton  and
Stanley A. Mulaik
Edward E. Cureton
Affiliation:
University of Tennessee and Georgia Institute of Technology
Stanley A. Mulaik
Affiliation:
University of Tennessee and Georgia Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

Kaiser’s iterative algorithm for the varimax rotation fails when (a) there is a substantial cluster of test vectors near the middle of each bounding hyperplane, leading to non-bounding hyperplanes more heavily overdetermined than those at the boundaries of the configuration of test vectors, and/or (b) there are appreciably more than m (m factors) tests whose loadings on one of the factors of the initial F- matrix, usually the first, are near-zero, leading to overdetermination of the hyperplane orthogonal to this initial F- axis before rotation. These difficulties are overcome by weighting the test vectors, giving maximum weights to those likely to be near the primary axes, intermediate weights to those likely to be near hyperplanes but not near primary axes, and near-zero weights to those almost collinear with or almost orthogonal to the first initial F- axis. Applications to the Promax rotation are discussed, and it is shown that these procedures solve Thurstone’s hitherto intractable “invariant” box problem as well as other more common problems based on real data.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 2 , June 1975 , pp. 183 - 195
Copyright
Copyright © 1975 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

The research on which this paper is based was supported by Grant No. GJ-36029 from the National Science Foundation. The computer programming was done by Mr. Richard C. Durfee of the Oak Ridge National Laboratory.

References

Butler, J. M.. Simplest data factors and simple structure in factor analysis. Educational and Psychological Measurement, 1964, 24, 755–763.CrossRefGoogle Scholar
Cureton, E. E. and Mulaik, S. A.. On simple structure and the solution to Thurstone’s “invariant” box problem. Multivariante Behaviorial Research, 1971, 6, 375–387.CrossRefGoogle ScholarPubMed
Eber, H. E.. Maxplane meets Thurstone’s “factorially invariant” box problem. Multivariate Behavioral Research, 1968, 3, 249–254.CrossRefGoogle ScholarPubMed
Harman, H. H.. Modern Factor Analysis, 1960, Chicago: University of Chicago Press.Google Scholar
Harris, C. W. and Kaiser, H. F.. Oblique factor analytic solutions by orthogonal transformations. Psychometrika, 1964, 29, 347–362.CrossRefGoogle Scholar
Hendrickson, A. E. and White, P. O.. Promax: a quick method for rotation to oblique simple structure. British Journal of Statistical Psychology, 1964, 17, 65–70.CrossRefGoogle Scholar
Kaiser, H. F.. The varimax criterion for analytic rotation in factor analysis. Psychometrika, 1958, 23, 187–200.CrossRefGoogle Scholar
Landahl, H. D.. Centroid orthogonal transformations. Psychometrika, 1938, 3, 219–223.CrossRefGoogle Scholar
Thurstone, L. L.. Multiple Factor Analysis, 1947, Chicago: University of Chicago Press.Google Scholar