Hostname: page-component-f554764f5-rvxtl Total loading time: 0 Render date: 2025-04-10T08:00:08.383Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Equivalence of Two Oblique Congruence Rotation Methods, and Orthogonal Approximations

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge
Jos M. F. ten Berge*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M. F. ten Berge, Psychologisch lnstituut, Oude Boteringestraat 34, Groningen, Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

Tucker's method of oblique congruence rotation is shown to be equivalent to a procedure by Meredith. This implies that Monte Carlo studies on congruence by Nesselroade, Baltes and Labouvie and by Korth and Tucker are highly comparable. The problem of rotating two matrices orthogonally to maximal congruence has not yet been solved. An approximate solution to this problem can be derived from Tucker's method. Even better results can be obtained from a Procrustes rotation followed by rotation to simple structure.

Keywords

factor-matching
Type
Notes And Comments
Information
Psychometrika , Volume 44 , Issue 3 , September 1979 , pp. 359 - 364
Copyright
Copyright © 1979 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.)

Article purchase

Temporarily unavailable

References

References Notes

Ten Berge, J. M. F. Optimizing factorial invariance. Unpublished doctoral dissertation University of Groningen, Department of Psychology, 1977.Google Scholar
Tucker, L. R. A method for synthesis of factor analysis studies, 1951, Washington D. C.: Department of the Army.CrossRefGoogle Scholar

References

Cliff, N. Orthogonal rotation to congruence. Psychometrika, 1966, 31, 33–42.CrossRefGoogle Scholar
Evans, G. T. Transformation of factor matrices to achieve congruence. British Journal of Mathematical and Statistical Psychology, 1971, 24, 22–48.CrossRefGoogle Scholar
Fischer, G. H. & Roppert, J. Ein Verfahren der Transformationsanalyse faktorenanalytischer Ergebnisse. In Roppert, J. & Fischer, G. H. (Eds.), Linear Strukturen in Mathematik und Statistik, 1965, Wien/Würzburg: Physika-Verlag.Google Scholar
Gibson, W. A. Properties and applications of Gramian factoring. Psychometrika, 1967, 32, 425–434.CrossRefGoogle Scholar
Horst, P. Factor analysis of data matrices, 1965, New York: Holt.Google Scholar
Kettenring, J. R. Canonical analysis of several sets of variables. Biometrika, 1971, 58, 433–451.CrossRefGoogle Scholar
Korth, B. & Tucker, L. R. The distribution of chance congruence coefficients from simulated data. Psychometrika, 1975, 40, 361–372.CrossRefGoogle Scholar
Meredith, W. Rotation to achieve factorial invariance. Psychometrika, 1964, 29, 187–206.CrossRefGoogle Scholar
Nesselroade, J. R., Baltes, P. B. & Labouvie, E. W. Evaluating factor invariance in oblique space: Baseline data generated from random numbers. Multivariate Behavioral Research, 1971, 6, 233–241.CrossRefGoogle ScholarPubMed
Taylor, P. A. The use of factor models in curriculum evaluation: A mathematical model relating two factor structures. Educational and Psychological Measurement, 1967, 27, 305–321.CrossRefGoogle Scholar
Ten Berge, J. M. F. Orthogonal procrustes rotation for two or more matrices. Psychometrika, 1977, 42, 267–276.CrossRefGoogle Scholar