Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-13T10:38:26.743Z Has data issue: false hasContentIssue false
  • English
  • Français

Procrustes Matching by Congruence Coefficients

Published online by Cambridge University Press:  01 January 2025

Bruce Korth and
L.R Tucker
Bruce Korth*
Affiliation:
University of Illinois at Chicago Circle
L.R Tucker
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Dr. Bruce Korth, Department of Psychology, University of Illinois at Chicago Circle, Box 4348, Chicago, Illinois 60680
Get accessRights & Permissions [Opens in a new window]

Abstract

Matching by Procrustes methods involves the transformation of one matrix to match with another. A special least squares criterion, the congruence coefficient, has advantages as a criterion for some factor analytic interpretations. A Procrustes method maximizing the congruence coefficient is given. This solution is identical to Mosier's [1939] approximate solution, but is an exact solution for maximum congruence.

Keywords

factor analysis

Information

Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 4 , December 1976, pp. 531 - 535
Copyright
Copyright © 1976 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

Reference Note

Tucker, L. R. A method of synthesis of factor analysis studies, 1951, Washington, D.C.: Department of the Army.CrossRefGoogle Scholar

References

Burt, C. Factor analysis and canonical correlations. British Journal of Psychology, Statistical Section, 1949, 1, 95–106.CrossRefGoogle Scholar
Cattell, R. B. Personality and motivation, structure and measurement, 1957, Yonkers-on-Hudson, New York: World Book.Google Scholar
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, 22, 24–48.Google Scholar
Horst, P. A non-graphical method for transforming an arbitrary factor matrix into a simple structure factor matrix. Psychometrika, 1941, 6, 79–99.CrossRefGoogle Scholar
Korth, B. A. and Tucker, L. R. The distribution of chance congruence coefficients from simulated data. Psychometrika, 1975, 40, 361–372.CrossRefGoogle Scholar
Lawley, D. W. and Maxwell, A. E. Factor transformation methods. British Journal of Mathematical and Statistical Psychology, 1964, 17, 97–103.CrossRefGoogle Scholar
Mosier, C. I. Determining a simple sturcture when loadings for certain tests are known. Psychometrika, 1939, 4, 149–162.CrossRefGoogle Scholar
Pinneau, S. R. and Newhouse, A. Measures of invariance and comparability in factor analysis for fixed variables. Psychometrika, 1964, 29, 271–281.CrossRefGoogle Scholar
Thurstone, L. L. Multiple factor analysis: A development and expansion of the vectors of the mind, 1947, Chicago: University of Chicago Press.Google Scholar