Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-09T19:52:14.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Measures of Invariance and Comparability in Factor Analysis for Fixed Variables

Published online by Cambridge University Press:  01 January 2025

Samuel R. Pinneau  and
Albert Newhouse
Samuel R. Pinneau
Affiliation:
San Fernando Valley State College
Albert Newhouse
Affiliation:
University of Houston
Get access Rights & Permissions [Opens in a new window]

Abstract

New procedures are presented for measuring invariance and matching factors for fixed variables and for fixed or different subjects. Two of these, the coefficient of invariance for factor loadings and the coefficient of factor similarity, utilize factor scores computed from the different sets of factor loadings and one of the original standard score matrices. Another, the coefficient of subject invariance, is obtained by using one of the sets of factor loadings in conjunction with the different standard score matrices. These coefficients are correlations between factor scores of the appropriate matrices. When the best match of factors is desired, rather than degree of resemblance, the method of assignment is proposed.

Information

Type
Original Paper
Information
Psychometrika , Volume 29 , Issue 3 , September 1964 , pp. 271 - 281
Copyright
Copyright © 1964 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

Burt, C. Factor analysis and canonical correlations. Brit. J. statist. Psychol., 1949, 1, 95–106.CrossRefGoogle Scholar
Cattell, R. B. Factor analysis, New York: Harper, 1952.Google Scholar
Greville, T. N. E. Some applications of the pseudoinverse of a matrix. SIAM Review, 1960, 2, 15–22.CrossRefGoogle Scholar
Haggard, E. A. Intraclass correlation and the analysis of variance, New York: Dryden, 1958.Google Scholar
Harman, H. H. Modern factor analysis, Chicago: Univ. Chicago Press, 1960.Google Scholar
Henrysson, S. Applicability of factor analysis in the behavioral sciences: A methodological study, Stockholm: Almqvist and Wiksell, 1957.Google Scholar
Horst, P. Relations amongm sets of measures. Psychometrika, 1961, 26, 129–149.10.1007/BF02289710CrossRefGoogle Scholar
Horst, P. Generalized canonical correlations and their applications to experimental data. J. clin. Psychol., 1961, Monograph Supplement No. 14, 331–347.10.1002/1097-4679(196110)17:4<331::AID-JCLP2270170402>3.0.CO;2-D3.0.CO;2-D>CrossRefGoogle ScholarPubMed
Horst, P. Matrix algebra for social scientists, New York: Holt, Rinehart and Winston, 1963.Google Scholar
Silver, R. An algorithm for the assignment problem. Comm. ACM, 1960, 3, 605–606.10.1145/367436.367476CrossRefGoogle Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Tucker, L. R. A method for synthesis of factor analysis studies, Washington, D. C.: Department of the Army, 1951.10.21236/AD0047524CrossRefGoogle Scholar
Wrigley, C. S. Objectivity in factor analysis. Educ. psychol. Measmt, 1958, 18, 463–476.CrossRefGoogle Scholar
Wrigley, C. S. and Neuhaus, J. O. The matching of two sets of factors. Amer. Psychologist, 1955, 10, 418–419.Google Scholar