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Rotation to Achieve Factorial Invariance

Published online by Cambridge University Press:  01 January 2025

William Meredith
William Meredith*
Affiliation:
University of California, Berkeley
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Abstract

Under certain conditions it is reasonable to assume that the same factor pattern matrix will describe the regression of observed on factor scores in different populations. However, ordinary factoring procedures will not reveal in general the existence of such a factor pattern matrix. Two procedures for rotating any number of factor pattern matrices based on different populations to conform to a single “best fitting” factor pattern matrix are developed in this paper. It is assumed that the same number of factors have been determined for each population. Both procedures will yield oblique results in the various populations. The procedures are illustrated with data taken from the 1939 Holzinger-Swineford monograph. Four groups of individuals are utilized.

Type
Original Paper
Information
Psychometrika , Volume 29 , Issue 2 , June 1964 , pp. 187 - 206
Copyright
Copyright © 1964 Psychometric Society

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References

Eckart, C. and Young, G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218.CrossRefGoogle Scholar
Harman, H. Modern factor analysis, Chicago: Univ. Chicago Press, 1960.Google Scholar
Holzinger, K. and Swineford, F. A study in factor analysis: The stability of a bi-factor solution, Chicago: Univ. Chicago Press, 1939.Google Scholar
Horst, P. Generalized canonical correlations and their application to experimental data. J. clin. Psychol., 1961, 14, 332–347.Google Scholar
Lawley, D. N. A note on Karl Pearson's selection formulae. Proc. roy. Soc. Edinburgh, 1943, 62, 28–30.Google Scholar
Meredith, W. Notes on factorial invariance. Psychometrika, 1964, 29, 177–186.CrossRefGoogle Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–112.CrossRefGoogle Scholar