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Two-Matrix Orthogonal Rotation Procedures

Published online by Cambridge University Press:  01 January 2025

A. Ralph Hakstian
A. Ralph Hakstian*
Affiliation:
University of British Columbia
*
Requests for reprints should be sent to A. Ralph Hakstian, Department of Psychology, University of British Columbia, Vancouver, British Columbia, Canada.
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Abstract

Examples are presented in which it is either desirable or necessary to transform two sets of orthogonal axes to simple structure positions by means of the same transformation matrix. A solution is then outlined which represents a two-matrix extension of the general “orthomax” orthogonal rotation criterion. In certain circumstances, oblique two-matrix solutions are possible using the procedure outlined and the Harris-Kaiser [1964] logic. Finally, an illustrative example is presented in which the preceding technique is applied in the context of an inter-battery factor analysis.

Keywords

factor transformationsimple structuresimultaneous rotation of matrices
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 2 , June 1976 , pp. 267 - 272
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

The work reported herein was supported by Grant S72-1886 from the Canada Council. The author acknowledges the helpful contributions of Nancy Reid and Lawrence Ward to parts of this paper.

References

Cliff, N. Orthogonal rotation to congruence. Psychometrika, 1966, 31, 33–42.CrossRefGoogle Scholar
Hakstian, A. R. Procedures for the factor analytic treatment of measures obtained on different occasions. British Journal of Mathematical and Statistical Psychology, 1973, 26, 219–239.CrossRefGoogle Scholar
Hakstian, A. R., and Cattell, R. B. An examination of inter-domain relationships among some ability and personality traits. Educational and Psychological Measurement, in press.Google Scholar
Harris, C. W., and Kaiser, H. F. Oblique factor analytic solutions by orthogonal transformations. Psychometrika, 1964, 29, 347–362.CrossRefGoogle Scholar
Horst, P. Matrix algebra for social scientists, 1963, New York: Holt, Rinehart and Winston.Google Scholar
Kaiser, H. F. The varimax criterion for analytic rotation in factor analysis. Psychometrika, 1958, 23, 187–200.CrossRefGoogle Scholar
Meredith, W. Rotation to achieve factorial invariance. Psychometrika, 1964, 29, 187–206.CrossRefGoogle Scholar
Schönemann, P. H. A generalized solution of the orthogonal Procrustes problem. Psychometrika, 1966, 31, 1–10.CrossRefGoogle Scholar
Tucker, L. R. An inter-battery method of factor analysis. Psychometrika, 1958, 23, 111–135.CrossRefGoogle Scholar