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The Harris-Kaiser Independent Cluster Rotation as a Method for Rotation to Simple Component Weights

Published online by Cambridge University Press:  01 January 2025

Henk A. L. Kiers  and
Jos M. F. Ten Berge
Henk A. L. Kiers*
Affiliation:
University of Groningen
Jos M. F. Ten Berge
Affiliation:
University of Groningen
*
Please send requests for reprints to Henk A. L. Kiers, Department of Psychology (P/OP), Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS.
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Abstract

Procedures for oblique rotation of factors or principal components typically focus on rotating the pattern matrix such that it becomes optimally simple. An important oblique rotation method that does so is Harris and Kaiser's (1964) independent cluster (HKIC) rotation. In principal components analysis, a case can be made for interpreting the components on the basis of the component weights rather than on the basis of the pattern, so it seems desirable to rotate the components such that the weights rather than the pattern become optimally simple. In the present paper, it is shown that HKIC rotates the components such that both the pattern and the weights matrix become optimally simple. In addition, it is shown that the pattern resulting from HKIC rotation is columnwise proportional to the associated weights matrix, which implies that the interpretation of the components does not depend on whether it is based on the pattern or on the component weights matrix. It is also shown that the latter result only holds for HKIC rotation and slight modifications of it.

Keywords

simple structureoblique rotationprincipal components analysis
Type
Original Paper
Information
Psychometrika , Volume 59 , Issue 1 , March 1994 , pp. 81 - 90
Copyright
Copyright © 1994 The Psychometric Society

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Footnotes

This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to an anonymous reviewer for the correction of some disturbing errors in the original manuscript.

References

Brogden, H. E. (1969). Pattern, structure, and the interpretation of factors. Psychological Bulletin, 72, 375–378.CrossRefGoogle Scholar
Crawford, C. B., Ferguson, G. A. (1970). A general rotation criterion and its use in orthogonal rotation. Psychometrika, 35, 321–332.CrossRefGoogle Scholar
Ferguson, G. A. (1954). The concept of parsimony in factor analysis. Psychometrika, 19, 281–290.CrossRefGoogle Scholar
Gorsuch, R. L. (1974). Factor Analysis, Philadelphia: Saunders.Google Scholar
Hakstian, A. R. (1971). A comparative evaluation of several prominent methods of oblique factor transformation. Psychometrika, 36, 175–193.CrossRefGoogle Scholar
Harman, H. H. (1967). Modern factor analysis 2nd ed.,, Chicago: University of Chicago Press.Google Scholar
Harris, R. J. (1975). A primer of multivariate statistics, New York: Academic Press.Google Scholar
Harris, C. W., Kaiser, H. F. (1964). Oblique factor analytic solutions by orthogonal transformations. Psychometrika, 29, 347–362.CrossRefGoogle Scholar
Hendrickson, A. E., White, P. O. (1964). PROMAX: A quick method for rotation to oblique simple structure. British Journal of Statistical Psychology, 17, 65–70.CrossRefGoogle Scholar
Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200.CrossRefGoogle Scholar
Millsap, R. E., Meredith, W. (1988). Component analysis in cross-sectional and longitudinal data. Psychometrika, 53, 123–134.CrossRefGoogle Scholar
Mulaik, S. A. (1972). The foundations of factor analysis, New York: McGraw-Hill.Google Scholar
ten Berge, J. M. F. (1986). Some relationships between descriptive comparisons of components from different studies. Multivariate Behavioral Research, 21, 29–40.CrossRefGoogle ScholarPubMed