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A General Rotation Criterion and Its Use in Orthogonal Rotation

Published online by Cambridge University Press:  01 January 2025

Charles B. Crawford  and
George A. Ferguson
Charles B. Crawford
Affiliation:
McGill University, Montreal
George A. Ferguson
Affiliation:
McGill University, Montreal
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Abstract

Measures of test parsimony and factor parsimony are defined. Minimizing their weighted sum produces a general rotation criterion for either oblique or orthogonal rotation. The quartimax, varimax and equamax criteria are special cases of the expression. Two new criteria are developed. One of these, the parsimax criterion, apparently gives excellent results. It is argued that one of the most important factors bearing on the choice of a rotation criterion for a particular problem is the amount of information available on the number of factors that should be rotated.

Type
Original Paper
Information
Psychometrika , Volume 35 , Issue 3 , September 1970 , pp. 321 - 332
Copyright
Copyright © 1970 The Psychometric Society

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Footnotes

*

This research was supported by the National Research Council of Canada research grant 291-13 to Dr. G. A. Ferguson.

References

Carroll, J. B. An analytical solution for approximating simple structure in factor analysis. Psychometrika, 1953, 18, 23–38.Google Scholar
Cooley, W. W. & Lohnes, P. R. Multivariate procedures for the behavioral sciences, 1962, New York: John Wiley & Sons.Google Scholar
Ferguson, G. A. The concept of parsimony in factor analysis. Psychometrika, 1954, 19, 281–290.CrossRefGoogle Scholar
Harman, H. Modern factor analysis, 1960, Chicago: University of Chicago Press.Google Scholar
Harman, H. Modern factor analysis, 2nd edition, Chicago: University of Chicago Press, 1967.Google Scholar
Kaiser, H. F. The varimax criterion for analytic rotation in factor analysis. Psychometrika, 1958, 23, 187–200.Google Scholar
Kaiser, H. F. Varimax rotation for primary mental abilities. Psychometrika, 1960, 25, 153–158.CrossRefGoogle Scholar
Kaiser, H. F. Psychometric approaches to factor analysis. Paper presented at the Invitational Conference on Testing Problems, Princeton, N. J.: October, 1964.Google Scholar
Neuhaus, J. O. & Wrigley, C. The quartimax method: an analytical approach to orthogonal simple structure. British Journal of Statistical Psychology, 1954, 7, 81–91.Google Scholar
Saunders, D. R. An analytic method for rotation to orthogonal simple structure. Princeton, Educational Testing Service Research Bulletin, 53-10, 1953.CrossRefGoogle Scholar
Saunders, D. R. Trans-varimax: some properties of the ratiomax and equamax criteria for blind orthogonal rotation. Paper read at American Psychological Association Meeting, St. Louis, September 5, 1962.Google Scholar