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The Varimax Criterion for Analytic Rotation in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Henry F. Kaiser
Henry F. Kaiser*
Affiliation:
University of Illinois
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Abstract

An analytic criterion for rotation is defined. The scientific advantage of analytic criteria over subjective (graphical) rotational procedures is discussed. Carroll's criterion and the quartimax criterion are briefly reviewed; the varimax criterion is outlined in detail and contrasted both logically and numerically with the quartimax criterion. It is shown that the normal varimax solution probably coincides closely to the application of the principle of simple structure. However, it is proposed that the ultimate criterion of a rotational procedure is factorial invariance, not simple structure –although the two notions appear to be highly related. The normal varimax criterion is shown to be a two-dimensional generalization of the classic Spearman case, i.e., it shows perfect factorial invariance for two pure clusters. An example is given of the invariance of a normal varimax solution for more than two factors. The oblique normal varimax criterion is stated. A computational outline for the orthogonal normal varimax is appended.

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 3 , September 1958 , pp. 187 - 200
Copyright
Copyright © 1958 The Psychometric Society

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Footnotes

*

Part of the material in this paper is from the writer's Ph.D. thesis. I am indebted to my committee, Professors F. T. Tyler, R. C. Tryon, and H. D. Carter, chairman, for many helpful suggestions and criticisms. Dr. John Caffrey suggested the name varimax, and wrote the original IBM 602A computer program for this criterion.

I am also indebted to the staff of the University of California Computer Center for help in programming the procedures described in the paper for their IBM 701 electronic computer. Since their installation is partially supported by a grant from the National Science Foundation, the assistance of this agency is acknowledged.

References

Carroll, J. B. An analytical solution for approximating simple structure in factor analysis. Psychometrika, 1953, 18, 23–38.CrossRefGoogle Scholar
Ferguson, G. A. The concept of parsimony in factor analysis. Psychometrika, 1954, 19, 281–290.CrossRefGoogle Scholar
Holzinger, K. J. and Harman, H. H. Factor analysis, Chicago: Univ. Chicago Press, 1941.Google Scholar
Kaiser, H. F. An analytic rotational criterion for factor analysis. Amer. Psychologist, 1955, 10, 438–438. (Abstract).Google Scholar
Kaiser, H. F. Note on Carroll's analytic simple structure. Psychometrika, 1956, 21, 89–92.CrossRefGoogle Scholar
Kaiser, H. F. The varimax method of factor analysis. Unpublished doctoral dissertation, Univ. California, 1956.Google Scholar
Neuhaus, J. O. and Wrigley, C. The quartimax method: an analytical approach to orthogonal simple structure. Brit. J. statist. Psychol., 1954, 7, 81–91.CrossRefGoogle Scholar
Saunders, D. R. An analytic method for rotation to orthogonal simple structure (pp. 53–10). Princeton: Educational Testing Service Research Bulletin, 1953.CrossRefGoogle Scholar
Thomson, G. H. The factorial analysis of human ability 5th ed., New York: Houghton Mifflin, 1951.Google Scholar
Thurstone, L. L. Theory of multiple factors, Ann Arbor: Edwards Bros., 1932.Google Scholar
Thurstone, L. L Primary mental abilities. Psychometric Monogr. No. 1, 1938.CrossRefGoogle Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar