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Quartic Rotation Criteria and Algorithms

Published online by Cambridge University Press:  01 January 2025

Douglas B. Clarkson  and
Robert I. Jennrich
Douglas B. Clarkson*
Affiliation:
IMSL Incorporated
Robert I. Jennrich
Affiliation:
Department of Mathematics, University of California at Los Angeles
*
Requests for reprints should be sent to Douglas B. Clarkson, IMSL Inc., 2500 Park West Tower One, 2500 CityWest Boulevard, Houston, Texas 77042.
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Abstract

Most of the currently used analytic rotation criteria for simple structure in factor analysis are summarized and identified as members of a general symmetric family of quartic criteria. A unified development of algorithms for orthogonal and direct oblique rotation using arbitrary criteria from this family is given. These algorithms represent fairly straightforward extensions of present methodology, and appear to be the best methods currently available.

Keywords

factor analysissimple structurefactor loadingsplanar rotations
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 2 , June 1988 , pp. 251 - 259
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

The research done by R. I. Jennrich was supported by NSF Grant MCS-8301587.

References

Carroll, J. B. (1953). An analytical solution for approximating simple structure in factor analysis. Psychometrika, 18, 23–38.CrossRefGoogle Scholar
Carroll, J. B. (1957). Biquartimin criterion for rotation to oblique simple structure in factor analysis. Science, 126, 1114–1115.CrossRefGoogle ScholarPubMed
Carroll, J. B. (1960). IBM 704 program for generalized analytic rotation solution in factor analysis. Unpublished manuscript, Harvard University.Google Scholar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
Harman, H. H. (1960). Modern factor analysis, Chicago: University of Chicago Press.Google Scholar
Harman, H. H. (1976). Modern factor analysis 3rd ed.,, Chicago: University of Chicago Press.Google 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
Jennrich, R. I. (1970). Orthogonal Rotation Algorithms. Psychometrika, 35, 229–335.CrossRefGoogle Scholar
Jennrich, R. I., Sampson, P. F. (1966). Rotation for simple loadings. Psychometrika, 31, 313–323.CrossRefGoogle ScholarPubMed
Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200.CrossRefGoogle Scholar
Kaiser, H. F. (1959). Computer program for varimax rotation in factor analysis. Educational and Psychological Measurement, 19, 413–420.CrossRefGoogle Scholar
Luenberger, D. G. (1973). Introduction to linear and nonlinear programming, Reading: Addison-Wesley.Google Scholar
Nevels, K. (1986). A direct solution for pairwise rotations in Kaiser's varimax method. Psychometrika, 51, 327–329.CrossRefGoogle Scholar
Newhaus, J. O., Wrigley, C. (1954). The quartimax method: An analytic approach to orthogonal simple structure. British Journal of Mathematical and Statistical Psychology, 7, 81–91.CrossRefGoogle Scholar
Saunders, D. R. (1953). An analytic method for rotation to orthogonal simple structure, Princeton, NJ: Educational Testing Service.CrossRefGoogle Scholar
Saunders, D. R. (1961). The rationale for an “oblimax” method of transformation in factor analysis. Psychometrika, 26, 317–324.CrossRefGoogle Scholar
ten Berge, J. M. F. (1984). A joint treatment of varimax rotation and the problem of diagonalizing symmetric matricies simultaneously in the least-squares sense. Psychometrika, 43, 433–435.Google Scholar