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A Comparative Evaluation of Several Prominent Methods of Oblique Factor Transformation

Published online by Cambridge University Press:  01 January 2025

A. Ralph Hakstian
A. Ralph Hakstian*
Affiliation:
University of Alberta
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Abstract

The oblimax, promax, maxplane, and Harris-Kaiser techniques are compared. For five data sets, of varying reliability and factorial complexity, each having a graphic oblique solution (used as criterion), solutions obtained using the four methods are evaluated on (1) hyperplane-counts, (2) agreement of obtained with graphic within-method primary factor correlations and angular separations, (3) angular separations between obtained and corresponding graphic primary axes. The methods are discussed and ranked (descending order): Harris-Kaiser, promax, oblimax, maxplane. The Harris-Kaiser procedure—independent cluster version for factorially simple data, P'P proportional to Φ, with equamax rotations, for complex—is recommended.

Keywords

Public PolicyStatistical TheoryPrimary FactorComparative EvaluationFactor Correlation
Type
Original Paper
Information
Psychometrika , Volume 36 , Issue 2 , June 1971 , pp. 175 - 193
Copyright
Copyright © 1971 The Psychometric Society

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Footnotes

*

This paper is based upon part of the author's doctoral dissertation [Hakstian, 1969] completed at the University of Colorado. The author is greatly indebted to Dr. Gene V Glass, who, as thesis advisor, generously contributed his time, erudition, and encouragement.

References

Baehr, M. E. A comparison of graphic and analytic solutions for both oblique and orthogonal simple structures for factors of employee morale. Psychometrika, 1963, 28, 199–209.CrossRefGoogle Scholar
Bargmann, R. The statistical significance of simple structure in factor analysis. Frankfurt-Main: Hochschule fuer Internationale Paedagogische Forschung, 1953. Cited by R. B. Cattell, The meaning and strategic use of factor analysis. In Cattell, R. B. (Eds.), Handbook of multivariate experimental psychology, 1966, Chicago: Rand-McNally.Google Scholar
Burt, C. The factorial study of temperamental traits. British Journal of Psychology, Statistical Section, 1948, 1, 178–203.CrossRefGoogle Scholar
Butler, J. M. Simplest data factors and simple structure in factor analysis. Educational and Psychological Measurement, 1964, 24, 755–763.CrossRefGoogle Scholar
Carroll, J. B. An analytical solution for approximating simple structure in factor analysis. Psychometrika, 1953, 18, 23–38.CrossRefGoogle Scholar
Carroll, J. B. Biquartimin criterion for rotation to oblique simple structure in factor analysis. Science, 1957, 126, 1114–1115.CrossRefGoogle ScholarPubMed
Cattell, R. B., & Baggaley, A. R. The salient variable similarity index for factor matching. British Journal of Statistical Psychology, 1960, 13, 33–46.CrossRefGoogle Scholar
Cattell, R. B., Balcar, K. R., Horn, J. L., & Nesselroade, J. R. Factor matching procedures: An improvement of the s index; with tables. Educational and Psychological Measurement, 1969, 29, 781–792.CrossRefGoogle Scholar
Cattell, R. B., & Dickman, K. W. A dynamic model of physical influences demonstrating the necessity of oblique simple structure. Psychological Bulletin, 1962, 59, 389–400.CrossRefGoogle ScholarPubMed
Cattell, R. B., & Muerle, J. L. The “maxplane” program for factor rotation to oblique simple structure. Educational and Psychological Measurement, 1960, 20, 569–590.CrossRefGoogle Scholar
Coan, R. W. A comparison of oblique and orthogonal factor solutions. Journal of Experimental Education, 1959, 27, 151–166.CrossRefGoogle Scholar
Eber, H. W. Toward oblique simple structure: Maxplane. Multivariate Behavioral Research, 1966, 1, 112–125.CrossRefGoogle Scholar
Eyman, R. K., Dingman, H. F., & Meyers, C. E. Comparison of some computer techniques for factor analytic rotation. Educational and Psychological Measurement, 1962, 22, 201–214.CrossRefGoogle Scholar
Fruchter, B., & Novak, E. A comparative study of three methods of rotation. Psychometrika, 1958, 23, 211–221.CrossRefGoogle Scholar
Gorsuch, R. L. A comparison of biquartimin, maxplane, promax, and varimax. Unpublished manuscript, Vanderbilt University, 1968.Google Scholar
Hakstian, A. R. Methods of oblique factor transformation, 1969, Ann Arbor, Michigan: University Microfilms.Google Scholar
Harman, H. H. Modern factor analysis, 1960, Chicago: University of Chicago Press.Google Scholar
Harman, H. H. Modern factor analysis, 2nd ed., Chicago: University of Chicago Press, 1967.Google Scholar
Harris, C. W., & Kaiser, H. F. Oblique factor analytic solutions by orthogonal transformations. Psychometrika, 1964, 29, 347–362.CrossRefGoogle Scholar
Hendrickson, A. E., & White, P. O. PROMAX: A quick method for rotation to oblique simple structure. British Journal of Statistical Psychology, 1964, 17, 65–70.CrossRefGoogle Scholar
Horn, J. L. Second-order factors in questionnaire data. Educational and Psychological Measurement, 1963, 23, 117–134.CrossRefGoogle Scholar
Jennrich, R. I., & Sampson, P. F. Rotation for simple loadings. Psychometrika, 1966, 31, 313–323.CrossRefGoogle ScholarPubMed
Kaiser, H. F. The varimax criterion for analytic rotation in factor analysis. Psychometrika, 1958, 23, 187–200.CrossRefGoogle Scholar
Kaiser, H. F. Varimax solution for Primary Mental Abilities. Psychometrika, 1960, 25, 153–158.CrossRefGoogle Scholar
Kashiwagi, S. Geometric vector orthogonal rotation method in multiple-factor analysis. Psychometrika, 1965, 30, 515–530.CrossRefGoogle ScholarPubMed
Mosier, C. I. Determining a simple structure when loadings for certain tests are known. Psychometrika, 1939, 4, 149–162.CrossRefGoogle Scholar
Neuhaus, J. O., & Wrigley, C. The quartimax method: An analytic approach to orthogonal simple structure. British Journal of Statistical Psychology, 1954, 7, 81–91.CrossRefGoogle Scholar
Pinneau, S. R., & Newhouse, A. Measures of invariance and comparability in factor analysis for fixed variables. Psychometrika, 1964, 29, 271–281.CrossRefGoogle Scholar
Rimoldi, H. J. A. Study of some factors related to intelligence. Psychometrika, 1948, 13, 27–46.CrossRefGoogle ScholarPubMed
Saunders, D. R. The rationale for an “oblimax” method of transformation in factor analysis. Psychometrika, 1961, 26, 317–324.CrossRefGoogle Scholar
Schönemann, P. H. Varisim: A new machine method for orthogonal rotation. Psychometrika, 1966, 31, 235–248.CrossRefGoogle ScholarPubMed
Sokal, R. R. Thurstone's analytical method for simple structure and a mass modification thereof. Psychometrika, 1958, 23, 237–257.CrossRefGoogle Scholar
Tenopyr, M. L., & Michael, W. B. A comparison of two computer-based procedures of orthogonal analytic rotation with a graphical method when a general factor is present. Educational and Psychological Measurement, 1963, 23, 587–597.CrossRefGoogle Scholar
Thurstone, L. L.. Multiple-factor analysis, 1947, Chicago: University of Chicago Press.Google Scholar
Tucker, L. R. A method for synthesis of factor analysis studies, 1951, Washington, D. C.: Department of the Army.CrossRefGoogle Scholar
Wrigley, C., & Neuhaus, J. O. The matching of two sets of factors, 1955, Task A. Urbana, Illinois: University of Illinois.Google Scholar
Wrigley, C., Saunders, D. R., & Neuhaus, J. O. Application of the quartimax method of rotation to Thurstone's Primary Mental Abilities study. Psychometrika, 1958, 23, 151–170.CrossRefGoogle Scholar