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An Empirical Study of the Factor Analysis Stability Hypothesis

Published online by Cambridge University Press:  01 January 2025

Harold P. Bechtoldt
Harold P. Bechtoldt*
Affiliation:
University of Iowa
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Abstract

Note is taken of four related sources of confusion as to the usefulness of Thurstone's factor analysis model and of their resolutions. One resolution uses Tucker's distinction between exploratory and confirmatory analyses. Eight analyses of two sets of data demonstrate the procedures and results of a confirmatory study with statistical tests of some, but not all, relevant hypotheses in an investigation of the stability (invariance) hypothesis. The empirical results provide estimates, as substitutes for unavailable sampling formulations, of effects of variation in diagonal values, in method of factoring, and in samples of cases. Implications of these results are discussed.

Information

Type
Original Paper
Information
Psychometrika , Volume 26 , Issue 4 , December 1961 , pp. 405 - 432
Copyright
Copyright © 1961 The Psychometric Society

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Footnotes

*

The computational costs of this study were defrayed, in part, by a research small grant M-1922 from the National Institute of Health, and, in part, by support under project 176-0002 by the University of Iowa Computing Center, Dr. J. P. Dolch, Director. The assistance of Dr. Kern Dickman and Mr. Leonard Wevrick of the University of Illinois and of Mr. Norman Luther of the University of Iowa in handling the computing problems is gratefully acknowledged.

References

Anderson, T. W. Introduction to multivariate statistical analysis, New York: Wiley, 1958.Google Scholar
Anderson, T. W. and Rubin, H. Statistical inference in factor analysis. Proceedings of the Third Berkeley Symposium on mathematical statistics and probability. Vol. 5. Berkeley: Univ. California Press, 1956, 111–150.Google Scholar
Bargmann, R. Signifikanzuntersuchungen der einfachen struktur in der faktorenanalyse. Sonderdruck, Mit. d. Math. Stat., Wurzburg: Physica-Verlag, 1954.Google Scholar
Bargmann, R. A study of independence and dependence in multivariate normal analysis. Univ. North Carolina, Inst. Statist. Mimeo. Ser. No. 186, 1957.Google Scholar
Bartlett, M. S. Tests of significance in factor analysis. Brit. J. Psychol., Statist. Sec., 1950, 3, 77–85.CrossRefGoogle Scholar
Bechtoldt, H. P. Factor analysis of the Airman Classification Battery with civilian reference tests. HRRC res. Bull., 1953, 53–59.Google Scholar
Bechtoldt, H. P. Statistical tests of hypotheses in confirmatory factor analysis. Amer. Psychologist, 1958, 13, 380–380.Google Scholar
Bechtoldt, H. P. Construct validity: a critique. Amer. Psychologist, 1959, 14, 619–629.CrossRefGoogle Scholar
Bechtoldt, H. P. Comments on “Intraclass correlation vs. factor analytic techniques for determining groups of profiles. Psychol.Bull., 1960, 57, 157–162.CrossRefGoogle ScholarPubMed
Bechtoldt, H. P. and Moren, R. I. Correlational analyses of test-retest data with a thirty-year intertrial interval. Proc. Iowa Acad. Sci., 1957, 64, 514–519.Google Scholar
Bergmann, G. The logic of psychological concepts. Phil. Sci., 1951, 18, 93–110.CrossRefGoogle Scholar
Bergmann, G. Philosophy of science, Madison: Univ. Wisconsin Press, 1957.Google Scholar
Brodbeck, M. The philosophy of science and educational research. Rev. educ. Res., 1957, 27, 427–440.Google Scholar
Brodbeck, M. Models, meaning, and theories. In Gross, L. (Eds.), Symposium on sociological theory, Evanston: Row Peterson, 1958.Google Scholar
Burt, C. L. Tests of significance in factor analysis. Brit. J. Psychol., Statist. Sec., 1952, 5, 109–133.CrossRefGoogle Scholar
Carroll, J. B. An analytic solution for approximating simple structure in factor analysis. Psychometrika, 1953, 18, 23–38.CrossRefGoogle Scholar
Cattell, R. B. Extracting the correct number of factors in factor analysis. Educ. psychol. Measmt, 1958, 18, 791–840.CrossRefGoogle Scholar
Cureton, E. E. The principal compulsions of factor-analysts. Harvard educ. Rev., 1939, 9, 287–295.Google Scholar
Cureton, E. E. A note on the use of Burt's formula for estimating factor significance. Brit. J. statist. Psychol., 1955, 8, 28–28.CrossRefGoogle Scholar
Dahlstrom, W. G. Research in clinical psychology: factor analytic contributions. J. clin. Psychol., 1957, 13, 211–220.3.0.CO;2-4>CrossRefGoogle ScholarPubMed
Eysenck, H. J. The logical basis of factor analysis. Amer. Psychologist, 1953, 8, 105–114.CrossRefGoogle Scholar
Federer, W. T. Testing proportionality of covariance matrices. Ann. math. Statist., 1951, 22, 102–106.CrossRefGoogle Scholar
French, J. W. The description of aptitude and achievement tests in terms of rotated factors, Chicago: Univ. Chicago Press, 1951.Google Scholar
French, J. W. Manual for kit of selected tests for reference aptitude and achievement factors, Princeton: Educ. Testing Serv., 1954.Google Scholar
Guilford, J. P. Psychometric methods. (2nd ed.), New York: McGraw-Hill, 1954.Google Scholar
Guilford, J. P. Three faces of intellect. Amer. Psychologist, 1959, 14, 469–479.CrossRefGoogle Scholar
Gulliksen, H. Theory of mental tests, New York: Wiley, 1950.CrossRefGoogle Scholar
Gulliksen, H. and Wilks, S. S. Regression tests for several samples. Psychometrika, 1950, 15, 91–114.CrossRefGoogle ScholarPubMed
Guttman, L. General theory and methods for matrix factoring. Psychometrika, 1944, 9, 1–16.CrossRefGoogle Scholar
Guttman, L. Multiple group methods for common factor analysis: their basis, computation, and interpretation. Psychometrika, 1952, 17, 209–222.CrossRefGoogle Scholar
Guttman, L. “Best possible” systematic estimates of communalities. Psychometrika, 1956, 21, 273–285.CrossRefGoogle Scholar
Guttman, L. What lies ahead for factor analysis. Educ. psychol. Measmt, 1958, 18, 497–515.CrossRefGoogle Scholar
Guttman, L. To what extent can communalities reduce rank?. Psychometrika, 1958, 23, 297–308.CrossRefGoogle Scholar
Henrysson, S. Applicability of factor analysis in the behavioral sciences, Stockholm: Almqvist and Wiksell, 1957.Google Scholar
Holzinger, K. J. and Harman, H. Factor analysis, Chicago: Univ. Chicago Press, 1941.Google Scholar
Howe, W. G. Some contributions to factor analysis. Oak Ridge National Laboratory. ORNL No. 1919, 1955.Google Scholar
Kaiser, H. F. The application of electronic computers to factor analysis. Educ. psychol. Measmt, 1960, 20, 141–151.CrossRefGoogle Scholar
Koopmans, T. C. and Reiersöl, O. The identification of structural characteristics. Ann. math. Statist., 1950, 21, 165–181.CrossRefGoogle Scholar
Lawley, D. N. The estimation of factor loadings by the method of maximum likelihood. Proc. roy. Soc. Edinburgh, 1940, 60, 64–82.CrossRefGoogle Scholar
Madansky, A. The fitting of straight lines when both variables are subject to error. J. Amer. statist. Ass., 1959, 54, 173–205.CrossRefGoogle Scholar
Maxwell, A. E. Statistical methods in factor analysis. Psychol. Bull., 1959, 56, 228–235.CrossRefGoogle ScholarPubMed
Michael, W. B. Symposium: The future of factor analysis. An over-view of the symposium. Educ. psychol. Measmt, 1958, 18, 455–461.CrossRefGoogle Scholar
McNemar, Q. On the sampling errors of factor loadings. Psychometrika, 1941, 6, 141–152.CrossRefGoogle Scholar
Peel, E. A. Factorial analysis as a psychological technique. Uppsala Symp. on Psychol. Factor Analysis, 1953, 7–22.Google Scholar
Pinzka, C. and Saunders, D. R. Analytical rotation to simple structure II. Extension to oblique solution, Princeton: Educ. Test Serv., 1954.Google Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–111.CrossRefGoogle Scholar
Rasch, G. On simultaneous factor analysis in several populations. Uppsala Symp. on Psychol. Factor Analysis, 1953, 65–71.Google Scholar
Reiersöl, O. On the identifiability of parameters in Thurstone's multiple-factor analysis. Psychometrika, 1950, 15, 121–149.CrossRefGoogle ScholarPubMed
Schmid, J. and Leiman, J. M. The development of hierarchical factor solutions. Psychometrika, 1957, 22, 53–61.CrossRefGoogle Scholar
Stukát, K. G. Suggestibility: a factorial and experimental analysis. (Acta Psychologica Gothoburgensia, II), Stockholm: Almqvist and Wiksell, 1958.Google Scholar
Thomson, G. The factorial analysis of human ability (5th ed.), Boston: Houghton Mifflin, 1953.Google Scholar
Thurstone, L. L. The vectors of mind, Chicago: Univ. Chicago Press, 1935.Google Scholar
Thurstone, L. L. Current misuse of the factorial methods. Psychometrika, 1937, 2, 73–76.CrossRefGoogle Scholar
Thurstone, L. L. Current issues in factor analysis. Psychol. Bull., 1940, 37, 189–236.CrossRefGoogle Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Thurstone, L. L. and Thurstone, T. G. Factorial studies of intelligence, Chicago: Univ. Chicago Press, 1941.Google Scholar
Thurstone, L. L. and Thurstone, T. G. Primary mental abilities (manual and tests), Chicago: Sci. Res. Assoc., 1950.Google Scholar
Tryon, R. C. Communality of a variable: formulation by cluster analysis. Psychometrika, 1957, 22, 241–259.CrossRefGoogle Scholar
Tryon, R. C. General dimensions of individual differences: cluster analysis vs. multiple factor analysis. Educ. psychol. Measmt, 1958, 18, 477–495.CrossRefGoogle Scholar
Tryon, R. C. Domain sampling formulation of cluster and factor analysis. Psychometrika, 1959, 24, 113–135.CrossRefGoogle Scholar
Tucker, L. R. The role of correlated factors in factor analysis. Psychometrika, 1940, 5, 141–152.CrossRefGoogle Scholar
Tucker, L. R. A method for synthesis of factor analysis studies, Washington, D. C.: Dept. Army: AGO, Personnel Res. Sec., 1951.CrossRefGoogle Scholar
Tucker, L. R. The objective definition of simple structure in linear factor analysis. Psychometrika, 1955, 20, 209–225.CrossRefGoogle Scholar
Tucker, L. R. An inter-battery method of factor analysis. Psychometrika, 1958, 23, 111–136.CrossRefGoogle Scholar
Wherry, R. J. Hierarchical factor solutions without rotation. Psychometrika, 1959, 24, 45–51.CrossRefGoogle Scholar
Wrigley, C. Objectivity in factor analysis. Educ. psychol. Measmt, 1958, 18, 463–476.CrossRefGoogle Scholar
Wrigley, C. The effect upon the communalities of changing the estimate of the number of factors. Brit. J. statist. Psychol., 1959, 12, 35–51.CrossRefGoogle Scholar
Young, G. and Householder, A. S. Factorial invariance and significance. Psychometrika, 1940, 5, 47–56.CrossRefGoogle Scholar