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Testing a Simple Structure Hypothesis in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

K. G. Jöreskog*
Affiliation:
University of Uppsala, Sweden

Abstract

It is assumed that the investigator has set up a simple structure hypothesis in the sense that he has specified the zero loadings of the factor matrix. The maximum-likelihood method is used to estimate the factor matrix and the factor correlation matrix directly without the use of rotation methods, and the likelihood-ratio technique is used to test the simple structure hypothesis. Numerical examples are presented.

Type
Original Paper
Copyright
Copyright © 1966 Psychometric Society

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Footnotes

*

The work was supported by a grant (NSF-GB 1985) from the National Science Foundation to Educational Testing Service. Reproduction in whole or in part for any purpose of the United States Government is permitted.

The work was carried out when the author was Visiting Research Statistician at Educational Testing Service. The author wishes to thank Dr. Frederic M. Lord for many helpful suggestions throughout the course of this study.

References

Anderson, T. W. An introduction to multivariate statistical analysis, New York: Wiley, 1958.Google Scholar
Anderson, T. W. and Rubin, H. Statistical inference in factor analysis. In Neyman, J. (Eds.), Proceedings of the third Berkeley symposium on mathematical statistics and probability. Vol. V. Berkeley: Univ. Calif. Press, 1956, 111150.Google Scholar
Box, G. E. P. A general distribution theory for a class of likelihood criteria. Biometrika, 1949, 36, 317346.CrossRefGoogle ScholarPubMed
Davidon, W. C. Variable metric method for minimization. A.E.C. Research and Development Report, ANL 5990, Argonne National Laboratory, 1959.CrossRefGoogle Scholar
Finkel, R. W. The method of resultant descents for the minimization of an arbitrary function. Paper 71, Preprints of Papers Presented at 14th National Meeting of Association of Computing Machinery, 1959.CrossRefGoogle Scholar
Howe, W. G. Some contributions to factor analysis. Report No. ORNL-1919, Oak Ridge, Tenn.: Oak Ridge National Laboratory, 1955.Google Scholar
Jöreskog, K. G. Statistical estimation in factor analysis, Stockholm: Almqvist & Wiksell, 1963.Google Scholar
Jöreskog, K. G. Computer program for estimating and testing a simple structure hypothesis in factor analysis, Princeton, N.J.: Educ. Test. Serv., 1965.Google Scholar
Jöreskog, K. G. On rotation to a specified simple structure, Princeton, N. J.: Educ. Test. Serv., 1965.Google Scholar
Lawley, D. N. Estimation in factor analysis under various initial assumptions. Brit. J. statist. Psychol., 1958, 11, 112.CrossRefGoogle Scholar
Lawley, D. N. and Maxwell, A. E. Factor analysis as a statistical method, London: Butterworths, 1963.Google Scholar
Reiersøl, O. On the identifiability of parameters in Thurstone's multiple factor analysis. Psychometrika, 1950, 15, 121149.CrossRefGoogle ScholarPubMed
Spang, H. A. III A review of minimization techniques for nonlinear functions. SIAM Rev., 1962, 4, 343365.CrossRefGoogle Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Wilks, S. S. The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. math. Statist., 1938, 9, 6062.CrossRefGoogle Scholar