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A Rationale and Test for the Number of Factors in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

John L. Horn
John L. Horn*
Affiliation:
University of Denver
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Abstract

It is suggested that if Guttman’s latent-root-one lower bound estimate for the rank of a correlation matrix is accepted as a psychometric upper bound, following the proofs and arguments of Kaiser and Dickman, then the rank for a sample matrix should be estimated by subtracting out the component in the latent roots which can be attributed to sampling error, and least-squares “capitalization” on this error, in the calculation of the correlations and the roots. A procedure based on the generation of random variables is given for estimating the component which needs to be subtracted.

Information

Type
Original Paper
Information
Psychometrika , Volume 30 , Issue 2 , June 1965 , pp. 179 - 185
Copyright
Copyright © 1965 Psychometric Society

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Footnotes

*

I wish to acknowledge the valuable help given by J. Jaspers and L. G. Humphreys in the development of the ideas presented in this paper.

References

Anderson, T. W. An introduction to multivariate statistical analysis, New York: Wiley, 1958.Google Scholar
Dickman, K. W. Factorial validity of a rating instrument. Unpublished doctoral dissertation, Univ. Illinois, 1960.Google Scholar
Guttman, L. Some necessary conditions for common-factor analysis. Psychometrika, 1954, 19, 149–161.CrossRefGoogle Scholar
Kaiser, H. The application of electronic computers to factor analysis. (Paper read at a symposium on application of computers to psychological problems. Meeting of Amer. Psychol. Ass., 1959).Google Scholar
Kendall, M. G. and Stuart, A. The advanced theory of statistics (Vols. I and II), London, Eng.: Griffin, 1958.Google Scholar
Rao, C. R. Advanced statistical methods in biometric research, New York: Wiley, 1952.Google Scholar