Psychometrika

, Volume 30, Issue 2, pp 179–185

A rationale and test for the number of factors in factor analysis

  • John L. Horn
Article

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.

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References

  1. [1]
    Anderson, T. W.An introduction to multivariate statistical analysis. New York: Wiley, 1958.Google Scholar
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    Dickman, K. W. Factorial validity of a rating instrument. Unpublished doctoral dissertation, Univ. Illinois, 1960.Google Scholar
  3. [3]
    Guttman, L. Some necessary conditions for common-factor analysis.Psychometrika, 1954,19, 149–161.Google Scholar
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    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
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    Kendall, M. G. and Stuart, A.The advanced theory of statistics (Vols. I and II). London, Eng.: Griffin, 1958.Google Scholar
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    Rao, C. R.Advanced statistical methods in biometric research. New York: Wiley, 1952.Google Scholar

Copyright information

© Psychometric Society 1965

Authors and Affiliations

  • John L. Horn
    • 1
  1. 1.University of DenverUSA

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