A rationale and test for the number of factors in factor analysis
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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.
KeywordsPublic Policy Correlation Matrix Statistical Theory Latent Root Sampling Error
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- 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 Unpublished doctoral dissertation, Univ.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.Google 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