A rationale and test for the number of factors in factor analysis
- 3k Downloads
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
Unable to display preview. Download preview PDF.
- 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 Unpublished doctoral dissertation, Univ.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