Some recent Developments in Factor Analysis and the Search for proper Communalities
This paper describes recent results on factor analytic theory which involve the so-called Ledermann bound, and discusses theoretical properties of Minimum Rank Factor Analysis as an alternative to Iterative Principal Factor Analysis and exploratory Maximum Likelihood Factor Analysis. In terms of the residual eigenvalues, the three methods have closely related object functions, and will often give highly similar solutions in practice. Nevertheless, there are important differences between the methods. The most notable points are that Maximum Likelihood Factor Analysis is a method of fitting a statistical model, and that Minimum Rank Factor Analysis yields communalities in the classical sense, thus showing how much of the common variance is explained with any given number of factors.
Key wordsFactor analysis proper solutions Ledermann bound
Unable to display preview. Download preview PDF.
- Anderson, T.W., Rubin, H. (1956). Statistical inference in factor analysis. In J. Neyman (Ed.): Proceedings of the third Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, 5, 111–150.Google Scholar
- Bentler, P.M.,Ramshidian, M. (1994). Gramian matrices in covariance structure analysis. Applied Psychological Measurement, 18, 79–94.Google Scholar
- Bentler, P.M. (1995). EQS Structural Equation Program Manual. Multivariate Software, Encino (Cal.).Google Scholar
- Cudeck, R., Henly, S.J. (1991). Model selection in covariance structure analysis and the problem of sample size: A clarification. Psychological Bulletin,, 109, 512–519.Google Scholar
- Harman, H.H. (1967). Modern factor analysis. Chicago: The University of Chicago Press.Google Scholar
- Ihara, M.,Kano, Y. (1986). A new estimator of the uniqueness in factor analysis. Psychometrika, 51, 563–566.Google Scholar
- Joreskog, KG., Sorbom, D. (1996). LISREL 8: Users reference guide. Scientific Software Incorporation, Chicago.Google Scholar
- Mulaik, S.A. (1986). Factor analysis and Psychometrika: Major developments. Psychometrika, 51, 23–33.Google Scholar
- Shapiro, A. (1985). Identifiability of factor analysis: Some results and open problems. Linear Algebra and its Applications, 70, 1–7.Google Scholar
- Wilson, E. B.,Worcester, J. (1939). The resolution of six tests into three general factors. Proc. National Academy of Sciences, U.S.A., 25, 73–77.Google Scholar