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Asymptotic Distributions of the Estimators of Communalities in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Masanori Ichikawa
Masanori Ichikawa*
Affiliation:
Tokyo University of Foreign Studies
*
Requests for reprints should be sent to Masanori Ichikawa, Tokyo University of Foreign Studies, 4-51-21 Nishi-ga-Hara, Kita-Ku, Tokyo 114, JAPAN.
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Abstract

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that the common practice of equating the asymptotic standard error of the communality estimate to the unique variance estimate is correct for standardized communality but not correct for unstandardized communality. In a Monte Carlo simulation the accuracy of the normal approximation to the distributions of the estimators are assessed when the sample size is 150 or 300.

Keywords

factor analysiscommunalityasymptotic distributionmaximum likelihood methodMonte Carlo
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 3 , September 1992 , pp. 399 - 404
Copyright
Copyright © 1992 The Psychometric Society

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Footnotes

This study was carried out in part under the ISM Cooperative Research Program (90-ISM-CRP-9).

References

Anderson, T. W. (1984). An introduction to multivariate statistical analysis 2nd ed.,, New York: Wiley.Google Scholar
Anderson, T. W., Rubin, H. (1956). Statistical inference in factor analysis. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 5, 111–150.Google Scholar
Boomsma, A. (1985). Nonconvergence, improper solutions, and starting values in LISREL maximum likelihood estimation. Psychometrika, 50, 229–242.CrossRefGoogle Scholar
Box, G. E. P., Muller, M. E. (1958). A note on the generation of random normal deviates. Annals of Mathematical Statistics, 29, 610–611.CrossRefGoogle Scholar
Francis, I. (1974). Factor analysis: fact or fabrication. Mathematical Chronicle, 3, 9–44.Google Scholar
Fushimi, M. (1989). Ransuu [Random number], Tokyo: University of Tokyo Press.Google Scholar
Jennrich, R. I., Thayer, D. T. (1973). A note on Lawley's formulas for standard errors in maximum likelihood factor analysis. Psychometrika, 38, 571–580.CrossRefGoogle Scholar
Lawley, D. N. (1967). Some new results in maximum likelihood factor analysis. Proceedings of the Royal Society of Edinburgh, Series A, 67, 256–264.Google Scholar
Lawley, D. N., Maxwell, A. E. (1971). Factor analysis as a statistical method 2nd ed.,, London: Butterworth.Google Scholar
Seber, G. A. F. (1984). Multivariate observations, New York: Wiley.CrossRefGoogle Scholar