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The Influence of Communality and N on the Sampling Distributions of Factor Loadings

Published online by Cambridge University Press:  01 January 2025

Roger Pennell
Roger Pennell*
Affiliation:
University of Southern California
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Abstract

The effects of N and communality on the variability of zero and nonzero factor loadings were assessed using a Monte Carlo approach. It was found that increasing N or communality resulted in decreased sampling error of individual factor loadings, but for zero loadings N was found to have the greatest influence. It was also found that distributions of factor loadings become relatively elongated as communality increases.

Keywords

Public PolicyFactor LoadingGreat InfluenceStatistical TheorySampling Error
Type
Original Paper
Information
Psychometrika , Volume 33 , Issue 4 , December 1968 , pp. 423 - 439
Copyright
Copyright © 1968 Psychometric Society

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Footnotes

*

This article is based upon a dissertation submitted to the Graduate School of the University of Southern California in partial fulfillment of the requirements for the Ph.D. degree. The research was supported in part by NSF Grant GB4230. Computing assistance was obtained from the Western Data Processing Center, Health & Sciences Computing Facility and the Computing Sciences Laboratory. The author wishes to thank Drs. Norman Cliff and Forrest Young for valuable suggestions and a reading of the manuscript.

†

Presently at the Educational Testing Service.

References

Box, G. E. P. Some theorems on quadratic forms applied in the study of analysis of variance problems: II. Effect of inequality of variance and of correlation of errors in the two way classification. Annals of Mathematical Statistics, 1954, 25, 484–498.CrossRefGoogle Scholar
Browne, M. A comparison of factor analytic techniques. Unpublished Master's Thesis, University of the Witwaldersrand, Union of South Africa, 1965.Google Scholar
Cliff, N. Orthogonal rotation to congruence. Psychometrika, 1966, 31, 33–42.CrossRefGoogle Scholar
Cliff, N. and Pennell, R.. The influence of communality, factor strength and loading size on the sampling characteristics of factor loadings. Psychometrika, 1967, 32, 309–326.CrossRefGoogle ScholarPubMed
Cliff, N. and Hamburger, C. D. The study of sampling errors in factor analysis by means of artificial experiments. Psychological Bulletin, 1967, 68 (In press).CrossRefGoogle Scholar
Jöreskog, K. G. Statistical estimation in factor analysis, Stockholm: Almquist and Wiksell, 1963.Google Scholar