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The Influence of Communality, Factor Strength, and Loading Size on the Sampling Characteristics of Factor Loadings

Published online by Cambridge University Press:  01 January 2025

Norman Cliff  and
Roger Pennell
Norman Cliff
Affiliation:
University of Southern California
Roger Pennell
Affiliation:
University of Southern California
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Abstract

A Monte Carlo approach is employed in determining whether or not certain variables produce systematic effects on the sampling variability of individual factor loadings. A number of sample correlation matrices were generated from a specified population, factored, and transformed to a least-squares fit to the population values. Influences of factor strength, communality and loading size are discussed in relation to the statistics summarizing the results of the above procedures. Influences producing biased estimators of the population values are also discussed.

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 3 , September 1967 , pp. 309 - 326
Copyright
Copyright © 1967 The Psychometric Society

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Footnotes

*

This study was supported in part by NSF Grant GB 4230. Computing assistance was obtained from the Western Data Processing Center and Health Sciences Computing Facility, UCLA, sponsored by NIH Grant FR-3.

†

In a study such as this, ambiguities regarding the use of certain terms inevitably arise, since there is more than one sense in which “factor” and “variable” need to be used. We will attempt to avoid ambiguity by always using “factor” in its factor-analytic rather than its more general sense. We will use the parochial term “test” rather than “variable” to refer to the rows of the factor matrix. “Variables” will sometimes be used for the sake of brevity in referring to the various characteristics of factor loadings whose influence we are investigating.

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