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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).

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