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New Lower and Upper Bounds for Communality in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Haruo Yanai  and
Masanori Ichikawa
Haruo Yanai*
Affiliation:
The National Center for University Entrance Examination, Tokyo, Japan
Masanori Ichikawa
Affiliation:
Tokyo University of Foreign Studies
*
Requests for reprints should be sent to Haruo YANAI, Research Division, National Center for University Entrance Examination, 2-19-23, Komaba, Meguro-Ku, Tokyo 153, JAPAN.
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Abstract

We derive several relationships between communalities and the eigenvalues for a p × p correlation matrix Σ under the usual factor analysis model. For suitable choices of j, λj(Σ), where λj(Σ) is the j-th largest eigenvalue of Σ, provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - λp (Σ) improves on the use of squared mulitiple correlation coefficient as a lower bound.

Keywords

factor analysisCommunalitysquared multiple correlationupper boundlower boundeigenvalue
Type
Notes And Comments
Information
Psychometrika , Volume 55 , Issue 2 , June 1990 , pp. 405 - 409
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

This research was done while the second author was at Tokyo Institute of Technology.

References

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