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Note on the Squared Multiple Correlation as a Lower Bound to Communality

Published online by Cambridge University Press:  01 January 2025

David J. Jackson  and
Dan L. Tweed
David J. Jackson
Affiliation:
National Institute of Mental Health
Dan L. Tweed*
Affiliation:
University of Maryland
*
Requests for reprints should be sent to Dan L. Tweed, 1109 Symons Hall, University of Maryland, College Park, Maryland 20742.
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Abstract

It is demonstrated that the squared multiple correlation of a variable with the remaining variables in a set of variables is a function of the communalities and the squared canonical correlations between the observed variables and common factors. This equation is shown to imply a strict inequality between the squared multiple correlation and communality.

Keywords

multiple correlationcommon factorscanonical correlations
Type
Notes and Comments
Information
Psychometrika , Volume 45 , Issue 2 , June 1980 , pp. 281 - 284
Copyright
Copyright © 1980 The Psychometric Society

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References

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