Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-10T04:30:18.421Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Darroch, J. N. A set of inequalities in factor analysis. Psychometrika, 1965, 30, 449–453.CrossRefGoogle ScholarPubMed
Dwyer, P. S. The contribution of an orthogonal multiple factor solution to multiple correlation. Psychometrika, 1939, 4, 163–171.CrossRefGoogle Scholar
Guttman, L. “Best possible” systematic estimates of communalities. Psychometrika, 1956, 21, 273–285.CrossRefGoogle Scholar
Harris, C. W. Some Rao-Guttman relationships. Psychometrika, 1962, 27, 247–263.CrossRefGoogle Scholar
Harris, C. W. Note on the squared multiple correlation as a lower bound to communality. Psychometrika, 1978, 43, 283–284.CrossRefGoogle Scholar
Lawley, D. N. & Maxwell, A. E. Factor analysis as a statistical method, 2nd ed., New York: Elsevier, 1972.Google Scholar