Hostname: page-component-f554764f5-68cz6 Total loading time: 0 Render date: 2025-04-12T19:47:37.565Z 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

Chester W. Harris
Chester W. Harris*
Affiliation:
University Of California, Santa Barbara The Center for the Study of Evaluation, U.C.L.A.
*
Requests for reprints should be sent to Chester W. Harris, Department of Education, University of California, Santa Barbara, Santa Barbara, California 93106.
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple proof that the squared multiple correlation of a variable with the remaining variables in the set of variables is a lower bound to the communality of that variable is presented.

Type
Notes and Comments
Information
Psychometrika , Volume 43 , Issue 2 , June 1978 , pp. 283 - 284
Copyright
Copyright © 1978 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

Dwyer, P. S. The contribution of an orthogonal multiple factor solution to multiple correlation. Psychometrika, 1939, 4, 163–171.CrossRefGoogle Scholar
Guttman, L. Multiple rectilinear prediction and the resolution into components. Psychometrika, 1940, 5, 75–99.CrossRefGoogle Scholar
Horst, P. Matrix algebra for social scientists, 1963, New York: Holt, Rinehart and Winston, Inc..Google Scholar
Mulaik, S. A. The foundations of factor analysis, 1972, New York: McGraw-Hill.Google Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–111.CrossRefGoogle Scholar
Roff, M. Some properties of the communality in multiple factor theory. Psychometrika, 1936, 1(2), 1–6.CrossRefGoogle Scholar