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The Asymptotic Distribution of Commonality Components

Published online by Cambridge University Press:  01 January 2025

Larry V. Hedges  and
Ingram Olkin
Larry V. Hedges
Affiliation:
University of Chicago and Stanford University
Ingram Olkin*
Affiliation:
University of Chicago and Stanford University
*
Requests for reprints should be addressed to Ingram Olkin, Sequoia Hall, Department of Statistics, Stanford University, Stanford, California, 94305.
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Abstract

Commonality components have been defined as a method of partitioning squared multiple correlations. In this paper, the asymptotic joint distribution of all 2k − 1 squared multiple correlations is derived. The asymptotic joint distribution of linear combinations of squared multiple correlations is obtained as a corollary. In particular, the asymptotic joint distribution of commonality components are derived as a special case. Simultaneous and nonsimultaneous asymptotic confidence intervals for commonality components can be obtained from this distribution.

Keywords

commonality analysismultiple regression
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 3 , September 1981 , pp. 331 - 336
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

This work was supported in part by the Spencer Foundation and the National Science Foundation.

The authors are grateful to Bryna Siegel-Gorlick for her help in obtaining the data used in Example 4.3, and to the referees for their comments and suggestions.

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