Psychometrika

, Volume 46, Issue 3, pp 331–336 | Cite as

The asymptotic distribution of commonality components

  • Larry V. Hedges
  • Ingram Olkin
Article

Abstract

Commonality components have been defined as a method of partitioning squared multiple correlations. In this paper, the asymptotic joint distribution of all 2 k − 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.

Key words

commonality analysis multiple regression 

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Copyright information

© The Psychometric Society 1981

Authors and Affiliations

  • Larry V. Hedges
    • 1
    • 2
  • Ingram Olkin
    • 1
    • 2
  1. 1.University of ChicagoUSA
  2. 2.Sequoia Hall, Department of StatisticsStanford UniversityStanford

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