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Approximate Uniqueness Estimates for Singular Correlation Matrices

Published online by Cambridge University Press:  01 January 2025

C. T. Finkbeiner  and
L. R. Tucker
C. T. Finkbeiner*
Affiliation:
The Procter & Gamble Company
L. R. Tucker
Affiliation:
University of Illinois at Urbana-Champaign Educational Testing Service
*
Requests for reprints should be sent to: C. T. Finkbeiner, The Procter & Gamble Company, Winton Hill Technical Center, 6110 Center Hill Road, Cincinnati, Ohio 45224.
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Abstract

The residual variance (one minus the squared multiple correlation) is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is given for the case when the correlation matrix is singular. The approximation is computationally simpler than the exact solution, especially since it can be applied routinely without prior knowledge as to the singularity or nonsingularity of the correlation matrix.

Keywords

uniquenessescommunalitiesfactor analysis
Type
Notes And Comments
Information
Psychometrika , Volume 47 , Issue 4 , December 1982 , pp. 517 - 521
Copyright
Copyright © 1982 The Psychometric Society

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References

Jöreskog, K. G. Factor analysis by least-squares and maximum-likelihood methods. In Enslein, K., Ralston, A. & Wilf, H. S. (Eds.), Statistical Methods for Digital Computers, 1977, New York: Wiley.Google Scholar
Roff, M. Some properties of the communality in multiple factor theory. Psychometrika, 1936, 1, 1–6.CrossRefGoogle Scholar
Tucker, L. R, Cooper, L. G., & Meredith, W. Obtaining squared multiple correlations from a correlation matrix which may be singular. Psychometrika, 1972, 37, 143–148.CrossRefGoogle Scholar