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A Numerical Approach to the Approximate and the Exact Minimum Rank of a Covariance Matrix

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge  and
Henk A. L. Kiers
Jos M. F. ten Berge*
Affiliation:
University of Groningen
Henk A. L. Kiers
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M. F. ten Berge, Vakgroep Psychologie, Rijksuniversiteit Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS.
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Abstract

A concept of approximate minimum rank for a covariance matrix is defined, which contains the (exact) minimum rank as a special case. A computational procedure to evaluate the approximate minimum rank is offered. The procedure yields those proper communalities for which the unexplained common variance, ignored in low-rank factor analysis, is minimized. The procedure also permits a numerical determination of the exact minimum rank of a covariance matrix, within limits of computational accuracy. A set of 180 covariance matrices with known or bounded minimum rank was analyzed. The procedure was successful throughout in recovering the desired rank.

Keywords

communality estimationminimum rankfactor analysis
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 2 , June 1991 , pp. 309 - 315
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

The authors are obliged to Paul Bekker for stimulating and helpful comments.

References

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