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Computational Aspects of the Greatest Lower Bound to the Reliability and Constrained Minimum Trace Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge ,
Tom A. B. Snijders  and
Frits E. Zegers
Jos M. F. ten Berge*
Affiliation:
University of Groningen
Tom A. B. Snijders
Affiliation:
University of Groningen
Frits E. Zegers
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M. F. ten Berge, Subfaculteit voor de Psychologie der Rijksuniversiteit, Oude Boteringestraat 34, 9712 GK Groningen. THE NETHERLANDS.
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Abstract

In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.

Keywords

communalityinternal consistencyHeywood casepositive semidefinite
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 2 , June 1981 , pp. 201 - 213
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

The authors are obliged to Charles Lewis and Dirk Knol for helpful comments, and to Frank Brokken and Henk Camstra for developing computer programs.

References

Reference Notes

Della Riccia, G. & Shapiro, A. Minimum rank and minimum trace of covariance matrices, 1980, Beer-Sheva, Israel: Dept. of Mathematics, Ben Gurion University of the Negev.Google Scholar
Hakim, M., Lochard, E. O., Olivier, J. P. & Térouanne, E. Sur les traces de Spearman (I) (Cahiers du bureau universitaire du recherche opérationelle, Serie recherche no. 25), 1976, Paris: Université Pierre et Marie Curie.Google Scholar

References

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