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Tests for Stability in Linear Structural Equation Systems

Published online by Cambridge University Press:  01 January 2025

P. M. Bentler  and
Edward H. Freeman
P. M. Bentler*
Affiliation:
University of California, Los Angeles
Edward H. Freeman
Affiliation:
University of California, Los Angeles
*
Address reprint requests to P. M. Bentler, Department of Psychology, University of California, Los Angeles, California 90024.
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Abstract

Interpretations regarding the effects of exogenous and endogenous variables on endogenous variables in linear structural equation systems depend upon the convergence of a matrix power series. Convergence depends upon the eigenvalues of the structural coefficient matrix. The test for convergence developed by Jöreskog and Sörbom is shown to be only sufficient, not necessary and sufficient.

Keywords

structural equationsnonrecursive modelslinear system stabilityeffect decomposition
Type
Notes And Comments
Information
Psychometrika , Volume 48 , Issue 1 , March 1983 , pp. 143 - 145
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

Supported in part by USPHS grants DA01070 and DA00017. The assistance of several unknown reviewers is gratefully acknowledged.

References

Ben-Israel, A., & Greville, T. N. E. Generalized inverses: Theory and applications, New York: Wiley, 1974.Google Scholar
Browne, E. T. The characteristic equation of a matrix. Bulletin of the American Mathematical Society, 1928, 34, 363–368.CrossRefGoogle Scholar
Fox, J. Effect analysis in structural equation models: Extensions and simplified methods of computation. Sociological Methods & Research, 1980, 9, 3–28.CrossRefGoogle Scholar
Jöreskog, K. G., & Sörbom, D. LISREL V, Chicago: International Educational Services, 1981.Google Scholar