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Estimation of Covariance Structure Models with Parameters Subject to Functional Restraints

Published online by Cambridge University Press:  01 January 2025

Sik-Yum Lee
Sik-Yum Lee*
Affiliation:
The Chinese University of Hong Kong
*
Request for reprints should be sent to Dr. S. Y. Lee, Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T. Hong Kong.
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Abstract

This paper demonstrates the feasibility of using the penalty function method to estimate parameters that are subject to a set of functional constraints in covariance structure analysis. Both types of inequality and equality constraints are studied. The approaches of maximum likelihood and generalized least squares estimation are considered. A modified Scoring algorithm and a modified Gauss-Newton algorithm are implemented to produce the appropriate constrained estimates. The methodology is illustrated by its applications to Heywood cases in confirmatory factor analysis, quasi-Weiner simplex model, and multitrait-multimethod matrix analysis.

Keywords

confirmatory factor analysiscovariance structure analysisequality constraintsGauss-Newton algorithmHeywood caseinequality constraintspenalty functionquasi-Weiner simplex modelScoring algorithm
Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 3 , September 1980 , pp. 309 - 324
Copyright
Copyright © 1980 The Psychometric Society

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Footnotes

The author is indebted to several anonymous reviewers for creative suggestions for improvement of this paper. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.

References

Reference Note

Lee, S. Y. & Bentler, P. M. Some Asymptotic properties of constrained generalized least squares estimation in covariance structure models. Manuscript submitted for publication, 1979.Google Scholar

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