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Estimation of covariance structure models with parameters subject to functional restraints

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.

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Reference note

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

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Correspondence to Sik-Yum Lee.

Additional information

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.

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Lee, SY. Estimation of covariance structure models with parameters subject to functional restraints. Psychometrika 45, 309–324 (1980). https://doi.org/10.1007/BF02293906

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Key words

  • confirmatory factor analysis
  • covariance structure analysis
  • equality constraints
  • Gauss-Newton algorithm
  • Heywood case
  • inequality constraints
  • penalty function
  • quasi-Weiner simplex model
  • Scoring algorithm