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Biometrika 1979 66(3):539-545; doi:10.1093/biomet/66.3.539
© 1979 by Biometrika Trust
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Constrained estimation in covariance structure analysis

SIK-YUM LEE

Department of Mathematics, Chinese University of Hong Kong

In covarianoe structure analysis, the method of weighted least squares for estimating parameters that are subject to functional constraints is developed. Statistical properties of the estimator are studied and a goodness-of-fit statistic is presented. Based on the penalty function technique, an algorithm is developed. This algorithm is able to produce not only the constrained weighted least squares estimator but also the constrained maximum likelihood estimator, if we choose an appropriate weight matrix iteratively. The feasibility of the proposed algorithm is demonstrated by an example in factor analysis.

Key Words: Augmented information matrix • Constrained maximum likelihood estimation • Constrained weighted least squares estimation • Covariance structure analysis • Factor analysis • Gauss-Newton algorithm • Penalty function


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