Some Properties of Estimated Scale Invariant Covariance Structures

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Abstract
Scale invariance is a property shared by many covariance structure models employed in practice. An example is provided by the well-known LISREL model subject only to classical normalizations and zero constraints on the parameters. It is shown that scale invariance implies that the estimated covariance matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. In this context, the paper considers two classes of fitting functions: weighted least squares and the class of functions proposed by Swain.