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Some Properties of Estimated Scale Invariant Covariance Structures

Published online by Cambridge University Press:  01 January 2025

T. K. Dijkstra
T. K. Dijkstra*
Affiliation:
University of Groningen, Institute of Econometric
*
Requests for reprints should be addressed to T. K. Dijkstra, University of Groningen, Institute of Econometrics, P.O. Box 800, 9700 AV Groningen, THE NETHERLANDS.
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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.

Keywords

fitting functionsscale invariancecovariance structuresLISREL
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 2 , June 1990 , pp. 327 - 336
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

Constructive comments by the referees are greatly appreciated. The author gratefully acknowledges Michael Browne's interest in his work.

References

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