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A Simple Gauss-Newton Procedure for Covariance Structure Analysis with High-Level Computer Languages

Published online by Cambridge University Press:  01 January 2025

Robert Cudeck ,
Kelli J. Klebe  and
Susan J. Henly
Robert Cudeck*
Affiliation:
University of Minnesota
Kelli J. Klebe
Affiliation:
University of Colorado, Colorado Springs
Susan J. Henly
Affiliation:
College of Nursing, University of North Dakota
*
Requests for reprints should be sent to Robert Cudeck, Department of Psychology, University of Minnesota, 75 East River Road, Minneapolis, MN 55455.
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Abstract

An implementation of the Gauss-Newton algorithm for the analysis of covariance structures that is specifically adapted for high-level computer languages is reviewed. With this procedure one need only describe the structural form of the population covariance matrix, and provide a sample covariance matrix and initial values for the parameters. The gradient and approximate Hessian, which vary from model to model, are computed numerically. Using this approach, the entire method can be operationalized in a comparatively small program. A large class of models can be estimated, including many that utilize functional relationships among the parameters that are not possible in most available computer programs. Some examples are provided to illustrate how the algorithm can be used.

Keywords

covariance structuresGauss-Newton methodsimplex modelssecond order factor analysisdichotomized variables
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 2 , June 1993 , pp. 211 - 232
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

We are grateful to M. W. Browne and S. H. C. du Toit for many invaluable discussions about these computing ideas. Thanks also to Scott Chaiken for providing the data in the first example. They were collected as part of the U.S. Air Force's Learning Ability Measurement Project (LAMP), sponsored by the Air Force Office of Scientific Research (AFOSR) and the Human Resource Directorate of the Armstrong Laboratory (AL/HRM).

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