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Power of the Likelihood Ratio Test in Covariance Structure Analysis

Published online by Cambridge University Press:  01 January 2025

Albert Satorra  and
Willem E. Saris
Albert Satorra*
Affiliation:
Department of Statistics and Econometrics, University of Barcelona
Willem E. Saris
Affiliation:
Department of Methods and Techniques, University of Amsterdam
*
Requests for reprints should be sent to Albert Satorra, Department of Statistics and Econometrics, Faculty of Economics, University of Barcelona, Avinguda Diagonal s/n, Barcelona-08034, Spain.
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Abstract

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.

Keywords

covariance structure analysismaximum likelihood estimationlikelihood ratio testpower of the testlocal alternativesnoncentral Chi-squarenoncentrality parameterMonte Carlo experiment
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 1 , March 1985 , pp. 83 - 90
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

This research was made possible by a grant from the Dutch Organization for Advancement of Pure Research (ZWO). The authors also like to acknowledge the helpful comments and suggestions from the editor and anonymous reviewers.

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