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Power of the likelihood ratio test in covariance structure analysis


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.

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Author information

Correspondence to Albert Satorra.

Additional information

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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Satorra, A., Saris, W.E. Power of the likelihood ratio test in covariance structure analysis. Psychometrika 50, 83–90 (1985). https://doi.org/10.1007/BF02294150

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Key words

  • covariance structure analysis
  • maximum likelihood estimation
  • likelihood ratio test
  • power of the test
  • local alternatives
  • noncentral Chi-square
  • noncentrality parameter
  • Monte Carlo experiment