The Issue of Isopower in Power Analysis for Tests of Structural Equation Models

Abstract

Two general frameworks have been proposed for evaluating statistical power of tests of model fit in structural equation modeling (SEM). Under the Satorra–Saris (1985) approach, to evaluate the power of the test of fit of Model A, a Model B, within which A is nested, is specified as the alternative hypothesis and considered as the true model. We then determine the power of the test of fit of A when B is true. Under the MacCallum–Browne–Sugawara (1996) approach, power is evaluated with respect to the test of fit of Model A against an alternative hypothesis specifying a true degree of model misfit. We then determine the power of the test of fit of A when a specified degree of misfit is assumed to exist as the alternative hypothesis. In both approaches the phenomenon of isopower is present, which means that different alternative hypotheses (in the Satorra–Saris approach) or combinations of alternative hypotheses and other factors (in the MacCallum–Browne–Sugawara approach) yield the same level of power. We show how these isopower alternatives can be defined and identified in both frameworks, and we discuss implications of isopower for understanding the results of power analysis in applications of SEM.

Notes

¹Software code written to obtain some of the results in this article can be obtained on request from the second author, Taehun Lee, by e-mailing [email protected].