Nested structural equation models: Noncentrality and power of restriction test

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Abstract
This article is concerned with the difference in noncentrality parameters of nested structural equation models and their utility in evaluating statistical power associated with the pertinent restriction test. Based on the seminal work by Browne and Du Toit (1992), Steiger (1989, 1990), Steiger and Lind (1980), and Steiger, Shapiro, and Browne (1985), asymptotic confidence intervals for that difference are discussed. The intervals represent a useful adjunct to widely employed goodness‐of‐fit indexes and test statistics when assessing plausibility of constraints in nested models. The approach also permits estimating power of the test of validity of the nesting restrictions (cf. MacCallum, Browne, & Sugawara, 1996). It is illustrated on data from a 2‐group cognitive training study.