A Study of the Sampling Variability and z-Values of Parameter Estimates From Misspecified Structural Equation Models

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Abstract
This article considers the sampling variability and z-values of parameter estimates from misspecified structural equation models. A Monte Carlo study is employed wherein a prototype structural model is analyzed under one incorrect restriction and two incorrect restrictions. True values of the misspecified parameters are varied to reflect increasing distances from the null hypothesis. Sample size differences are also considered. Comparisons are made between empirical variability and the standard errors of the misspecified model. For z-values, the empirical power of the z test is compared to the predicted power obtained from the Wald test. Results indicate standard errors are unaffected by misspecification when the specification error is small. The z test is affected in such a way that misspecification in one parameter can affect the power of the z test for another parameter. Sample size appears to interact with size and type of misspecification. Results are discussed in terms of current asymptotic theory as well as implications for practice.