UCLA

Problems about whether a hypothesized covariance structure models is an appropriate representation of the population covariance structure of multiple variables can be addressed using goodness-of-fit testing in structural equation modeling. Many test statistics and their extensions have been developed for various specific conditions and some of them have been extensively used in practice. However, their expected performances might break down under violations of multivariate normality or sufficiently large sample sizes. This paper evaluates the robustness of four modified goodness-of-fit test statistics T_SB(new), T_MV, T_YB and T_F in SEM. Monte Carlo simulation demonstrates that the robustness of covariance structure statistics vary as a function of the correctness of the model as well as distributional characteristics of observed data. Suggestions for application of these modified test statistics are given after taking both the literature and current simulation result into account. A surprising result was the failure of T_MV, the Satorra-Bentler mean-scaled and variance-adjusted test statistic, to perform correctly even asymptotically in one condition.