The Effect of Varying Degrees of Nonnormality in Structural Equation Modeling

This simulation study investigated the robustness of structural equation modeling to different degrees of nonnormality under 2 estimation methods, generalized least squares and maximum likelihood, and 4 sample sizes, 100, 250, 500, and 1,000. Each of the slight and severe nonnormality degrees was comprised of pure skewness, pure kurtosis, and both skewness and kurtosis. Bias and standard errors of parameter estimates were analyzed. In addition, an analysis of variance was conducted to investigate the effects of the 3 factors on several goodness-of-fit indexes. The study found that standard errors of parameter estimates were not significantly affected by estimation methods and nonnormality conditions. As expected, standard errors decreased at larger sample sizes. Parameter estimates were more sensitive to nonnormality than to sample size and estimation method. Chi-square was the least robust model fit index compared with Normed Fit Index, Nonnormed Fit Index, and Comparative Fit Index. Sample sizes of 100 or more are recommended for accurate parameter estimates.