The Effect of Varying Degrees of Nonnormality in Structural Equation Modeling

TLDR

This simulation study investigated the robustness of structural equation modeling to different degrees of nonnormality under two estimation methods, generalized least squares and maximum likelihood, and four sample sizes (100, 250, 500, and 1,000). The study varied nonnormality (pure skewness, pure kurtosis, or both) across slight and severe levels, analyzed bias and standard errors of parameter estimates, and performed ANOVA to assess the effects of estimation method, nonnormality, and sample size on goodness‑of‑fit indices. Standard errors were largely unaffected by estimation method or nonnormality but improved with larger samples, while parameter estimates were more sensitive to nonnormality; chi‑square was the least robust fit index, and sample sizes of at least 100 are recommended for accurate estimates.

Abstract

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.