The management of nonnormal data in structural equation modeling

The use of structural equation modeling demands that the researcher acknowledges the underlying assumptions, and therefore the limitations, of normal theory estimation methods, examines the appropriateness of the data, and then selects the estimation method that is suitable for optimal results. The problem of accurately selecting the estimation method to use is compounded by fact that the degree of multivariate nonnormality is often not initially assessed. The question of whether the data are normal enough for maximum likelihood or generalized least squares estimation methods or are too nonnormal and require another estimation method has not been thoroughly addressed. Therefore, there exists a need for an a priori assessment of the degree of nonnormality through the use of an omnibus test of multivariate normality. Once these normality values have been determined, guidelines are needed to help direct the researcher to the appropriate estimation method. Given these issues, it was through a Monte Carlo study using EQS that the stability of six estimation methods had been investigated. Various conditions were introduced to true models that included sample size and levels of nonnormality. In addition, this study examined post hoc, multivariate statistics for their effectiveness in determining the degree of nonnormality and the appropriate estimation method to use under the various conditions. Through the use of graphical presentations, maximum likelihood appeared rather robust as compared to the alternatives when observed through the various fit indices and in particular with larger sample sizes. Through an analysis of variance (ANOVA), it was determined that nonnormality, sample size and the choice of estimation method had diverse effects on the goodness of fit statistics and indices. It was also concluded that multivariate tests such as Mardia's kurtosis and Henze-Zirkler were effective in determining nonnormality, but the results relating to the degree of nonnormality remained unresolved due to variations in the test statistics based on sample size and number of variables in the models. Recommendations for further research were proposed.