Performance of Modified Test Statistics in Covariance and Correlation Structure Analysis Under Conditions of Multivariate Nonnormality

Questions of whether hypothesized structure models are appropriate representations of the pattern of association among a group of variables can be addressed using a wide variety of statistical procedures. These procedures include covariance structure analysis techniques and correlation structure analysis techniques, in which covariance structure procedures are based on distribution theory for covariances, and correlation structure procedures are based on distribution theory for correlations. The present article provides an overview of standard and modified normal theory and asymptotically distribution-free covariance and correlation structure analysis techniques and also details Monte Carlo simulation results on the Type I and Type II error control as a function of structure model type, number of variables in the model, sample size, and distributional nonnormality. The present Monte Carlo simulation demonstrates clearly that the robustness and nonrobustness of structure analysis techniques vary as a function of the structure of the model and the data conditions. Implications of these results for users of structure analysis techniques are considered in the context of current software availability.