Generating Non-normal Data for Simulation of Structural Equation Models Using Mattson's Method

SEM researchers use Monte-Carlo simulations to ascertain the robustness of statistical estimators and the performance of various fit indices under varying conditions of non-normality. The efficacy of these Monte-Carlo simulations is closely related to the generation of non-normal data. Traditionally, SEM researchers have used approaches proposed by Fleishman (1978) and Vale and Maurelli (1983) to generate multivariate non-normal random numbers. However, both approaches do not provide a method to determine univariate skewness and kurtosis of the observed variables when a non-normal distribution is specified for some or all of the latent variables. Mattson (1997) proposed a method for generating data on the latent variables with controlled skewness and kurtosis of the observed variables. We empirically test the applicability of Mattson's theoretical method in a Monte-Carlo simulation. Specifically, we assess the impact of data generation, selection of transformation method, sample size and degree of skewness/kurtosis on the performance of the method. Our results suggest that Mattson's method seems to be a good approach to generate data with defined levels of skewness and kurtosis. In addition, based on the results of our analysis, we provide practicing researchers recommendations regarding their empirical implementation schemes.