A Cautionary Note on the Use of the Vale and Maurelli Method to Generate Multivariate, Nonnormal Data for Simulation Purposes

To further understand the properties of data-generation algorithms for multivariate, nonnormal data, two Monte Carlo simulation studies comparing the Vale and Maurelli method and the Headrick fifth-order polynomial method were implemented. Combinations of skewness and kurtosis found in four published articles were run and attention was specifically paid to the quality of the sample estimates of univariate skewness and kurtosis. In the first study, it was found that the Vale and Maurelli algorithm yielded downward-biased estimates of skewness and kurtosis (particularly at small samples) that were also highly variable. This method was also prone to generate extreme sample kurtosis values if the population kurtosis was high. The estimates obtained from Headrick's algorithm were also biased downward, but much less so than the estimates obtained through Vale and Maurelli and much less variable. The second study reproduced the first simulation in the Curran, West, and Finch article using both the Vale and Maurelli method and the Heardick method. It was found that the chi-square values and empirical rejection rates changed depending on which data-generation method was used, sometimes sufficiently so that some of the original conclusions of the authors would no longer hold. In closing, recommendations are presented regarding the relative merits of each algorithm.