Principles and Procedures for Generating Non-Normal Data Using Mixture Models

Evaluating the performance of statistical procedures under varying degrees of multivariate non-normality has become increasingly important in methodological research. While various data generation methods have been introduced for this purpose, they tend to generate non-normal data with limited forms based primarily on skewness. This restricts their ability to produce data that reflect the diverse characteristics of non-normality observed in empirical research (e.g., multimodal, J-shaped or U-shaped distributions). As an approach that allows more flexible incorporation of non-normal features, the mixture method can be employed, which utilizes the principles of mixture models. Although this method has several distinct advantages, it has been seldom employed in actual simulation studies, largely because of limited prior research and the absence of comprehensive guidelines. Therefore, this study aims to provide a systematic overview of the mixture method for generating non-normal data. Specifically, it examines the method’s underlying principles, describes the procedures for generating non-normal data, and presents an illustrative example of its practical application.