How to Generate Non-normal Data for Simulation of Structural Equation Models

Area of Science:

• Statistics
• Psychometrics
• Computational Statistics

Background:

• Structural equation modeling (SEM) often requires normally distributed data for accurate simulations.
• Generating non-normal data that adheres to a specified SEM structure presents a methodological challenge.
• Existing methods may lack flexibility in controlling specific distributional characteristics.

Purpose of the Study:

• To propose a flexible procedure for generating non-normal data suitable for structural equation model simulations.
• To demonstrate how univariate skewness and kurtosis of observed variables can be controlled.
• To illustrate the application of the procedure using real-world examples and software.

Main Methods:

• A transformation method is applied to univariate random variables to generate latent and error variables.
• Data for observed variables are computed based on the specified structural equation model.
• Restrictions are imposed on covariance matrices for latent and error variables.
• Univariate distributions are utilized, allowing for a wide selection of distributions.

Main Results:

• The proposed procedure successfully generates non-normal data for SEM simulations.
• Controlling skewness and kurtosis in latent and error variables allows for a wide range of characteristics in observed variables.
• The method is demonstrated to be effective for two distinct structural equation models.
• The PRELIS software can be utilized to implement the data generation procedure.

Conclusions:

• The developed procedure offers a practical and flexible approach to generating non-normal data for SEM simulations.
• Researchers can effectively manipulate skewness and kurtosis to better match real-world data characteristics.
• The method enhances the utility of SEM simulations by accommodating a broader range of data distributions.