Non-Normality Propagation among Latent Variables and Indicators in PLS-SEM Simulations

Structural equation modeling employing the partial least squares method (PLS-SEM) has been extensively used in business research. Often the use of this method is justified based on claims about its unique performance with small samples and non-normal data, which call for performance analyses. We address the issue of how one creates normal and non-normal data for such performance analyses. A method is proposed for the generation of data for exogenous latent variables and errors directly, from which data for endogenous latent variables and indicators are subsequently obtained based on model parameters. Our discussion places emphasis on the issue of non-normality propagation among latent variables and indicators, showing that this propagation can be severely impaired if certain steps are not taken. A key step is inducing non-normality in structural and indicator errors, in addition to exogenous latent variables. Illustrations of the method and its steps are provided through simulations based on a simple model of the effect of e-collaboration technology use on job performance.