Comparison of Frequentist and Bayesian Regularization in Structural Equation Modeling

Research in regularization, as applied to structural equation modeling (SEM), remains in its infancy. Specifically, very little work has compared regularization approaches across both frequentist and Bayesian estimation. The purpose of this study was to address just that, demonstrating both similarity and distinction across estimation frameworks, while specifically highlighting more recent developments in Bayesian regularization. This is accomplished through the use of two empirical examples that demonstrate both ridge and lasso approaches across both frequentist and Bayesian estimation, along with detail regarding software implementation. We conclude with a discussion of future research, advocating for increased evaluation and synthesis across both Bayesian and frequentist frameworks.