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Abstract
Regularization is a powerful tool to combat overfitting and drive sparsity in complex models. Regularization was initially applied in regression modeling but has been increasingly utilized in structural equation modeling where its utility in identifying the essential components has helped improve modeling. As structural equation models have increased in complexity both in the number of indicators but also the number of latent factors, researchers have begun to investigate how applying Bayesian regularization to these systems can further push the limits on modeling complex models with limited sample sizes. One area where research is limited is the application of Bayesian regularizations methods in models with multiple latent mediators. This study first seeks to investigate how the Bayesian regularization methods of ridge, LASSO, horseshoe, spike-and-slab, and spike-and-slab LASSO perform in capturing mediating variables of various strengths when examined under various sample sizes, number of possible mediators, and strength of latent factors. Secondly, an investigation into the sensitivity to prior settings was conducted on versions of Bayesian LASSO, Bayesian adaptive LASSO, horseshoe, and spikeand-slab. Finally, this study evaluated an empirical study investigating how these Bayesian regularization methods function with real data with multiple latent mediators.
