Date of Graduation

5-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Educational Statistics and Research Methods (PhD)

Degree Level

Graduate

Department

Counseling, Leadership, and Research Methods

Advisor/Mentor

Liang, Xinya

Committee Member

Zhang, Jihong

Second Committee Member

Shields, Grant

Third Committee Member

Lo, Wen-Juo

Keywords

Bayesian Statistics; Horseshoe; Latent Factors; Mediation; Regularization; Spike-and-Slab

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 spike-and-slab. Finally, this study evaluated an empirical study investigating how these Bayesian regularization methods function with real data with multiple latent mediators.

Download

Share

COinS