A1257
Title: Projection predictive variable selection for Bayesian regularized SEM
Authors: Sara van Erp - Utrecht University (Netherlands) [presenting]
Paul-Christian Burkner - Excellence Cluster for Simulation Technology - University of Stuttgart (Germany)
Aki Vehtari - Aalto University (Finland)
Abstract: Regularized structural equation modeling (SEM) provides a useful tool to estimate models with many parameters relative to the sample size without overfitting. An alternative to classical regularization in SEM is Bayesian regularized SEM, in which a shrinkage prior distribution serves as a penalty function. Advantages in terms of flexibility in shrinkage prior choice and automatic uncertainty estimates have resulted in various applications of Bayesian regularized SEM. The goal of Bayesian regularized SEM is often to select a more parsimonious model by including only those parameters in the model which show substantial effects after regularization. Currently, ad-hoc methods are used in SEM to decide if a parameter estimate should be set to zero or not, for example, by relying on an arbitrary threshold value or on the 95\% credibility interval. However, it has been shown that the optimal selection criterion depends on various sample and model characteristics. Thus, a formal selection method that works well across different types of SEMs and conditions is needed. A promising method that is available in regression models is projection predictive variable selection, which offers a practical approach to selecting the model that offers nearly similar predictions as a reference model. An extension of the projection predictive method is presented to SEM to determine which parameter estimates are set to zero, thereby performing automatic model selection.
