On the Improvement of Predictive Modeling Using Bayesian Stacking and Posterior Predictive Checking

Model uncertainty is pervasive in real world analysis situations and is an often-neglected issue in applied statistics. However, standard approaches to the research process do not address the inherent uncertainty in model building and, thus, can lead to overconfident and misleading analysis interpretations. One strategy to incorporate more flexible models is to base inferences on predictive modeling. This approach provides an alternative to existing explanatory models, as inference is focused on the posterior predictive distribution of the response variable. Predictive modeling can advance explanatory ambitions in the social sciences and in addition enrich the understanding of social phenomena under investigation. Bayesian stacking is a methodological approach rooted in Bayesian predictive modeling. In this paper, we outline the method of Bayesian stacking but add to it the approach of posterior predictive checking (PPC) as a means of assessing the predictive quality of those elements of the stacking ensemble that are important to the research question. Thus, we introduce a viable workflow for incorporating PPC into predictive modeling using Bayesian stacking without presuming the existence of a true model. We apply these tools to the PISA 2018 data to investigate potential inequalities in reading competency with respect to gender and socio-economic background. Our empirical example serves as rough guideline for practitioners who want to implement the concepts of predictive modeling and model uncertainty in their work to similar research questions.