  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.
