16: Nonparametric Within-Between Model: Extending BART for Multilevel Modeling

Music City Center 

The within-between model is a robust approach that addresses the constraints inherent in both fixed effects and random effects models by distinctly modeling within-group and between-group effects. This paper introduces a nonparametric extension of the Within-Between model for the analysis of hierarchical data using Bayesian Additive Regression Trees. Our extension permits flexible nonlinear relationships while preserving the interpretability benefits of the linear Within-Between framework. We establish theoretical guarantees on posterior concentration rates under appropriate conditions and present a framework for deriving interpretable summaries of the intricate nonparametric effects using surrogate models. Through simulation studies, we demonstrate the superior performance of our approach compared to existing methods, including linear fixed effects, random effects, and standard BART extensions, particularly when the true relationships are nonlinear. We illustrate the practical applicability of our method through its application to the National Education Longitudinal Study, wherein we analyze student dropout status while accounting for both student-level and school-level effects.

BART

Multilevel Modelling

Within-Between Model

Nonparametric Regression 

Section on Nonparametric Statistics