Personalized Predictive Modeling with Input-dependent Weighting under Incomplete Information: A Bayesian Treed Regression Approach

When multiple candidate models with different perspectives---particularly those with multilevel data structures---are used to explain student achievement, researchers face significant model uncertainty. Current popular ensemble learning methods impose restrictive assumption that candidate models collectively capture all relevant predictive information. This assumption becomes problematic across many research contexts, particularly in educational assessment, where theoretical frameworks often provide incomplete representations of the complex processes underlying student learning. We address this limitation through three key methodological advances: (1) using nonparametric approaches that learn how model weights should vary across different contexts, (2) removing the sum-to-one constraint while adding an intercept term to capture unexplained variation, and (3) delivering personalized predictions with well-calibrated uncertainty quantification within a computationally efficient framework. Our proposed method flexibly identifies the relative importance of different predictors across cluster levels and assigns optimal model weights accordingly. Through simulation studies and empirical analysis of PISA 2018 data, we demonstrate substantial improvements in predictive accuracy, uncertainty calibration, and computational performance over current popular methods. This methodology offers the greatest advantages when applied to heterogeneous student populations across diverse educational settings, where the relevance of different candidate models varies systematically by context.