Prediction-guided hierarchical clustering for population-level regression

We address how to pool information across many related populations in regression-type models, balancing the risks of over-pooling and under-pooling. We propose a prediction-guided hierarchical clustering framework in which each population is equipped with a parametric regression or generalized linear mixed model, and clusters correspond to sets of populations that share a common parameter vector. A Bayesian posterior predictive loss, based on proper scoring rules, drives an agglomerative algorithm on the space of partitions: clusters are merged only when doing so reduces estimated predictive loss, yielding a data-driven and interpretable pooling structure. The method can be viewed as a discrete alternative to continuous shrinkage in multilevel models and as a predictive refinement of clusterwise regression and clustered multi-task learning. Simulation studies in Gaussian and mixed continuous–binary settings show that the procedure reliably avoids harmful global pooling and can yield modest predictive gains through selective pooling, while remaining close to fully local fits when beneficial pooling is limited. In a real-data application to the Gapminder country–year panel, it yields interpretable clusters of countries with similar life-expectancy trajectories conditional on economic development and provides a conservative, prediction-guided pooling rule.