Gradient boosting for hierarchical data in small area estimation

Abstract Small Area Estimation (SAE) combines survey data with auxiliary sources such as administrative records, census data, or alternative datasets that typically offer broader coverage. By integrating these sources, SAE enhances the accuracy of (direct) survey estimates. To account for the hierarchical structure of survey data, model-based SAE methods often rely on Linear Mixed Models (LMMs). However, the distributional (e.g., normality) and structural (e.g., linearity) assumptions of LMMs may not always hold in practice, and the accuracy of model-based SAE depends on the validity of these assumptions. To address these limitations, we propose a Mixed Effect Gradient Boosting (MEGB) approach, which combines the flexibility of gradient boosting machines with the ability of mixed models to account for hierarchical data structures. MEGB extends standard gradient boosting by incorporating random effects, allowing it to capture unobserved heterogeneity across domains while retaining a nonparametric framework that models nonlinearities and interactions in the data. MEGB supports the derivation of area-level means from unit-level data and uses a nonparametric bootstrap to estimate the Mean Squared Error (MSE). Its performance is assessed through a model-based simulation study, comparing MEGB to established estimators, and further demonstrated using real-world data. The results suggest that MEGB offers promising area mean estimates and may outperform existing SAE methods in various scenarios.