Gradient Boosting for Hierarchical Data in Small Area Estimation

Abstract: This paper introduces Mixed Effect Gradient Boosting (MEGB), which combines the strengths of Gradient Boosting with Mixed Effects models to address complex, hierarchical data structures often encountered in statistical analysis. The methodological foundations, including a review of the Mixed Effects model and the Extreme Gradient Boosting method, leading to the introduction of MEGB are shown in detail. It highlights how MEGB can derive area-level mean estimations from unit-level data and calculate Mean Squared Error (MSE) estimates using a nonparametric bootstrap approach. The paper evaluates MEGB's performance through model-based and design-based simulation studies, comparing it against established estimators. The findings indicate that MEGB provides promising area mean estimations and may outperform existing small area estimators in various scenarios. The paper concludes with a discussion on future research directions, highlighting the possibility of extending MEGB's framework to accommodate different types of outcome variables or non-linear area level indicators.