Gradient Boosting for Hierarchical Data in Small Area Estimation

TL;DR

This paper presents MEGB, a novel method combining Gradient Boosting and Mixed Effects models to improve area-level mean estimation in hierarchical data, demonstrating promising results over existing estimators.

Contribution

The introduction of MEGB, integrating Gradient Boosting with Mixed Effects models, offers a new approach for small area estimation with hierarchical data structures.

Findings

MEGB provides accurate area mean estimations.

MEGB outperforms traditional estimators in simulations.

Bootstrap-based MSE estimates are effective.

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.