Nonlinear Small Area Poverty Estimation with MARS-Based Feature Reduction

Abstract

The use of small area estimation combined with multivariate adaptive regression splines (SAE-MARS) is intended to address the lack of estimation precision in cases with nonlinear patterns. Compared to previous studies, which generally treated MARS solely as a tool to capture nonlinear functions without feature/variable selection, the novelty of this study lies in introducing a stepwise variable reduction procedure based on GCV to eliminate uninformative predictors. Two modeling schemes were constructed: using all variables (SAE-MARS-full) and reducing insignificant variables (SAE-MARS-reduced). The SAE-MARS method was implemented using two-stage modeling. The first stage formed the MARS model, and then proceeded to the second stage to construct the SAE. SAE-MARS can deliver a sharp reduction in standard error; however, this does not apply globally. The SAE-MARS-reduced model performed slightly better because of its simpler structure and high level of model accuracy. Although the decrease in average global RRMSE between the two SAE-MARS models appears modest (13.02% for SAE-MARS-reduced compared to 13.37% for SAE-MARS-full), feature reduction yields a very consistent precision advantage across all regions. Thus, the proposed SAE-MARS-reduced model is empirically proven to effectively handle nonlinear patterns, produce highly precise estimates, and demonstrate that eliminating unimportant variables in the MARS process is crucial.​​​