修改后的 Fay-Herriot 模型融合机器学习：用于贫困与农业住户人均支出的小区域估计

Aug 6, 2026

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Accurately measuring household welfare, especially for poor and agricultural populations, is crucial for effective and inclusive policy making. Per capita expenditure is a key welfare indicator, yet estimates at small-area levels are often unreliable because of limited sample sizes. Small Area Estimation (SAE) improves precision by using auxiliary information, but standard Fay-Herriot models rely on linearity. This study modifies the Fay-Herriot fixed-effect stage by integrating Random Forest after EM-based parameter estimation to better capture nonlinear patterns. Applied to agricultural households, the FH-RF model outperforms FH-EM in predictive accuracy.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

AccessFree to download

Introduction

Household welfare measurement and per capita expenditure

Small Area Estimation (SAE) and the Fay-Herriot model

Integrating machine learning and Random Forest

Study comparison and contribution

A modified Fay-Herriot model with machine learning for small area estimation of per capita expenditure among the poor and agricultural households Ari Shobri Bukhari1,2, Khairil Anwar Notodiputro1*, Indahwati 1, and Anwar Fitrianto1 1School of Data Science, Mathematics, and Informatics, IPB University, Jl. Meranti Wing, Dramaga Campus IPB, Bogor, West Java, 16680, Indonesia 2Badan Pusat Statistik (Statistics Indonesia), Jl. Dr. Sutomo No. 6–8, Central Jakarta 10710, Indonesia Abstract. Accurately measuring household welfare, particularly among poor and agricultural populations, is essential for effective and inclusive policy formulation. Per capita expenditure serves as a key welfare indicator, yet direct estimates at small-area levels are often unreliable due to limited sample sizes. Small Area Estimation (SAE) offers a cost-efficient alternative by leveraging auxiliary data, but standard models such as Fay-Herriot (FH) assume linearity and may perform poorly under nonlinear data structures. This study introduces a novel modification to the FH model by incorporating Random Forest (RF), a machine learning method, into the fixed effect estimation stage, following initial parameter estimation via the ExpectationMaximization (EM) algorithm. The resulting FH-RF model is designed to capture complex nonlinear patterns while maintaining compatibility with area-level auxiliary data. When applied to estimate per capita expenditure among agricultural households, the FH-RF model outperforms the FH-EM model in predictive accuracy. Results further reveal that agricultural households exhibit spending patterns more closely aligned with the general population than with poor households, indicating distinct welfare dynamics. The proposed model highlights the potential of machine learning to enhance SAE methodology and inform data-driven poverty and agricultural policy interventions. 1 Introduction Measuring household welfare is a fundamental aspect of formulating inclusive and equitable development policies. In particular, assessing the welfare of households that depend on the agricultural sector is highly relevant for Indonesia, given its agrarian characteristics. The agricultural sector not only contributes significantly to national food security but also absorbs a large portion of the labor force [1, 2] . Thus, having accurate information on the * [Corresponding author:](Corresponding author: khairil@apps.ipb.ac.id)[ ](Corresponding author: khairil@apps.ipb.ac.id)[khairil@apps.ipb.ac.id](Corresponding author: khairil@apps.ipb.ac.id) © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 ([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)). BIO Web of Conferences 186, 02012 (2025) [https://doi.org/10.1051/bioconf/202518602012](https://doi.org/10.1051/bioconf/202518602012) ISOTOBAT 2025 socioeconomic conditions of agricultural households is essential for designing effective social protection programs and improving rural welfare. Per capita expenditure is widely used as a proxy for household welfare due to its relative stability and measurability compared to income, which is often underreported and volatile. This indicator has been central in poverty and inequality analysis, as well as in setting national poverty lines [3] . In Indonesia, per capita expenditure data is collected through the National Socioeconomic Survey (Susenas), which provides reliable estimates at national and provincial levels. However, for smaller domains—such as agricultural or poor households atthe district/city level—direct estimates often suffer from high sampling errors due to limited sample sizes [4] . To overcome this challenge, Small Area Estimation (SAE) offers a cost-efficient alternative by combining survey data with auxiliary information from censuses or administrative sources [3-5] . SAE method

FAQs

为什么需要在小区域层面估计人均支出？

因为贫困或农业住户等较小领域在样本量不足时，直接估计往往存在较高抽样误差，难以支撑精准政策。

标准 Fay-Herriot 模型的主要假设是什么？

它基于线性混合模型框架，并假设协变量与响应变量之间存在线性关系。

FH-RF 模型相较于 FH-EM 的关键改进是什么？

FH-RF 将固定效应阶段的线性预测器替换为随机森林，并在 EM 算法完成初始参数估计后用于捕捉非线性模式。

Aug 6, 2026

Upload by Violet