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Journal : InPrime: Indonesian Journal Of Pure And Applied Mathematics

Spatial Bayesian Small Area Estimation of Stunting Prevalence at the Subdistrict Level Wulandari, Ita; Darmawan, Ede Surya; Zamzanah, Sofi
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 7 No. 2 (2025)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/8gpjhz91

Abstract

Achieving Sustainable Development Goal (SDG) 3—ensuring healthy lives and promoting well-being for all—requires reliable health indicators at disaggregated levels. However, conventional large-scale surveys often fail to capture local disparities due to limited sample sizes, leading to unreliable small-area estimates. This study proposes a hierarchical Bayesian Small Area Estimation (HB SAE) framework using a beta distribution and spatial Conditional Autoregressive (CAR) priors to estimate sub-district-level stunting prevalence in Banten Province, Indonesia. The model accounts for both the bound nature of prevalence data and spatial dependence across neighboring areas. Using data from the 2023 Indonesian Health Survey and auxiliary variables from the 2024 Village Potential Data (Podes), the proposed approach demonstrates improved analytical performance. Compared to direct estimation, the HB SAE model reduced the number of sub-districts with Relative Standard Errors (RSE) above 25% from 55 to 44, achieving lower Mean Squared Error (MSE) values and more stable estimates. These results confirm that incorporating spatial effects enhances the precision and reliability of stunting prevalence estimates. The findings provide analytically grounded evidence for localized, data-driven interventions to accelerate efforts to reduce stunting and strengthen policy planning at the sub-district level. Keywords: Bayesian hierarchical model; small area estimation; spatial analysis; stunting prevalence; CAR model.   Abstrak Pencapaian Sustainable Development Goal (SDG) 3, yaitu menjamin kehidupan yang sehat dan meningkatkan kesejahteraan bagi semua orang, memerlukan indikator kesehatan yang andal hingga tingkat wilayah kecil. Namun, survei berskala besar sering kali tidak mampu menggambarkan variasi lokal akibat keterbatasan ukuran sampel, sehingga menghasilkan estimasi yang tidak stabil pada wilayah kecil. Penelitian ini mengusulkan kerangka kerja Hierarchical Bayesian Small Area Estimation (HB SAE) menggunakan distribusi beta dengan prior spasial Conditional Autoregressive (CAR) untuk mengestimasi prevalensi stunting di tingkat kecamatan di Provinsi Banten, Indonesia. Model ini mempertimbangkan sifat terbatas (bounded) dari data prevalensi dan ketergantungan spasial antarwilayah. Dengan memanfaatkan data Survei Kesehatan Indonesia 2023 serta variabel bantu dari data Potensi Desa (Podes) 2024, model HB SAE menunjukkan kinerja analitis yang lebih baik. Dibandingkan dengan estimasi langsung, model HB SAE menurunkan jumlah kecamatan dengan Relative Standard Error (RSE) di atas 25% dari 55 menjadi 44, dengan nilai Mean Squared Error (MSE) yang lebih rendah dan hasil estimasi yang lebih stabil. Hasil ini menunjukkan bahwa penambahan efek spasial meningkatkan ketepatan dan reliabilitas estimasi prevalensi stunting. Temuan ini memberikan dasar analitis yang kuat untuk mendukung intervensi berbasis data dalam percepatan penurunan stunting dan perencanaan kebijakan di tingkat kecamatan. Kata Kunci: Model hierarkis Bayes; Small area estimation; Analisis spasial; Prevalensi stunting; Model CAR. 2020MSC: 62F15, 62M30.
Co-Authors Achir Yani S. Hamid Adang Bachtiar Agung Waluyo Amelia Kusumawardhani Amelia Kusumawardhani Setiawan Amelia Rahayu Amelia Rizki Alfriantin Anhari Achadi Arani Nadhira Arif, Umi Fikria Asnawi Abdullah Azni, Nurkarti Basabih, Masyitoh Bernadeth Novita Budisusilowati Budhi Mulyadi Bunga Listia Paramita Chintia, Amelia Cicilya Candi David R. I. Hutajulu Dewi Irawati Diah Ekawati Diah Ekawati Diah Ekawati Dian Pitaloka Sri Mumpuni Elvira Elvira Eska Perdini Suhendi Etty Rekawati Fahnida Zeydra Thohari Farid Fauzan Mahubessy Feni Dwi Lestari Fika Maulani Fadrianti Fransisca, Martha Hafnidar A. Rani Hartono, Widy Hendra Ayusra Hermansyah Hermansyah Ida Bagus Sila Wiweka Ilyas, Jaslis Immanuel Natanael Tarigan Indriana, Yuki Melati Irene Jesihka Pandiangan Irmayanto, Randi Isroil Samihardjo Ita Wulandari Julian Simanjuntak Kusumawardhani Setiawan , Amelia Mardiati Najib Mardiati Najib Marianus Ruba Marianus Ruba Martha Fransisca Martini Heniastaty Patuwondatu Mila Fitriana Muhammad Fachmi Adi Pratama Mustafa, Ghulam Nadia Irina Darmawan Nadia Irina Darmawan Ngabila Salama Nidya Eka Putri Nova Perdana Novie Irawaty L. Manurung Nurkarti Azni Nyoman Dwi Maha Udiyana Ovi Norfiana Paramita, Stephanie Permanasari, Vetty Yulianty Prasetyo, Chandra Istanti Pratiwi Pujiyanto Pujiyanto Puput Oktamianti Purbosari Purbosari Purnawan Junadi Purnawan Junadi Putri Ardhani Putu Darmika Randi Irmayanto Ratna Sitorus Rendy Setya Wardana Rheine Indira Putrie Sesunan Rifda Amalia Choirunnisa Rinie Indah Chandra Wirasati Rita Mutia Royani Royani Sabarinah Prasetyo Sabarinah Sabarinah Saza Fitria Septama, Andis Sidhi Laksono Siti Yunianti Sjaaf, Amal Chalik Stephanie Paramita Stephanie Paramita Suci Nurul Andini Syarif Rahman Hasibuan Syifa Silviana Tintin Sukartini Sukartini, Tintin Sukartini Tulus Kurnia Indah Ulfah, Annisa Ulianto Ulianto Wirasati, Rinie Indah Chandra Yaslis Ilyas Yasrizal, Meutia Arini Zamzanah, Sofi