THREEFOLD HIERARCHICAL SMALL AREA ESTIMATION MODEL FOR ESTIMATING PREVALENCE OF STUNTING IN WEST NUSA TENGGARA

  • Logananta Puja Kusuma Program in Statistics and Data Science, School of Data Science, Mathematics, and Informatics, IPB University, Indonesia https://orcid.org/0009-0005-5024-9984
  • Kusman Sadik Program in Statistics and Data Science, School of Data Science, Mathematics, and Informatics, IPB University, Indonesia https://orcid.org/0000-0001-8361-8057
  • Anang Kurnia Program in Statistics and Data Science, School of Data Science, Mathematics, and Informatics, IPB University, Indonesia https://orcid.org/0000-0001-9409-2361
DOI: https://doi.org/10.30598/barekengvol20iss4pp3339-3352
Keywords: Hierarchical Bayes, Poisson-Gamma, Small area estimation, Stunting, Threefold model

Abstract

Stunting is a condition of growth failure in toddlers due to chronic malnutrition, becoming an issue in various regions of Indonesia. West Nusa Tenggara Province has one of Indonesia's highest stunting prevalence rates, calculated at 29.8% in 2024, which is more than twice the national target of 14%. Appropriate and efficient policy-making for stunting reduction requires reliable estimates for small areas like districts. This study aims to produce more reliable district-level estimates of stunting prevalence for districts level area, while direct estimation from the Survei Kesehatan Indonesia (SKI) is unreliable due to limited sample size. This research develops a threefold hierarchical Bayesian (HB) Small Area Estimation (SAE) model based on the Poisson-Gamma distribution to model the number of stunted toddlers as discrete count data with overdispersion. The proposed model incorporates auxiliary variables from official sources and includes three hierarchical random effects representing district, regency/municipality, and grouped regency/municipality levels based on geographical structure. The results show that the threefold HB SAE model achieves convergent parameter estimates and provides more stable and precise district-level stunting prevalence estimates compared to direct estimators. The multilevel model performs better than one random effect model as reflected by the lower LOOIC. The findings also suggest that districts in Sumbawa Island, particularly in the eastern part and areas located farther from regency/municipality capitals, tend to have higher stunting prevalence. However, this study is limited by the assumption of independence among area-level random effects and restricted availability of auxiliary variables. This study contributes methodologically by extending Poisson-based SAE literature through the application of a threefold HB framework in stunting estimation and provides district-level stunting statistics that support evidence-based policymaking and targeted interventions aligned with SDG Target 2.2.

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References

A. S. Rambi and Budyanra, “DETERMINANTS OF STUNTING IN THE UNDER-FIVE IN WEST NUSA TENGGARA PROVINCE WITH MULTILEVEL BINARY LOGISTIC REGRESSION,” Jurnal Matematika, Statistika, dan Komputasi, vol. 21, no. 1, pp. 103–119, September 2024. doi: https://doi.org/10.20956/j.v21i1.35765.

B. S. Renyoet, D. Martianto and D. Sukandar, “POTENSI KERUGIAN EKONOMI KARENA STUNTING PADA BALITA DI INDONESIA TAHUN 2013,” J. Gizi Pangan, vol. 11, no. 3, pp. 247–254, November 2016.

Kementerian Kesehatan Republik Indonesia, Survei Kesehatan Indonesia. Jakarta: Kemenkes, 2024.

M. de Onis, E. Borghi, M. Arimond, P. Webb, T. Croft, K. Saha, L. M. De-Regil, F. Thuita, R. Heidkamp, J. Krasevec, C. Hayashi, and R. B. S. Flores-Ayala, “PREVALENCE THRESHOLDS FOR WASTING, OVERWEIGHT AND STUNTING IN CHILDREN UNDER 5 YEARS,” Public Health Nutrition, vol. 22, no. 1, pp. 175–179, January 2019. doi: https://doi.org/10.1017/S1368980018002434.

Badan Perencanaan Pembangunan Nasional, Pilar Pembangunan Ekonomi. Jakarta: Bapenas, 2022.

D. R. Sari, “ANALISIS FAKTOR-FAKTOR YANG MEMENGARUHI PREVALENSI STUNTING PADA BALITA DI JAWA BARAT”. [Thesis]. Bogor, ID: IPB University, 2025. [Online]. Available: IPB Repository.

A. Kurnia, “PREDIKSI TERBAIK EMPIRIK UNTUK MODEL TRANSFORMASI LOGARITMA DI DALAM PENDUGAAN AREA KECIL DENGAN PENERAPAN PADA DATA SUSENAS”. [Dissertation]. Bogor, ID: IPB University, 2009. [Online]. Available: IPB Repository.

R. E. Fay, and R. A. Heriott, “ESTIMATES OF INCOME FOR SMALL PLACES: AN APPLICATION OF JAMES-STEIN PROCEDURES TO CENSUS DATA,” Journal of the American Statistical Association, vol. 74, no. 366, pp. 269–277, June 1979. doi: https://doi.org/10.1080/01621459.1979.10482505.

J. N. K. Rao, “SMALL AREA ESTIMATION BY COMBINING TIME SERIES AND CROSS-SECTIONAL DATA,” Can J Stat, vol. 22, no. 4, pp. 511–528, December 1994. doi: https://doi.org/10.2307/3315407.

K. Sadik, Metode Prediksi Tak-Bias Linear Terbaik dan Bayes Berhirarki untuk Pendugaan Area Kecil Berdasarkan Model State Space. [Dissertation]. Bogor, ID: IPB University, 2009. [Online]. Available: IPB Repository.

E. Berg, “EMPIRICAL BEST PREDICTION OF SMALL AREA MEANS BASED ON A UNIT-LEVEL GAMMA-POISSON MODEL,” Journal of Survey Statistics and Methodology, vol. 11, no. 4, pp. 873–894, September 2023. doi: https://doi.org/10.1093/jssam/smac026.

A. C. Cameron, and R. K. Trivedi, Regression Analysis of Count Data Second Edition. New York: Cambridge University Press, 2013. doi: https://doi.org/10.1017/CBO9781139013567.

P. R. Sihombing, R. Mastiani, D. A. Sunarjo, and D. Muslianti, “COMPARISON OF GLM, GLMM, AND GEE POISSON MATHEMATICAL MODELING PERFORMANCE (CASE STUDY: NUMBER OF PULMONARY TUBERCULOSIS PATIENTS IN INDONESIA IN 2019-2021),” Jurnal Tambora, vol. 6, no 3, pp. 102-106, October 2022. doi: https://doi.org/10.36761/jt.v6i3.2081.

K. Reluga, M. J. Lombardia, and S. Sperlich, “SIMULTANEOUS INFERENCE FOR EMPIRICAL BEST PREDICTORS WITH A POVERTY STUDY IN SMALL AREAS,” Journal of the American Statistical Association, vol. 118, no. 541, pp. 583–595, August 2021. doi: https://doi.org/10.1080/01621459.2021.1942014.

P. Wididiati, H. Nurcahyanto, and A. Marom, "IMPLEMENTASI KEBIJAKAN PENANGANAN STUNTING DI KABUPATEN LOMBOK TIMUR (STUDI KASUS DI DESA LENEK DUREN KECAMATAN LENEK)," Journal of Management and Public Policy, vol. 11, no. 4, pp. 379 - 394, Oct. 2022.

A. H. Amry, and H. Rowa, “IMPLEMENTASI KEBIJAKAN PENANGULANGAN STUNTING DI KABUPATEN LOMBOK UTARA PROVINSI NUSA TENGGARA BARAT”. [Thesis]. Jatinangor, ID: IPDN, 2025. [Online]. Available: IPDN Repository.

D. B. Rein, “THE PREVALENCE OF BILATERAL HEARING LOSS IN THE UNITED STATES IN 2019: A SMALL AREA ESTIMATION MODELLING APPROACH FOR OBTAINING STATE, AND COUNTY LEVEL ESTIMATES BY DEMOGRAPHIC SUBGROUP,” The Lancet Regional Health – Americas, vol 30, no. 100670, February 2024. doi: https://doi.org/10.1016/j.lana.2023.100670.

L. Marcis, D. Morales, M. C. Pagliarella, and R. Salvatore, “THREE‑FOLD FAY–HERRIOT MODEL FOR SMALL AREA ESTIMATION AND ITS DIAGNOSTICS,” Statistical Methods & Applications, vol. 32, no. 5, pp. 1563–1609, May 2023. doi: https://doi.org/10.1007/s10260-023-00700-6.

J. N. K. Rao, “SOME RECENT ADVANCES IN MODEL-BASED SMALL AREA ESTIMATION,” Survey Methodology, vol. 25, no. 2, pp. 175–186, December 1999.

Y. F. Amin, Indahwati, and A. Kurnia, “TWOFOLD SUBAREA MODEL FOR ESTIMATING COMMUTER PROPORTION IN 10 METROPOLITAN AREAS,” BAREKENG: Journal of Mathematics and Its Application, vol. 18, no. 2, pp. 1009–1022, June 2024. doi: https://doi.org/10.30598/barekengvol18iss2pp1009-1022.

I. Wulandari, “KAJIAN MODEL POISSON UNTUK PENDUGAAN AREA KECIL DENGAN GALAT PENGUKURAN PADA PEUBAH PENYERTA”. [Dissertation]. Bogor, ID: IPB University, 2025. [Online]. Available: IPB Repository.

Tim Percepatan Stunting, Prediksi Angka Stunting Tahun 2020. Jakarta: TPPS, 2021.

A. R. Sari, and I. Rahmi. “PENERAPAN METODE SMALL AREA ESTIMATION DENGAN PENDEKATAN KERNEL UNTUK MENDUGA PERSENTASE STUNTING DI INDONESIA,” Jurnal Matematika Unand, vol. 8 no. 3, pp. 17-24, December 2019. doi: https://doi.org/10.25077/jmu.8.3.17-24.2019.

E. Sunandi, “HIERARCHICAL LIKELIHOOD METHODS FOR SMALL AREA ESTIMATION WITH BETA-BINOMIAL RESPONSE AND MEASUREMENT ERROR IN THE AUXILIARY VARIABLE”. [Dissertation]. Bogor, ID: IPB University, 2024. [Online]. Available: IPB Repository.

A. Yanke, Kajian Pendugaan Area Kecil dengan Pendekatan Model Campuran Logistik Kekar pada Data yang Mengandung Pencilan [Thesis]. Bogor, ID: IPB University, 2022. [Online]. Available: IPB Repository.

A. A. Mattjik, and I. M. Sumertajaya, Sidik Peubah Ganda. Bogor: IPB Press, 2011.

Published
2026-08-24
How to Cite
[1]
L. Puja Kusuma, K. Sadik, and A. Kurnia, “THREEFOLD HIERARCHICAL SMALL AREA ESTIMATION MODEL FOR ESTIMATING PREVALENCE OF STUNTING IN WEST NUSA TENGGARA”, BAREKENG: J. Math. & App., vol. 20, no. 4, pp. 3339-3352, Aug. 2026.
Issue
Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
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Articles

Copyright (c) 2026 Logananta Puja Kusuma, Kusman Sadik, Anang Kurnia

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