Modeling the Number of Poor Population using Geographically Weighted Negative Binomial Regression (GWNBR) in North Sumatera Province
DOI:
https://doi.org/10.30605/proximal.v9i2.9583Keywords:
Poverty, Overdispersion, Spatial Heterogeneity, Geographically Weighted Negative Binomial RegressionAbstract
Poverty remains a persistent and unevenly distributed development challenge across North Sumatra Province, so models capable of capturing this regional variation are urgently needed to support more precisely targeted poverty alleviation policies. This study develops a model for the number of poor people in 33 regencies/cities of North Sumatra Province in 2025 using Geographically Weighted Negative Binomial Regression (GWNBR). The response variable is the number of poor people (Y), while the explanatory variables are the Open Unemployment Rate (X1), Human Development Index (X2), Senior High School Education Level (X3), Labor Force Participation Rate (X4), and the percentage of households with access to proper sanitation (X5). The analysis consists of Poisson regression, Negative Binomial regression, Moran's I testing for spatial autocorrelation, the Breusch–Pagan test for spatial heterogeneity, and GWNBR using an Adaptive Bisquare weighting function. The Poisson model shows severe overdispersion, with a deviance-to-degrees-of-freedom ratio of 3,820.53. Moran's I indicates no significant spatial autocorrelation in the residuals (I = -0.0202; p = 0.1180), whereas the Breusch–Pagan test confirms significant spatial heterogeneity (BP = 15.7949; p = 0.0075). The GWNBR model produces a deviation of 18.420 and McFadden's R² of 0.150000 and captures differences in the effects of explanatory variables across locations. Based on significant local parameters, the study area is divided into two groups. Group 1 consists of Mandailing Natal Regency and South Nias Regency, with X1, X2, and X3 being significant, while Group 2 consists of the other 31 regencies/cities, with X2 and X3 being significant. These findings indicate that GWNBR can describe poverty-related factors locally and provide information relevant to location-specific poverty reduction policies. The results are expected to help local governments design region-specific poverty alleviation programs rather than relying on uniform province-wide policies, and it is recommended that future studies incorporate additional socioeconomic variables and more recent panel data to further improve the model's accuracy and policy relevance.References
Annisa Priliya, A., Sri Sulistijowati, & Sugiyanto. (2020). Modeling the Number of Malnutritional Toddlers Using the Geographically Weighted Negative Binomial Regression (GWNBR) Method with Adaptive Weighting Function. Journal of the National Seminar on Education and Mathematics (SENANDIKA), 31-38.
Ayunda, A., & Ismail Husein. (2025). Geographically Weighted Negative Binomial Regression (GWNBR) Modeling of Tuberculosis (TB) in North Sumatra. Zero: Journal of Science, Mathematics, and Applied Mathematics, 228-237.
Azkia, Dewi Sri, & Monica Raina. (2024). Geographically Weighted Negative Binomial Regression (GWNBR) Modeling of Stunting Incidents in Barito Kuala Regency in 2022. RAGAM: Journal of Statistics and Its Application, 42-55.
Brunsdon, C., Fotheringham, A. S., & Charlton, M. E. (1996). Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity. Geographical Analysis, 28(4), 281-298. https://doi.org/10.1111/j.1538-4632.1996.tb00936.x
Damayanti, C. M., & Yanti, T. (2022). Inverse Gaussian Poisson Regression (PIG) for Modeling the Number of Pneumonia Cases in Toddlers in Java Province in 2019. Journal of Statistical Research, 143-151.
Delvia, N., Mustafid, M., & Yasin, H. (2021). Geographically Weighted Negative Binomial Regression Untuk Menangani Overdispersi Pada Jumlah Penduduk Miskin. Jurnal Gaussian, 10(4), 532-543. https://doi.org/10.14710/j.gauss.10.4.532-543
Fitriani, R., & Jaya, I. G. N. M. (2020). Spatial Modeling of Confirmed COVID-19 Pandemic in East Java Province by Geographically Weighted Negative Binomial Regression. Communications in Mathematical Biology and Neuroscience, 2020, Article 17. https://doi.org/10.28919/cmbn/4874
Halim, A. O., Satyahadewi, N., & Preatin, P. (2025). Factor Analysis on Poverty in Kalimantan Island with Geographically Weighted Negative Binomial Regression. Pattimura International Journal of Mathematics (PIJMath), 4(1), 41-52. https://doi.org/10.30598/pijmathvol4iss1pp41-52
Harahap, R. (2022). Implementation of Geographically Weighted Regression (GWR) and Mixed Geographically Weighted Regression (MGWR) in Calculating the Number of Poor People. Jurnal Media Satistika, 11-32.
Jasmadi, I., Widodo, D. A., & Oktaviana, P. P. (2016). Pemodelan dan Pemetaan Kasus Jumlah Penduduk Miskin di Provinsi Jambi pada Tahun 2014 dengan Menggunakan Geographically Weighted Negative Binomial Regression. Jurnal Sains dan Seni ITS, 5(2), 350-354. https://doi.org/10.12962/j23373520.v5i2.16704
Nakaya, T., Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2005). Geographically Weighted Poisson Regression for Disease Association Mapping. Statistics in Medicine, 24(17), 2695-2717. https://doi.org/10.1002/sim.2129
Putri, D., & Fathurahman, M. (2024). Modeling the Number of Pulmonary Tuberculosis Cases in Indonesia with Geographically Weighted Negative Binomial Regression. Eksponensial, Journal of Applied Mathematics, 49-62.
Rahmadeni, F., & RJ (2019). Generalized Poisson Regression (GPR) Modeling in Neonatal Mortality Cases in Riau Province. Journal of Mathematical Science and Statistics: Journal of Research Results in Mathematics, Statistics, and Their Applications, 43-50.
Sitorus, A. L. T., & Simamora, E. (2023). Metode Geographically Weighted Panel Regression (GWPR) untuk Menganalisis Faktor yang Mempengaruhi Kemiskinan di Provinsi Sumatera Utara. Ranah Research: Journal of Multidisciplinary Research and Development, 6(1), 155-167. https://doi.org/10.38035/rrj.v6i1.808
Sriningsih, R., Soleh, M., Subhan, M., & Gusty, R. P. (2026). Spatial Heterogeneity of Tuberculosis Incidence Using Geographically Weighted Negative Binomial Regression (GWNBR) in Indonesia. Zero: Jurnal Sains, Matematika dan Terapan, 10(1), 132-143. https://doi.org/10.30829/zero.v10i1.28500
Suryadi, F., Jonathan, S., Jonatan, K., & Ohyver, M. (2023). Handling Overdispersion in Poisson Regression Using Negative Binomial Regression for Poverty Case in West Java. Procedia Computer Science, 216, 517-523. https://doi.org/10.1016/j.procs.2022.12.164
Winata, H. M. (2023). Mengatasi Overdispersi dengan Regresi Binomial Negatif pada Angka Kematian Ibu di Kota Bandung. Jurnal Gaussian, 11(4), 616-622. https://doi.org/10.14710/j.gauss.11.4.616-622
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