Modeling the Number of Poor Population using Geographically Weighted Negative Binomial Regression (GWNBR) in North Sumatera Province

Juliani Juliani (Universitas Islam Negeri Sumatera Utara)
Ismail Husein (Universitas Islam Negeri Sumatera Utara)

Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika
Vol. 9 No. 2 (2026): Exploring Mathematics through Education, Modeling, Finance, and Cultural Perspe

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.