Multiscale Geographically Weighted Spline Nonparametric Regression for Spatial Modeling of Poverty  in Eastern Indonesia

Indi Rizqy Fahrani; Henny Pramoedyo; Atiek Iriany

doi:10.31764/jtam.v10i4.40625

Multiscale Geographically Weighted Spline Nonparametric Regression for Spatial Modeling of Poverty in Eastern Indonesia

Indi Rizqy Fahrani, Henny Pramoedyo, Atiek Iriany

Abstract

Poverty in Eastern Indonesia remains spatially heterogeneous, and its determinants are unlikely to operate at a single geographic scale or to follow a predetermined functional form. This study applies a quantitative, spatial nonparametric regression approach, namely the Multiscale Geographically Weighted Spline Nonparametric Regression (MS-GWSNR) model, to poverty rates in 176 regencies/cities across Eastern Indonesia in 2025. The model uses secondary cross-sectional data from Statistics Indonesia (BPS) and the Geospatial Information Agency (BIG), with the Human Development Index (HDI), open unemployment rate (OUR), gross regional domestic product (GRDP) per capita, and population density as covariates. The model was estimated via a backfitting algorithm assigning a component-specific bandwidth to each covariate, benchmarked against single-bandwidth GWSNR and the linear MGWR. The spatial scale of each covariate was characterized by pairing its optimum bandwidth with the effective number of parameters (ENP). The results showed that the covariates operated at markedly different spatial scales: the intercept, HDI, OUR, and population density were local (bandwidth 10–14 nearest regencies), whereas GRDP per capita was nearly global (bandwidth 175, lowest ENP). HDI was the dominant determinant, significant in 89.8% of locations and generally associated with lower poverty. MS-GWSNR achieved the best fit among the compared models, raising the coefficient of determination from 85.69% (MGWR) and 87.54% (GWSNR) to 88.70% and reducing the RMSE from 3.3467 and 3.1232 to 2.9741, while also producing more stable local estimates. Notably, both MGWR and MS-GWSNR independently identified GRDP per capita as a near-global process, supporting the robustness of the multiscale finding.

Keywords

Poverty; Spatial Heterogeneity; Multiscale; Geographically Weighted Regression; Ttruncated Spline.

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DOI: https://doi.org/10.31764/jtam.v10i4.40625