Geographically Weighted Regression with Adaptive Gaussian and Bisquare Kernels for Dengue Cases in South Sulawesi

  • Nurul Amelia Universitas Negeri Makassar
  • Hardianti Hafid Universitas Negeri Makassar
  • Rahmat H S Universitas Negeri Makassar
Keywords: AIC , Adaptive Gaussian Kernel, Adaptive Bisquare Kernel, DBD, GWR

Abstract

This study aims to model the factors influencing the number of Dengue Fever (DBD) cases in South Sulawesi Province and to compare the performance of Adaptive Gaussian Kernel and Adaptive Bisquare Kernel weighting functions in the Geographically Weighted Regression (GWR) model. GWR is used because it can accommodate spatial heterogeneity, where the relationships between variables differ across locations due to variations in geographic conditions, population density, and environment. Model evaluation was conducted using the Akaike Information Criterion (AIC) and the coefficient of determination (R²). The results show that the GWR model with Adaptive Bisquare Kernel weighting performs better (AIC = 307.3784; R² = 0.9263) compared to the Adaptive Gaussian Kernel (AIC = 340.7891; R² = 0.6106). Thus, the Adaptive Bisquare Kernel is more suitable for modeling DBD cases in South Sulawesi Province as it better captures local spatial variation.

References

Abdullah, N. A., Amran, & Saleh. (2017). Pemodelan geographically weighted regression multikolinearitas menggunakan regresi ridge [Geographically weighted regression modeling of multicollinearity using ridge regression]. Jurnal FMIPA Universitas Hasanuddin. https://core.ac.uk/download/pdf/89562167.pdf

Agustin, G. K. (2017). Pemodelan geographically weighted regression (GWR) dengan fungsi pembobot adaptive Gaussian kernel dan adaptive bisquare kernel [Geographically weighted regression (GWR) modeling with adaptive Gaussian kernel and adaptive bisquare kernel weighting functions] [Undergraduate thesis, Universitas Brawijaya]. http://repository.ub.ac.id/id/eprint/155340/

Amaliasari, C. (2015). Penggunaan pembobot adaptive Gaussian kernel dan adaptive bisquare kernel pada model geographically weighted negative binomial regression (GWNBR) [The use of adaptive Gaussian kernel and adaptive bisquare kernel weights in the geographically weighted negative binomial regression (GWNBR) model] [Undergraduate thesis, Universitas Brawijaya].

Arthayanti, Y., Srinadi, I. G. A. M., & Gandhiadi, G. K. (2017). Geographically weighted ridge regression dalam kasus multikolinearitas pada Indeks Pembangunan Manusia di kabupaten/kota Provinsi Jawa Timur [Geographically weighted ridge regression in the case of multicollinearity on the Human Development Index in the regencies/cities of East Java Province]. Jurnal Matematika, 7(2), 124. https://doi.org/10.24843/jmat.2017.v07.i02.p89

Caraka, R. E., & Yasin, H. (2017). Geographically weighted regression (GWR): Sebuah pendekatan regresi geografis [Geographically weighted regression (GWR): A geographic regression approach]. Mobius. https://doi.org/10.5281/zenodo.1168741

Carolina, M. (2022). Perbandingan model geographically weighted regression (GWR) dengan fungsi pembobot fixed Gaussian kernel dan adaptive Gaussian kernel [Comparison of geographically weighted regression (GWR) models with fixed Gaussian kernel and adaptive Gaussian kernel weighting functions] [Undergraduate thesis, UIN Sunan Kalijaga Yogyakarta].

Chasco, C., Garcia, I., & Vicens, J. (2007). Modeling spatial variations in household disposable income with geographically weighted regression (MPRA Paper No. 9581). Munich Personal RePEc Archive.

Fatati, I. F., Wijayanto, H., & Sholeh, A. M. (2017). Analisis regresi spasial dan pola penyebaran pada kasus demam berdarah dengue (DBD) di Provinsi Jawa Tengah [Spatial regression analysis and distribution pattern of dengue hemorrhagic fever (DHF) cases in Central Java Province]. Media Statistika, 10(2), 95–105. https://doi.org/10.14710/medstat.10.2.95-105

Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: The analysis of spatially varying relationships. John Wiley & Sons.

Giofandi, E. A., Purwantiningrum, P., Madino, F., & Lumbantobing, A. (2023). Analisis faktor spasial terhadap kejadian demam berdarah dengue menggunakan pendekatan geographically weighted regression di Kota Pekanbaru, Provinsi Riau [Analysis of spatial factors of dengue hemorrhagic fever incidence using a geographically weighted regression approach in Pekanbaru City, Riau Province]. Jurnal Ilmu Lingkungan, 22(1), 50–59. https://doi.org/10.14710/jil.22.1.50-59

Ikbal, A., Purnamasari, A. I., & Ali, I. (2024). Analisis klasterisasi untuk prediksi jumlah kasus DBD berdasarkan jenis kelamin dan kabupaten/kota di Jawa Barat [Cluster analysis for predicting the number of DHF cases by sex and regency/city in West Java]. JATI (Jurnal Mahasiswa Teknik Informatika), 7(6), 3789–3796. https://doi.org/10.36040/jati.v7i6.8296

Li, Z., Fotheringham, A. S., Oshan, T. M., & Wolf, L. J. (2020). Measuring bandwidth uncertainty in multiscale geographically weighted regression using Akaike weights. Annals of the American Association of Geographers, 110(5), 1500–1520. https://doi.org/10.1080/24694452.2019.1704680

Lin, C., & Wen, T. (2011). Using geographically weighted regression (GWR) to explore spatial varying relationships of immature mosquitoes and human densities with the incidence of dengue. International Journal of Environmental Research and Public Health, 8(7), 2798–2815. https://doi.org/10.3390/ijerph8072798

Lutfiani, N., Sugiman, S., & Mariani, S. (2019). Pemodelan geographically weighted regression (GWR) dengan fungsi pembobot kernel Gaussian dan bi-square [Geographically weighted regression (GWR) modeling with Gaussian and bi-square kernel weighting functions]. Unnes Journal of Mathematics, 8(1), 82–91. https://doi.org/10.15294/ujm.v8i1.17103

Muna, M. L. L., Sutiningsih, D., Martini, M., Fauzi, M., & Dharmawan, Y. (2025). Geographically weighted regression (GWR) analysis of factors related to dengue hemorrhagic fever in Central Java Province, Indonesia. International Journal of Mosquito Research, 12(2), 19–24. https://doi.org/10.22271/23487941.2025.v12.i2a.830

Musdar, Y., Aswi, & Mar’ah, Z. (2024). Pemodelan geographically weighted Poisson regression untuk kasus DBD di Provinsi Sulawesi Selatan tahun 2022 [Geographically weighted Poisson regression modeling of DHF cases in South Sulawesi Province in 2022]. Jurnal MSA (Matematika dan Statistika serta Aplikasinya), 12(2), 16–21. https://doi.org/10.24252/msa.v12i2.51242

Nisa, K. (2022). Penerapan model geographically weighted Poisson regression untuk demam berdarah dengue di Kabupaten Bojonegoro [Application of the geographically weighted Poisson regression model to dengue hemorrhagic fever in Bojonegoro Regency]. Jurnal Statistika dan Komputasi, 1(1), 12–22. https://doi.org/10.32665/statkom.v1i1.444

Rahmawati, D., & Bimanto, H. (2021). Perbandingan spatial autoregressive model dan spatial error model dalam pemodelan indeks pembangunan manusia di Provinsi Jawa Timur [Comparison of the spatial autoregressive model and the spatial error model in modeling the human development index in East Java Province]. Jurnal Statistika dan Aplikasinya, 5(1), 41–50. https://doi.org/10.21009/JSA.05104

Sartika, E., & Murniati, S. (2021). Application of the geographically weighted regression (GWR) with the bi-square weighting function on the poverty model in the city/regency of West Java. In Proceedings of the 2nd International Seminar of Science and Applied Technology (ISSAT 2021) (Advances in Engineering Research, Vol. 207, pp. 201–207). Atlantis Press. https://doi.org/10.2991/aer.k.211106.031

Ulfie, S., & Amaliana, L. (2021). Model geographically weighted regression dengan fungsi pembobot adaptive dan fixed kernel pada kasus kematian ibu di Jawa Timur [Geographically weighted regression model with adaptive and fixed kernel weighting functions for maternal mortality cases in East Java]. Jurnal Statistika dan Aplikasinya, 5(2), 208–220. https://doi.org/10.21009/jsa.05209

Ulhaq, H. (2020). Geographically weighted logistic regression (GWLR) with Gaussian adaptive kernel weighting function, bisquare, and tricube in case of malnutrition of toddlers in Indonesia. Jurnal Litbang Edusaintech, 1(1), 5–13. https://doi.org/10.51402/jle.v1i1.2

Wahyudi, R., Fauzi, Y., & Rizal, J. (2023). Analisis kemiskinan ekstrem Provinsi Bengkulu menggunakan metode geographically weighted regression (GWR) dengan pembobot adaptive Gaussian kernel dan adaptive bi-square [Analysis of extreme poverty in Bengkulu Province using the geographically weighted regression (GWR) method with adaptive Gaussian kernel and adaptive bi-square weights]. Journal of Mathematics UNP, 8(2), 134. https://doi.org/10.24036/unpjomath.v8i2.14914

Published
2026-10-21
How to Cite
Amelia, N., Hardianti Hafid, & Rahmat H S. (2026). Geographically Weighted Regression with Adaptive Gaussian and Bisquare Kernels for Dengue Cases in South Sulawesi. VARIANSI: Journal of Statistics and Its Application on Teaching and Research, 8(02), 209-220. https://doi.org/10.35580/variansiunm552
Section
Articles