Robust Geographically Weighted Regression (RGWR) Modeling with S-Estimator for the Number of Tuberculosis Cases in West Java Province in 2024
Humaira Rizqi Tridianti(a), Fitriani Agustina(a*), Nar Herrhyanto(a), Fitri Rahmawati(a)

a) Mathematics Study Program, Universitas Pendidikan Indonesia
Jalan Dr. Setiabudhi No. 229 Bandung 40154 Indonesia
*fitriani_agustina[at]upi.edu

Abstract

Geographically Weighted Regression (GWR) is a development of multiple linear regression that considers spatial factors, so that the parameter estimation value is different in each location of observation. However, in the practice of data analysis, outliers are sometimes found that can affect the accuracy of parameter estimation which causes the estimated value of the parameters to be biased. To overcome this, robust regression with S-Estimator is used in GWR model, known as Robust GWR (RGWR). This study aims to obtain a GWR model that is more robust to the presence of outliers through the application of RGWR on Tuberculosis (TBC) cases in West Java Province in 2024. The independent variables used in the study are the number of poor people (&#119883-1), the number of HIV cases (&#119883-2), life expectancy index (&#119883-3), percentage of clean and healthy living behavior (&#119883-4), percentage of households that have access to proper sanitation (&#119883-5), population density (&#119883-6), and number of public hospitals (&#119883-7). Based on the analysis, 27 RGWR models were obtained for 27 districts/cities in West Java Province. This model produces an &#119877-2 value of 0.9543, which indicates that the number of TB cases in West Java in 2024 can be explained by the variables in the model, while the remaining 4.57% is influenced by other factors. In this study, the RGWR model has a larger &#119877- value and a smaller MAD and RMSE value compared to the GWR model. This indicates that RGWR is more suitable for modeling the number of TB cases in each district/city in West Java Province in 2024 compared to the GWR model.

Keywords: Spatial Heterogenity, Outlier, GWR, Robust GWR, Tuberculosis

Topic: Mathematics and Mathematics Education