A Robust Improved GTWR Framework for Spatiotemporal Heterogeneity and Outlier Effects: Evidence from Simulation and Applied Case Studies

Spatiotemporal data often exhibit strong heterogeneity, where relationships between predictors and responses vary across locations and time. Standard regression frameworks struggle with this non-stationarity, and although the Improved Geographically and Temporally Weighted Regression (I-GTWR) addresses spatiotemporal heterogeneity through localized weighting, its reliance on Least Squares makes it highly sensitive to outliers. Contaminated observations propagate through the kernel weighting structure, leading to biased parameter estimates and distorted coefficient surfaces. To address this weakness, this study proposes a Robust I-GTWR framework that integrates M, S, and MM-estimators to downweight extreme values while retaining the model’s adaptive spatiotemporal structure. A controlled simulation was designed to generate heterogeneous spatiotemporal coefficient fields and introduce high-leverage contamination at selected locations and years. Model performance was assessed using bias and RMSE. Results show that robust variants consistently produce lower error and narrower uncertainty distributions than standard I-GTWR, particularly under moderate-to-severe contamination. The method was further applied to tuberculosis incidence and six covariates across 27 regencies/cities in West Java from 2020–2024. Model comparison using AIC selected the M-estimator as the optimal specification. The resulting coefficient surfaces reveal persistent spatiotemporal heterogeneity, effects of population density, HIV prevalence, and sanitation vary substantially across regencies/cities and evolve over time. These findings confirm that robust estimation enhances stability without sacrificing the ability to detect non-stationary processes, making Robust I-GTWR a more reliable approach for contaminated spatiotemporal data and geographically targeted disease control strategies.