Advanced statistical methods for analyzing spatially varying relationships in overdispersed HIV case counts in East Java Province, Indonesia: GWRF vs. GWNBR

This study investigates the efficacy of Geographically Weighted Random Forest (GWRF) compared to Negative Binomial Regression (NBR) and Geographically Weighted Negative Binomial Regression (GWNBR) in modeling spatially varying, overdispersed count data using HIV cases from East Java Province, Indonesia.The dataset covers 38 regencies/cities and examines the relationship between HIV cases and five independent variables. GWNBR incorporates spatial weighting based on adaptive bisquare kernel function and Euclidean distance, while GWRF combines random forests with geographical weighting.GWRF emerges as the superior model based on RMSE, MAPE, and R² values, outperforming NBR and GWNBR. GWRF identifies five groups based on the three most important predictor variables. In approximately 60\% of the region, the percentage of drug users ($X_2$), the percentage of individuals living in poverty ($X_4$), and the open unemployment rate ($X_5$) are identified as important variables. Notably, the percentage of drug users and the open unemployment rate are consistently associated with HIV cases across nearly all regions. This study offers valuable insights into HIV transmission patterns and associated risk factors across the province, contributing to a better understanding of the spatial distribution of HIV cases and informing targeted interventions and resource allocations.