Mixed Geographically Weighted XGBoost (M-GWXGB) Model: A New Spatially Explicit Machine Learning Model

Analyzing spatially varying relationships constitutes a fundamental pursuit in geography, crucial for comprehending intricate spatial patterns. These relationships can arise from spatial heterogeneity or from nonlinearity. To distinguish these diverse relationships, researchers have developed spatially varying coefficient (SVC) models and machine learning (ML) techniques. When confronted with nonlinear relationships that also exhibit spatial nonstationarity, though, existing models might produce misleading conditional relationships. To address this research gap, this study introduces a mixed geographically weighted extreme gradient boosting (M-GWXGB) model, which integrates a semiparametric generalized additive model with a multiscale ML approach to estimate variable-specific spatial processes while addressing both spatial heterogeneity and nonlinearity. We calculate the marginal contributions to extract spatially varying and nonlinear relationships. We evaluate the efficiency of our proposed approach on three simulated data sets and a real-world data set, showing that M-GWXGB can avoid the misinterpretation of spatial variation as nonlinearity and vice versa. Additionally, our new model outperforms mainstream spatially explicit ML models (e.g., XGB, graph convolutional network [GCN], GWXGB) and SVCs (e.g., multiscale geographically weighted regression) in terms of predictability, interpretability, and the capability to estimate variable-specific spatial processes, particularly when spatial heterogeneity and nonlinearity coexist. Finally, we propose a roadmap to guide the application of the M-GWXGB model. Our empirical analysis yields valuable insights into leveraging M-GWXGB to elucidate complex geographical phenomena, highlighting its potential to understand spatially varying processes in spatial data.