Residualized Local Conditional Mutual Information (LCMI): a scalable information-theoretic framework for interpretable and nonlinear spatially varying effect modelling

Understanding nonlinear spatially varying effects remains a central challenge in spatial analysis. Existing spatial models often face a trade-off between local interpretability, nonlinear flexibility, and computational feasibility. To address this challenge, this study proposes a two-stage Local Conditional Mutual Information (LCMI) framework for interpretable, spatially explicit, and scalable modelling of nonlinear spatially varying effects. Stage I estimates residualized local conditional-dependence surfaces as a tractable approximation to conditional relevance, extracts global effect-shape functions, and decomposes each predictor into baseline, local nonlinear adjustment, and total contribution. Stage II uses these outputs as non-negative local information weights to reconstruct signed local coefficients on the recovered effect-shape basis through LCMI-guided weighted local regression. The framework embeds explanation directly into modelling rather than treating it as a separate post hoc step. Synthetic experiments show that the proposed framework accurately recovers nonlinear spatial effect surfaces while remaining computationally efficient. Scalability tests show that the method remains tractable at one million observations in a CPU environment. The study demonstrates that residualized information-theoretic local dependence can provide a practical, model-internal basis for interpretable and scalable spatial modelling of nonlinear geographic processes, while the resulting LCMI surfaces should be interpreted as conditional-dependence approximations rather than direct high-dimensional CMI estimates.