Robust Spatial Confounding Adjustment via Basis Voting

2025-10-25

AI Summary

Spatial causal effect estimation often suffers from nonidentification due to unobserved spatial confounding. Existing methods rely on the strong assumption that exposure variation occurs at higher frequencies than confounding—making them ill-suited for smooth environmental exposures. This paper proposes Basis Voting, a novel framework that ensures consistent causal identification under a substantially weaker condition: exposure and confounding need only differ in their support across a majority of spatial basis functions—requiring no prior knowledge of spectral properties. The method integrates basis expansion, projection-based estimation, and a majority-voting mechanism to yield a robust and computationally efficient estimator. Simulation and empirical studies demonstrate that, whenever exposure and confounding signals are separable across most basis functions, Basis Voting delivers stable, unbiased causal estimates. This advances spatial causal inference—particularly in environmental epidemiology—by providing a more flexible and practically applicable tool.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Estimating causal effects of spatially structured exposures is complicated by unmeasured spatial confounders, which undermine identifiability in spatial linear regression models unless structural assumptions are imposed. We develop a general framework for causal effect estimation that relaxes the commonly assumed requirement that exposures contain higher-frequency variation than confounders. We propose basis voting, a plurality-rule estimator - novel in the spatial literature - that consistently identifies causal effects only under the assumption that, in a spatial basis expansion of the exposure and confounder, there exist several basis functions in the support of the exposure but not the confounder. This assumption generalizes existing assumptions of differential basis support used for identification of the causal effect under spatial confounding, and does not require prior knowledge of which basis functions satisfy this support condition. We also show that the standard projection-based estimator used in other methods relying on differential support is inefficient, and provide a more efficient novel estimator. Extensive simulations and a real-world application demonstrate that our approach reliably recovers unbiased causal estimates whenever exposure and confounder signals are separable on a plurality of basis functions. Importantly, by not relying on higher-frequency variation, our method remains applicable to settings where exposures are smooth spatial functions, such as distance to pollution sources or major roadways, common in environmental studies.

Problem

• Estimating causal effects with unmeasured spatial confounders in regression models
• Relaxing requirement for higher-frequency variation in exposures than confounders
• Providing efficient estimation when exposure and confounder signals are separable

Innovation

• Basis voting estimator identifies causal effects
• Relaxes requirement for higher-frequency exposure variation
• Efficient estimator for separable exposure and confounder signals