Primary Submission Category: Design-Based Causal Inference
Spatial Error Models and Unmeasured Spatial Confounding: The Underlying Experiment
Authors: Sophie Woodward, Francesca Dominici, Jose Zubizarreta,
Presenting Author: Sophie Woodward*
Regression models incorporating spatially structured error terms, known as spatial error models, are commonly used to address unmeasured spatial confounding. Despite their prevalence, the extent to which these models mitigate unmeasured spatial confounding remains contentious. In this work, we examine three canonical types of spatial error models — random effects, conditional autoregressive models, and Gaussian processes — and reinterpret their generalized least squares (GLS) estimators through the lens of weighting for causal inference with a binary treatment. Our proposed framework offers new insights into how spatial error models construct contrasts between treated and control units in space. We also provide diagnostics to characterize covariate balance, study representativeness, effective sample size, sign reversal, and the use of spatial information. Crucially, we demonstrate that the design-conditional bias of GLS estimators is determined by the relative spatial smoothness of the unmeasured confounder and the treatment. Extending these insights, we propose a spatial balancing weights estimator that targets the average treatment effect for a specified population, is sample bounded, accommodates nonlinearity and treatment effect heterogeneity, and mitigates bias from spatially smooth unmeasured confounders. We evaluate the finite-sample performance of our proposed method in simulation and apply it to estimate the effect of Superfund cleanups on birth weight.