A0576
Title: A spectral adjustment for spatial confounding
Authors: Yawen Guan - University of Nebraska - Lincoln (United States) [presenting]
Garritt Page - Brigham Young University (United States)
Brian Reich - North Carolina State University (United States)
Massimo Ventrucci - Department of Statistical Sciences, University of Bologna (Italy)
Shu Yang - North Carolina State University (United States)
Abstract: Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting, it may be possible under certain conditions. We derive necessary conditions on the coherence between the treatment variable and the unmeasured confounder that ensure the causal effect of the treatment is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. The key assumption that ensures identifiability is that confounding present at global scales dissipates at local scales. We show that this assumption in the spectral domain is equivalent to adjusting for global-scale confounding in the spatial domain by adding a spatially smoothed version of the treatment variable to the mean of the response variable. Within this general framework, we propose a sequence of confounder adjustment methods that range from parametric adjustments based on the Matern coherence function to more robust semi-parametric methods that use smoothing splines. These ideas are applied to areal and geostatistical data for both simulated and real datasets.