Brian J. Reich (North Carolina State University)
Title:Â A Spectral Adjustment for Spatial Confounding.
Abstract:Â Brian is the Gertrude M Cox Distinguished Professor of Statistics at North Carolina State University. He completed his PhD in Biostatistics in 2005 under the direction of Jim Hodges of the University of Minnesota. After graduation, he joined NC State first as a post-doc with Montse Fuentes and then as a member of the statistics faculty in 2008. His research interests include spatial statistics, extreme value analysis, variable selection and dimension reduction. In addition to these methodological interests, Brian applies these methods to environmental areas such as ecology, air pollution, and climate change, as well as data from the physical and materials sciences. Please visit:
Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. In this paper, we derive necessary conditions on the coherence between the treatment variable of interest 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.