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    A spectral adjustment for spatial confounding

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    Type
    Preprint
    Authors
    Guan, Yawen
    Page, Garritt L.
    Reich, Brian J
    Ventrucci, Massimo
    Yang, Shu
    Date
    2020-12-22
    Permanent link to this record
    http://hdl.handle.net/10754/666727
    
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    Abstract
    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
    Sponsors
    This work was partially supported by the National Institutes of Health (R01ES031651-01,R01ES027892-01) and King Abdullah University of Science and Technology (3800.2).
    Publisher
    arXiv
    arXiv
    2012.11767
    Additional Links
    https://arxiv.org/pdf/2012.11767
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