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Title: Spatial confounding and spatial+ Authors:  Emiko Dupont - University of Bath (United Kingdom) [presenting]
Simon Wood - University of Edinburgh (United Kingdom)
Nicole Augustin - University of Edinburgh (United Kingdom)
Abstract: Spatial confounding is an issue that can arise when regression models for spatially varying data are used for effect estimation. Such models include spatial random effects to account for the spatial correlation structure in the data. But as spatial random effects are not independent of spatially dependent covariates, they can interfere with the covariate effect estimates and make them unreliable. Traditional methods for dealing with this problem restrict spatial effects to the orthogonal complement of the covariates, however, recent results show that this approach can be problematic. Spatial+ is a novel method for dealing with spatial confounding when the covariate of interest is spatially dependent but not fully determined by spatial location. Theoretical analysis of estimates as well as simulations show that bias, in this case, arises as a direct result of spatial smoothing and, moreover, that it can be avoided by a simple adjustment to the model matrix in the spatial regression model.