Demystifying Spatial Confounding

Thomas Kneib, University of Göttingen

Co-authors: Emiko Dupont, University of Bath; Isa Marques, The Ohio State University

Abstract: Spatial confounding is a fundamental issue in spatial regression models which arises because spatial random effects, included to approximate unmeasured spatial variation, are typically not independent of covariates in the model. This can lead to significant bias in covariate effect estimates. We develop a broad theoretical framework that brings mathematical clarity to the mechanisms of spatial confounding, providing explicit analytical expressions for the resulting bias. Using our results, we can explain subtle and counter-intuitive behaviours. We also propose a general approach for dealing with spatial confounding bias in practice and illustrate it with an application to air temperature in Germany.