Demystifying Spatial Confounding

T. Kneib

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, relying on an explicit analytical expression for the resulting bias. We see that the problem is directly linked to spatial smoothing and identify exactly how the size and occurrence of bias relate to the features of the spatial model as well as the underlying confounding scenario. We propose a general approach for dealing with spatial confounding bias in practice, applicable for any spatial model specification. We illustrate our approach with an application to air temperature in Germany.

Keywords: Confounding bias, spatial regression, spatial random effects, smoothing, spatial+

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