On Alleviating Spatial Confounding Issues With the Bayesian Lasso

Abstract

ABSTRACTSpatial confounding usually refers to an issue that often arises in the context of fitting a spatial linear mixed model: the collinearity between fixed and spatial random effects. As a consequence, this can lead to erroneous covariate–response associations, with the resulting scientific or social impact. Different methods have been proposed in the literature to alleviate spatial confounding. However, recent research suggests that restricted spatial regression, the most commonly used, produces anticonservative confidence intervals and hence performs worse than the original spatial linear mixed model in terms of coverage. In this paper, we propose the use of the Bayesian Lasso for alleviating spatial confounding. Specifically, we propose a joint model that includes the fixed‐effects modeling process and the spatial linear mixed modeling framework subject to a penalty on the effect of the covariate on the response. The model proposed is tested for the Slovenia dataset, which is typically used for the study of this topic. We show that the model yields a covariate–response association relatively coherent with that inferred from the fixed‐effects model, while allowing for the inclusion of spatial random effects, thus performing better in terms of goodness‐of‐fit and spatial smoothing than the fixed‐effects model. A second application is also shown for a COVID‐19 dataset corresponding to the Greater London area, which provides similar insights about the proposed methodology.