On alleviating spatial confounding issues with the Bayesian Lasso

Abstract Spatial confounding usually refers to an issue that often arises in the context of fitting a spatial linear mixed model: the collinearity between the fixed effects and the spatial random effects. As a major consequence, this can lead to the inference of 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 to date, performs worse than the original spatial linear mixed model, and should be avoided for this purpose. In this paper, we propose the use of the Bayesian version of the standard Lasso method for alleviating spatial confounding. Specifically, we propose a joint model that includes the fixed-effects modeling process (not including spatial random effects) 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 usually used for the study of this topic. The model provides an estimate of the covariate-response association of interest which is close to 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 simulation study is also carried out, which allows us to verify that the covariate effect estimated through the model proposed is coherent with the one given by the fixed-effects model. The simulation study also enables us to reinforce the idea that finding the most suitable modeling framework for estimating a covariate-response association in a spatial context is not an easy task.