Addressing spatial confounding in geostatistical regression models: An R‐ INLA approach

Abstract Spatial confounding, which has been studied extensively in recent years, can explain inconsistencies between results obtained by regression models with and without spatial modelling. While the most common solutions for spatial confounding mitigation often target areal data or geostatistical data modelling by splines, we aim to extend some resolution methods for geostatistical data modelling by Gaussian Markov Random Fields (GMRF) using R‐INLA methodology, aided by the R‐inlabru package. We focus on four sought‐after approaches for alleviating spatial confounding: Restricted spatial regression (RSR), geoadditive structural equation model (gSEM), Spatial+, and its simplified version, called here Spatial+2.0. We show how each can be implemented from geostatistical data in a GMRF framework using R‐inlabru. Next, a simulation study that produces a spatial confounding phenomenon in a geostatistical context is carried out to assess the coherence of the proposed extensions with the expectations of these methods. Then we apply the expanded approaches to a case study, linking cadmium (Cd) concentration in terrestrial mosses to Cd concentration in air. Our findings support the feasibility of our extended approach of spatial confounding resolution methods to geostatistical data using R‐inlabru in keeping with the previous contexts, although certain precautions and limitations must be considered.