Regression models for spatially varying data use spatial random effects to model unexplained spatial variation in the response variable. But as these random effects cannot be assumed to be independent of spatially dependent covariates, they may interfere with the estimation of covariate effects in the model. Thus, covariate effect estimates in spatial models may be unreliable. This complex problem, known as spatial confounding, has gained much attention in recent years, but has so far only been studied for models with linear covariate effects. However, as illustrated by a forestry example in which we assess the effect of soil, climate, and water budget variables on tree health, the covariate effects of interest are in practice often unknown and non-linear. We consider, for the first time, spatial confounding in spatial models with non-linear effects implemented in the generalized additive models (GAMs) framework. We show that spatial+, a recently developed method for the linear case, can be adapted to alleviate confounding for non-linear effect estimates as well. We demonstrate our findings through a simulation study and illustrate how the method can be implemented in practice by applying it to our forestry example.
(Joint work with Nicole Augustin, University of Edinburgh)