  The concept of spatial confounding is closely connected to spatial
regression, although no general definition has been established. A generally
accepted idea of spatial confounding in spatial regression models is the change
in fixed effects estimates that may occur when spatially correlated random
effects collinear with the covariate are included in the model. Different
methods have been proposed to alleviate spatial confounding in spatial linear
regression models, but it is not clear if they provide correct fixed effects
estimates. In this article, we consider some of those proposals to alleviate
spatial confounding such as restricted regression, the spatial+ model, and
transformed Gaussian Markov random fields. The objective is to determine which
one provides the best estimates of the fixed effects. Dowry death data in Uttar
Pradesh in 2001, stomach cancer incidence data in Slovenia in the period
1995-2001 and lip cancer incidence data in Scotland between the years 1975-1980
are analyzed. Several simulation studies are conducted to evaluate the
performance of the methods in different scenarios of spatial confounding.
Results reflect that the spatial+ method seems to provide fixed effects
estimates closest to the true value.
