Re-thinking Spatial Confounding in Spatial Linear Mixed Models

In the last two decades, considerable research has been devoted to a phenomenon known as spatial confounding. Spatial confounding is thought to occur when there is collinearity between a covariate and the random effect in a spatial regression model. This collinearity is considered highly problematic when the inferential goal is estimating regression coefficients, and various methodologies have been proposed to "alleviate" it. Recently, it has become apparent that many of these methodologies are flawed, yet the field continues to expand. In this paper, we offer the first attempt to synthesize work in the field of spatial confounding. We propose that there are at least two distinct phenomena currently conflated with the term spatial confounding. We refer to these as the analysis model and the data generation types of spatial confounding. We show that these two issues can lead to contradicting conclusions about whether spatial confounding exists and whether methods to alleviate it will improve inference. Our results also illustrate that in most cases, traditional spatial linear mixed models do help to improve inference of regression coefficients. Drawing on the insights gained, we offer a path forward for research in spatial confounding.