Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love

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Effects of spatial autocorrelation and imperfect detection on species distribution models (2018, background): “However, more care should be taken with the interpretation of the model coefficients since covariates may be collinear with the spatial term (Hanks, Schliep, Hooten, & Hoeting, 2015; Hodges & Reich, 2010).”
Bayesian Workflow (2020, background): “For example, Hodges and Reich (2010) describe how structured model components such as spatial effects can have complex interactions with linear covariate effects.”
Basis-Function Models in Spatial Statistics (2021, methodology): “This approach has been taken up by Hodges & Reich (2010), Paciorek (2010), Hughes & Haran (2013), and Bradley et al. (2015), and the use of these basis functions in Equations 9 and 10 has become known as restricted spatial regression (RSR).”
Structural Equation Models for Dealing With Spatial Confounding (2018, methodology): “Based on the same data, Hodges and Reich (2010) introduced restricted spatial regression via an orthogonalization of the spatial effect and the covariate information.”
Hierarchical statistical modeling of big spatial datasets using the exponential family of distributions (2013, methodology): “(2006) and Hodges and Reich (2010) used a reparameterization of (13) to show that such a SGLMM exhibits spatial confounding for fully Bayesian inference.”