Spatial+: A novel approach to spatial confounding

2022/03/08 by Emiko Dupont, Simon N. Wood, Nicole H. Augustin · 1 voice · 72 citations
Economics, Econometrics and Finance · Mathematics · #Artificial intelligence #Collinearity #Computer science #Confounding #Covariate #Econometrics #Economic and Environmental Valuation #Health Systems, Economic Evaluations, Quality of Life #Inference #Kriging #Mathematics #Smoothing #Spatial analysis #Spatial and Panel Data Analysis #Spatial dependence #Spatial ecology #Spatial heterogeneity #Spatial variability #Statistics

paper · pdf · doi:10.1111/biom.13656

published in Biometrics 78(4), 1279-1290 (Oxford University Press)

openalex publication_date 2022/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In spatial regression models, collinearity between covariates and spatial effects can lead to significant bias in effect estimates. This problem, known as spatial confounding, is encountered modeling forestry data to assess the effect of temperature on tree health. Reliable inference is difficult as results depend on whether or not spatial effects are included in the model. We propose a novel approach, spatial+, for dealing with spatial confounding when the covariate of interest is spatially dependent but not fully determined by spatial location. Using a thin plate spline model formulation we see that, in this case, the bias in covariate effect estimates is a direct result of spatial smoothing. Spatial+ reduces the sensitivity of the estimates to smoothing by replacing the covariates by their residuals after spatial dependence has been regressed away. Through asymptotic analysis we show that spatial+ avoids the bias problems of the spatial model. This is also demonstrated in a simulation study. Spatial+ is straightforward to implement using existing software and, as the response variable is the same as that of the spatial model, standard model selection criteria can be used for comparisons. A major advantage of the method is also that it extends to models with non-Gaussian response distributions. Finally, while our results are derived in a thin plate spline setting, the spatial+ methodology transfers easily to other spatial model formulations.

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Discussions

• Spatial+: a relatively easy way to address spatial confounding doi.org/10.1111/biom... Comparison with other methods: doi.org/10.1007/s131... #statistics #rspatial [bsky, 17 points, 2 comments]

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