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Spatial+: A novel approach to spatial confounding

Spatial+: a novel approach to spatial confounding
Authors: Emiko Dupont; Simon N. Wood; Nicole H. Augustin;

Spatial+: A novel approach to spatial confounding

Abstract

AbstractIn 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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United Kingdom
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Keywords

FOS: Computer and information sciences, Mathematics - Statistics Theory, collinearity, Statistics Theory (math.ST), spatial confounding, Statistics - Applications, Applications of statistics to biology and medical sciences; meta analysis, Methodology (stat.ME), Collinearity, Bias, bias reduction, FOS: Mathematics, partial thin plate spline regression, Computer Simulation, Applications (stat.AP), Statistics - Methodology, Spatial Regression, Partial thin plate spline regression, Models, Statistical, forestry, Forestry, Bias reduction, Spatial confounding, Biometric Methodology, Software

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
59
Top 1%
Top 10%
Top 1%
Green
hybrid