Two-stage Spatial Regression Models for Spatial Confounding
arxiv(2024)
摘要
Public health data are often spatially dependent, but standard spatial
regression methods can suffer from bias and invalid inference when the
independent variable is associated with spatially-correlated residuals. This
could occur if, for example, there is an unmeasured environmental contaminant.
Geoadditive structural equation modeling (gSEM), in which an estimated spatial
trend is removed from both the explanatory and response variables before
estimating the parameters of interest, has previously been proposed as a
solution, but there has been little investigation of gSEM's properties with
point-referenced data. We link gSEM to results on double machine learning and
semiparametric regression based on two-stage procedures. We propose using these
semiparametric estimators for spatial regression using Gaussian processes with
Matèrn covariance to estimate the spatial trends, and term this class of
estimators Double Spatial Regression (DSR). We derive regularity conditions for
root-n asymptotic normality and consistency and closed-form variance
estimation, and show that in simulations where standard spatial regression
estimators are highly biased and have poor coverage, DSR can mitigate bias more
effectively than competitors and obtain nominal coverage.
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