  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
associated with the independent and outcome variables in a spatial regression
analysis. 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 Mat\`ern 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.
