Two-Stage Estimators for Spatial Confounding with Point-Referenced Data

Music City Center 

Public health data are often spatially dependent, but spatial regression methods can suffer
from bias and invalid inference when the independent variable is associated with spatially-correlated residuals. This
could occur if an unmeasured environmental contaminant is 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 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 Matérn covariance to estimate the spatial trends, and term these estimators Double Spatial
Regression (DSR). We derive regularity conditions for root-n asymptotic normality and consistency and closed-form
variance estimation, and show in simulations that DSR outperforms competitors.

bias reduction

double machine learning

Gaussian process

semiparametric regression 

Section on Statistics in Epidemiology