  The estimation of regression parameters in spatially referenced data plays a
crucial role across various scientific domains. A common approach involves
employing an additive regression model to capture the relationship between
observations and covariates, accounting for spatial variability not explained
by the covariates through a Gaussian random field. While theoretical analyses
of such models have predominantly focused on prediction and covariance
parameter inference, recent attention has shifted towards understanding the
theoretical properties of regression coefficient estimates, particularly in the
context of spatial confounding. This article studies the effect of misspecified
covariates, in particular when the misspecification changes the smoothness. We
analyze the theoretical properties of the generalize least-square estimator
under infill asymptotics, and show that the estimator can have
counter-intuitive properties. In particular, the estimated regression
coefficients can converge to zero as the number of observations increases,
despite high correlations between observations and covariates. Perhaps even
more surprising, the estimates can diverge to infinity under certain
conditions. Through an application to temperature and precipitation data, we
show that both behaviors can be observed for real data. Finally, we propose a
simple fix to the problem by adding a smoothing step in the regression.
