  In regression models for spatial data, it is often assumed that the marginal
effects of covariates on the response are constant over space. In practice,
this assumption might often be questionable. In this article, we show how a
Gaussian process-based spatially varying coefficient (SVC) model can be
estimated using maximum likelihood estimation (MLE). In addition, we present an
approach that scales to large data by applying covariance tapering. We compare
our methodology to existing methods such as a Bayesian approach using the
stochastic partial differential equation (SPDE) link, geographically weighted
regression (GWR), and eigenvector spatial filtering (ESF) in both a simulation
study and an application where the goal is to predict prices of real estate
apartments in Switzerland. The results from both the simulation study and
application show that the MLE approach results in increased predictive accuracy
and more precise estimates. Since we use a model-based approach, we can also
provide predictive variances. In contrast to existing model-based approaches,
our method scales better to data where both the number of spatial points is
large and the number of spatially varying covariates is moderately-sized, e.g.,
above ten.
