  Spatially varying coefficient (SVC) models are a type of regression model for
spatial data where covariate effects vary over space. If there are several
covariates, a natural question is which covariates have a spatially varying
effect and which not. We present a new variable selection approach for Gaussian
process-based SVC models. It relies on a penalized maximum likelihood
estimation (PMLE) and allows variable selection both with respect to fixed
effects and Gaussian process random effects. We validate our approach both in a
simulation study as well as a real world data set. Our novel approach shows
good selection performance in the simulation study. In the real data
application, our proposed PMLE yields sparser SVC models and achieves a smaller
information criterion than classical MLE. In a cross-validation applied on the
real data, we show that sparser PML estimated SVC models are on par with ML
estimated SVC models with respect to predictive performance.
