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

Maximum Likelihood Estimation of Spatially Varying Coefficient Models for Large Data with an Application to Real Estate Price Prediction