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.

在空间数据的回归模型中，通常假设协变量对响应的边际效应在空间上是恒定的。在实践中，这种假设可能经常令人怀疑。在本文中，我们展示了如何使用最大似然估计（MLE）来估计基于高斯过程的空间变化系数（SVC）模型。此外，我们提出了一种通过应用协方差渐缩来扩展到大数据的方法。在模拟研究和目标应用中，我们将我们的方法与现有方法进行比较，例如使用随机偏微分方程（SPDE）链接的贝叶斯方法，地理加权回归（GWR）和特征向量空间滤波（ESF）。预测瑞士房地产公寓的价格。仿真研究和应用的结果均表明，MLE方法可提高预测准确性和更精确的估计。由于我们使用基于模型的方法，因此我们还可以提供预测方差。与现有的基于模型的方法相比，我们的方法可以更好地扩展到空间点数量大且空间变化协变量数量适度（例如大于10）的数据。