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.

翻译：空间差异系数(SVC)模型是空间数据的一种回归模型,空间数据中共变效应随空间而异。如果有多个共变,自然的问题是共变具有空间差异效应,而不是。我们为基于高斯进程SVC模型提出了一个新的变量选择方法。它依赖于一个受罚的最大可能性估计(PMLE),允许在固定效应和高斯过程随机效应方面进行变量选择。我们在模拟研究和真实的世界数据集中验证了我们的方法。我们的新办法显示模拟研究中的选择性能良好。在实际数据应用中,我们提议的PMLE生成了稀释性SVC模型,并实现了比经典MLE小的信息标准。在对真实数据进行交叉校验时,我们显示,稀疏PML估计的SVC模型与预测性能的ML估计SVC模型是相同的。