Variable Selection for Spatially Varying Coefficient Models

• Activity Number: 321 - Machine Learning and Variable Selection
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 3:30 PM to 5:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Jakob A. Dambon* and Fabio Sigrist and Reinhard Furrer
• Companies: University of Zurich and Lucerne University of Applied Sciences and Arts and University of Zurich
• Keywords: Adaptive LASSO; Coordinate descent algorithm; Model-based optimization; Penalized maximum likelihood estimation; Spatial statistics

Abstract

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.