Joint Variable Selection of both Fixed and Random Effects for Gaussian Process-based Spatially Varying Coefficient Models

TL;DR

This paper introduces a new penalized maximum likelihood approach for variable selection in Gaussian process-based spatially varying coefficient models, effectively identifying relevant covariates and improving model sparsity without sacrificing predictive accuracy.

Contribution

It proposes a novel joint variable selection method for both fixed and random effects in SVC models using PMLE, validated through simulations and real data.

Findings

Good selection performance in simulations

Produces sparser models with better information criteria

Maintains predictive accuracy comparable to classical methods

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.