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Joint variable selection of both fixed and random effects for Gaussian process-based spatially varying coefficient models


Dambon, Jakob A; Sigrist, Fabio; Furrer, Reinhard (2022). Joint variable selection of both fixed and random effects for Gaussian process-based spatially varying coefficient models. International Journal of Geographical Information Science, 36(12):2525-2548.

Abstract

Spatially varying coefficient (SVC) models are a type of regression models 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 and allows joint variable selection both with respect to fixed effects and Gaussian process random effects. We validate our approach in a simulation study as well as a real world data set. In the simulation study, the penalized maximum likelihood estimation correctly identifies zero fixed and random effects, while the penalty-induced bias of non-zero estimates is negligible. In the real data application, our proposed penalized maximum likelihood estimation yields sparser SVC models and achieves a smaller information criterion than classical maximum likelihood estimation. In a cross-validation study applied on the real data, we show that our proposed penalized maximum likelihood estimation consistently yields the sparsest SVC models while achieving similar predictive performance compared to other SVC modeling methodologies.

Abstract

Spatially varying coefficient (SVC) models are a type of regression models 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 and allows joint variable selection both with respect to fixed effects and Gaussian process random effects. We validate our approach in a simulation study as well as a real world data set. In the simulation study, the penalized maximum likelihood estimation correctly identifies zero fixed and random effects, while the penalty-induced bias of non-zero estimates is negligible. In the real data application, our proposed penalized maximum likelihood estimation yields sparser SVC models and achieves a smaller information criterion than classical maximum likelihood estimation. In a cross-validation study applied on the real data, we show that our proposed penalized maximum likelihood estimation consistently yields the sparsest SVC models while achieving similar predictive performance compared to other SVC modeling methodologies.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
07 Faculty of Science > Institute for Computational Science
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Information Systems
Social Sciences & Humanities > Geography, Planning and Development
Social Sciences & Humanities > Library and Information Sciences
Uncontrolled Keywords:Library and Information Sciences, Geography, Planning and Development, Information Systems Adaptive LASSOBayesian optimizationcoordinate descent algorithmmodel-based optimizationpenalized maximum likelihood estimationspatial statistics
Language:English
Date:2 December 2022
Deposited On:10 Feb 2023 11:43
Last Modified:28 Feb 2024 02:48
Publisher:Taylor & Francis
ISSN:1365-8816
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1080/13658816.2022.2097684
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)