Mitigating spatial confounding by explicitly correlating Gaussian random fields

Marques, I., Kneib, T. and Klein, N. (2022) Mitigating spatial confounding by explicitly correlating Gaussian random fields. Environmetrics, 33(5), e2727. (doi: 10.1002/env.2727)

Abstract

Spatial models are used in a variety of research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in such spatial regression models is spatial confounding. This phenomenon is observed when spatially indexed covariates modeling the mean of the response are correlated with a spatial random effect included in the model, for example, as a proxy of unobserved spatial confounders. As a result, estimates for regression coefficients of the covariates can be severely biased and interpretation of these is no longer valid. Recent literature has shown that typical solutions for reducing spatial confounding can lead to misleading and counterintuitive results. In this article, we develop a computationally efficient spatial model that explicitly correlates a Gaussian random field for the covariate of interest with the Gaussian random field in the main model equation and integrates novel prior structures to reduce spatial confounding. Starting from the univariate case, we extend our prior structure also to the case of multiple spatially confounded covariates. In simulation studies, we show that our novel model flexibly detects and reduces spatial confounding in spatial datasets, and it performs better than typically used methods such as restricted spatial regression. These results are promising for any applied researcher who wishes to interpret covariate effects in spatial regression models. As a real data illustration, we study the effect of elevation and temperature on the mean of monthly precipitation in Germany.

• Item Type: Articles
• Additional Information: The authors gratefully acknowledge the Deutsche Forschungsgemeinschaft for funding the project within the Research Training Group 2300.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Marques, Dr Isa
• Authors: Marques, I., Kneib, T., and Klein, N.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Environmetrics
• Publisher: Wiley
• ISSN: 1180-4009
• ISSN (Online): 1099-095X
• Published Online: 19 April 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Environmetrics 33(5):e2727
• Publisher Policy: Reproduced under a Creative Commons License