arXiv subjects

Isa Marques

Publications and source records attributed to Isa Marques.

3 recordsLinked to original sources

arXiv2023

Demystifying Spatial Confounding

Spatial confounding is a fundamental issue in spatial regression models which arises because spatial random effects, included to approximate unmeasured spatial variation, are typically not independent of covariates in the model. This can lead to significant bias in covariate effect estimates. The problem is complex and has been the topic of extensive research with sometimes puzzling and seemingly contradictory results. Here, we develop a broad theoretical framework that brings mathematical clarity to the mechanisms of spatial confounding, providing explicit analytical expressions for the resulting bias. We see that the problem is directly linked to spatial smoothing and identify exactly how the size and occurrence of bias relate to the features of the spatial model as well as the underlying confounding scenario. Using our results, we can explain subtle and counter-intuitive behaviours. Finally, we propose a general approach for dealing with spatial confounding bias in practice, applicable for any spatial model specification. When a covariate has non-spatial information, we show that a general form of the so-called spatial+ method can be used to eliminate bias. When no such information is present, the situation is more challenging but, under the assumption of unconfounded high frequencies, we develop a procedure in which multiple capped versions of spatial+ are applied to assess the bias in this case. We illustrate our approach with an application to air temperature in Germany.

stat.ME↗

arXiv2023

Bayesian spatial+: A joint model perspective

Spatial confounding is a common issue in spatial regression models, occurring when spatially varying covariates correlate with the spatial effect included in the model. This dependence, particularly at high spatial frequencies, can introduce bias in regression coefficient estimates when combined with smoothing penalties. The spatial+ framework is a widely used two-stage frequentist approach that mitigates spatial confounding by explicitly modeling and removing the spatial structure in the confounding covariate, then using the corresponding residuals in the second-stage model for the response. However, it does not propagate first-stage uncertainty, does not discuss a general inferential framework, and, crucially, cannot guarantee that covariate residuals and spatial effects in the response model are free of shared high-frequency structure, so confounding may persist. We propose Bayesian spatial+, a joint modeling approach that simultaneously addresses these limitations. Our framework naturally propagates uncertainty and enables straightforward posterior inference, while ensuring separation of spatial frequencies through specialized joint priors on smoothness parameters. We further introduce a cut-feedback strategy that prevents feedback between model components from reintroducing confounding. Simulation studies and real-world applications show substantial gains in bias reduction and interval coverage relative to existing approaches. Notably, in our comparisons, Bayesian spatial+ is the only method for which credible interval coverage remains stable as the sample size increases.

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arXiv2021

A multivariate Gaussian random field prior against spatial confounding

Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed covariates modeling the mean of the response are correlated with the spatial random effect. 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 paper, we develop a computationally efficient spatial model in a Bayesian framework integrating novel prior structure that reduces spatial confounding. Starting from the univariate case, we extend our prior structure to case of multiple spatially confounded covariates. In a simulation study, 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 daily precipitation in Germany.

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