ArticleBiometrics2022
Spatial+: A novel approach to spatial confounding.
Article in Biometrics, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 21 papers.
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Who cites it
21 citing papers in PubMed, 66 citations in OpenAlex.
- Spatial bias in quality of estimated delivery date records in the electronic health record.JAMIA open · 2026Article
- Bringing spatial confounding into the causal inferential fold.American journal of epidemiology · 2026Article
- UNLOCKING MULTI-SAMPLE DIFFERENTIAL EXPRESSION FOR SPATIAL TRANSCRIPTOMICS DATA WITH TESSERA.bioRxiv : the preprint server for biology · 2026Article
- Mitigating the risk of bias exacerbation when controlling for unmeasured spatial confounding for binary exposures.American journal of epidemiology · 2026Article
- Article
- Spatial inequalities in quality antenatal care in India: a district-level analysis.Frontiers in public health · 2026Article
- A Bayesian spatially-clustered coefficient model with temporal structures for hepatitis A data in South Korea.Journal of applied statistics · 2026Article
- Suicide mortality in Spain (2010-2022): temporal trends, spatial patterns, and risk factors.International journal of health geographics · 2025Article
- Semiparametric approaches for mitigating spatial confounding in large environmental epidemiology cohort studies.Environmetrics · 2025Article
- Article
- A Bayesian spatial-temporal varying coefficients model for estimating excess deaths associated with respiratory infections.Journal of the Royal Statistical Society. Series A, (Statistics in Society) · 2025Article
- Considering landscape heterogeneity improves the inference of inter-individual interactions from movement data.Movement ecology · 2025Article
- Racial residential segregation is associated with ambient air pollution exposure after adjustment for multilevel sociodemographic factors: Evidence from eight US-based cohorts.Environmental epidemiology (Philadelphia, Pa.) · 2025Article
- A Bayesian hierarchical model for disease mapping that accounts for scaling and heavy-tailed latent effects.Statistical methods in medical research · 2025Article
- Increase of Tree Species Mingling enhances the resistance ofForestry research · 2025Article
- Consistency of common spatial estimators under spatial confounding.Biometrika · 2025Article
- spconfShiny: An R Shiny application for calculating the spatial scale of smoothing splines for point data.PloS one · 2024Article
- Alleviating spatial confounding in frailty models.Biostatistics (Oxford, England) · 2023Article
- Spectral adjustment for spatial confounding.Biometrika · 2023Article
- Spatial+: A novel approach to spatial confounding.Biometrics · 2022Article
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Authors and funding
3 authors at 2 institutions in 1 country.
Funding
Abstract
In spatial regression models, collinearity between covariates and spatial effects can lead to significant bias in effect estimates. This problem, known as spatial confounding, is encountered modeling forestry data to assess the effect of temperature on tree health. Reliable inference is difficult as results depend on whether or not spatial effects are included in the model. We propose a novel approach, spatial+, for dealing with spatial confounding when the covariate of interest is spatially dependent but not fully determined by spatial location. Using a thin plate spline model formulation we see that, in this case, the bias in covariate effect estimates is a direct result of spatial smoothing. Spatial+ reduces the sensitivity of the estimates to smoothing by replacing the covariates by their residuals after spatial dependence has been regressed away. Through asymptotic analysis we show that spatial+ avoids the bias problems of the spatial model. This is also demonstrated in a simulation study. Spatial+ is straightforward to implement using existing software and, as the response variable is the same as that of the spatial model, standard model selection criteria can be used for comparisons. A major advantage of the method is also that it extends to models with non-Gaussian response distributions. Finally, while our results are derived in a thin plate spline setting, the spatial+ methodology transfers easily to other spatial model formulations.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.