Statistical Science

The Importance of Scale for Spatial-Confounding Bias and Precision of Spatial Regression Estimators

Christopher J. Paciorek

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Residuals in regression models are often spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When unmeasured confounding introduces spatial structure into the residuals, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual: one can reduce bias by fitting a spatial model only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals are independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.

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Statist. Sci., Volume 25, Number 1 (2010), 107-125.

First available in Project Euclid: 3 August 2010

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Epidemiology identifiability mixed model penalized likelihood random effects spatial correlation splines


Paciorek, Christopher J. The Importance of Scale for Spatial-Confounding Bias and Precision of Spatial Regression Estimators. Statist. Sci. 25 (2010), no. 1, 107--125. doi:10.1214/10-STS326.

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