RAND Statistics Seminar Series
The Importance of Scale for Spatial-Confounding Bias and Precision of Spatial Regression Estimators
Presented by Christopher Paciorek, Ph.D., University of California — Berkeley
Thursday, June 17, 2010
10:30 a.m. – 12:00 p.m. PT / 1:30pm – 3:00pm ET
Conference Room 1226, 1228
RAND Corporation, Santa Monica, CA
Please contact Denise Miller if you would like to attend this seminar.
Spatially correlated residuals are common in regression modeling. 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 the spatial residual is induced by an unmeasured confounder, 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: bias is reduced 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, with implications for the use of proxy information such as obtained from deterministic models and satellite retrievals. 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.
Chris Paciorek got his PhD in statistics from Carnegie Mellon University in 2003. He was a postdoc and an assistant professor in the Department of Biostatistics at Harvard School of Public Health and is now a visiting assistant professor in the Department of Statistics at UC –Berkeley. His research focuses on spatial statistics and Bayesian statistics applied to environmental applications, including environmental health, ecology, and climate.
Attending a Seminar
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