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

Increasingly, regression models are used when residuals are 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 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 can be considered 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.

Spatial heterogeneity of soil nutrients and plant species in herb-dominated communities of contrasting land use

Recent interest in spatial pattern in terrestrial ecosystems has come from an awareness of theintimate relationship between spatial heterogeneity of soil resources and maintenance of plant species diversity. Soil and vegetation can vary spatially inresponse to several state factors of the system. In this study, we examined fine-scale spatial variability of soil nutrients and vascular plant species in contrasting herb-dominated communities (a pasture and an oldfield) to determine degree of spatial dependenceamong soil variables and plant community characteristics within these communities by sampling at 1-m intervals. Each site was divided into 25 1-m 2 plots. Mineral soil was sampled (2-cm diameter, 5-cm depth) from each of four 0.25-m2 quarters and combined into a single composite sample per plot. Soil organic matter was measured as loss-on-ignition. Extractable NH4 and NO3 were determined before and after laboratory incubation to determine potential net N mineralization and nitrification. Cations were analyzed using inductively coupled plasma emission spectrometry. Vegetation was assessed using estimated percent cover. Most soiland plant variables exhibited sharp contrasts betweenpasture and old-field sites, with the old field having significantly higher net N mineralization/nitrification, pH, Ca, Mg, Al, plant cover, and species diversity, richness, and evenness. Multiple regressions revealedthat all plant variables (species diversity, richness,evenness, and cover) were significantly related to soil characteristics (available nitrogen, organic matter,moisture, pH, Ca, and Mg) in the pasture; in the old field only cover was significantly related to soil characteristics (organic matter and moisture). Both sites contrasted sharply with respect to spatial pattern of soil variables, with the old field exhibiting a higher degree of spatial dependence. These results demonstrate that land-use practices can exert profound influence on spatial heterogeneity of both soil properties and vegetation in herb-dominated communities.