A Closer Look at Errors in Variables Methods for Use in Regression Models with Spatially Misaligned Data

Abstract

Publicly available data are increasingly combined for subsequent statistical analyses. For example, the U.S. Centers for Disease Control and Prevention's Environmental Public Health Tracking (EPHT) Program is based almost entirely on the use of existing data. Because the data are frequently measured or associated with different geographic or spatial units, combing them for analysis usually requires prediction of one or more of the variables of interest. In this article, the effects of regressing health outcomes on a predicted environmental exposure is explored. We evaluate several statistical methods for regression with spatially misaligned data, including naïve kriging approaches and parametric bootstrap methods. First, the case where health outcomes are observed at points and environmental exposure is measured at other points resulting in spatial misalignment is considered both analytically and through simulation. In EPHT, the association between health outcomes and environmental exposure is often studied for areal units, such as counties or zip codes. Thus, a second simulation study focuses on this type of inference and also on estimation of the regression coefficient associated with environmental exposure when regressing health outcomes on predicted exposure when a trend in exposure is present. At the areal level, the naive approaches of regressing health outcomes on environmental exposure predicted using block kriging, either with or without the assumption of a general covariance structure for the residuals, performed surprisingly well. When the variability in the estimated regression coefficient is quite small, the partial parameter bootstrap outperformed the naive approaches.