A comparison of errors in variables methods for use in regression models with spatially misaligned data

When a response variable Y is measured on one set of points and a spatially varying predictor variable X is measured on a different set of points, X and Y have different supports and thus are spatially misaligned. To draw inference about the association between X and Y , X is commonly predicted at the points for which Y is observed, and Y is regressed on the predicted X. If X is predicted using kriging or some other smoothing approach, use of the predicted instead of the true (unobserved) X values in the regression results in unbiased estimates of the regression parameters. However, the naive standard errors of these parameters tend to be too small. In this article, two simulation studies are used to compare methods for providing appropriate standard errors in this spatial setting. Three of the methods are extended to the change-of-support case where X is observed at points, but Y is observed for areal units, and these approaches are also compared via simulation.