Department of Mathematics
Regression With Spatially Misaligned Covariates.
Lisa Madsen
Cornell University
When a response Y and a covariate X are measured in different spatial locations, we say the data are misaligned. This may occur when one of the variables is more difficult to measure, or when X and Y are measured by different agencies. Suppose we are interested in assessing the relationship of Y and X by estimating the parameters of a linear regression of Y on X, with X and Y misaligned. When X is generated by a spatially autocorrelated process, we can use the observed X's to predict (krige) the covariate at the locations Y was observed. The predicted X's can then be used in a standard regression analysis. This naive approach has an attractive simplicity. We will explore this method, obtaining expressions for the mean and variance of the estimator of the slope parameter, and assessing the performance of this estimator. We will show that it may be used with caution, and when the regression model has no intercept and E(X) is large, it performs nearly as well as if the data were not misaligned.
All interested persons are welcome.