Accounting for Spatial Autocorrelation in Linear Regression Models Using Spatial Filtering with Eigenvectors

Ordinary least squares linear regression models are frequently used to analyze and model spatial phenomena. These models are useful and easily interpreted, and the assumptions, strengths, and weaknesses of these models are well studied and understood. Regression models applied to spatial data frequently contain spatially autocorrelated residuals, however, indicating a misspecification error. This problem is limited to spatial data (although similar problems occur with time series data), so it has received less attention than more frequently encountered problems. A method called spatial filtering with eigenvectors has been proposed to account for this problem. We apply this method to ten real-world data sets and a series of simulated data sets to begin to understand the conditions under which the method can be most usefully applied. We find that spatial filtering with eigenvectors reduces spatial misspecification errors, increases the strength of the model fit, frequently increases the normality of model residuals, and can increase the homoscedasticity of model residuals. We provide a sample script showing how to apply the method in the R statistical environment. Spatial filtering with eigenvectors is a powerful geographic method that should be applied to many regression models that use geographic data.