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

• Published in: Annals of the Association of American Geographers 2013-01, Vol.103 (1), p.47-66
• Main Authors: Thayn, Jonathan B., Simanis, Joseph M.
• Format: Article
• Language: English
• Subjects: Autocorrelation; Bgi / Prodig; Correlation; Datasets; Economic models; eigenvectores; Eigenvectors; Errors; especificación espacial equivocada; filtrado espacial; General methodology; Geography; Linear regression; Methods, Models, and GIS; Modeling; Panel data; regresión lineal; Regression analysis; Simulation; Spatial analysis; Spatial filtering; spatial misspecification; Spatial models; Statistical analysis; Statistical and stochastic methods; Statistical models; 向量; 空间滤波; 空间设定错误; 线性回归
• ISSN: 0004-5608; 2469-4452; 1467-8306; 2469-4460
• DOI: 10.1080/00045608.2012.685048

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.