Journal of Geographical Systems

, Volume 2, Issue 2, pp 141–156 | Cite as

A linear regression solution to the spatial autocorrelation problem

  • Daniel A. Griffith


The Moran Coefficient spatial autocorrelation index can be decomposed into orthogonal map pattern components. This decomposition relates it directly to standard linear regression, in which corresponding eigenvectors can be used as predictors. This paper reports comparative results between these linear regressions and their auto-Gaussian counterparts for the following georeferenced data sets: Columbus (Ohio) crime, Ottawa-Hull median family income, Toronto population density, southwest Ohio unemployment, Syracuse pediatric lead poisoning, and Glasgow standard mortality rates, and a small remotely sensed image of the High Peak district. This methodology is extended to auto-logistic and auto-Poisson situations, with selected data analyses including percentage of urban population across Puerto Rico, and the frequency of SIDs cases across North Carolina. These data analytic results suggest that this approach to georeferenced data analysis offers considerable promise.

Key words: Eigenfunction, spatial autocorrelation, spatial autoregression, geographic weights matrix, georeferenced data 
JEL classification: C49, C13, R15 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Daniel A. Griffith
    • 1
  1. 1.Department of Geography and Interdisciplinary Statistics Program, Syracuse University, Syracuse, NY 13244-1020, USA (e-mail: and ASA/USDA-NASS Fellow, National Agricultural Statistics Service, Fairfax, VA, USAUS

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