, Volume 27, Issue 3, pp 716–748 | Cite as

Comparing implementations of global and local indicators of spatial association

  • Roger S. BivandEmail author
  • David W. S. Wong
Original Paper


Functions to calculate measures of spatial association, especially measures of spatial autocorrelation, have been made available in many software applications. Measures may be global, applying to the whole data set under consideration, or local, applying to each observation in the data set. Methods of statistical inference may also be provided, but these will, like the measures themselves, depend on the support of the observations, chosen assumptions, and the way in which spatial association is represented; spatial weights are often used as a representational technique. In addition, assumptions may be made about the underlying mean model, and about error distributions. Different software implementations may choose to expose these choices to the analyst, but the sets of choices available may vary between these implementations, as may default settings. This comparison will consider the implementations of global Moran’s I, Getis–Ord G and Geary’s C, local \(I_i\) and \(G_i\), available in a range of software including Crimestat, GeoDa, ArcGIS, PySAL and R contributed packages.


Software implementations Global spatial autocorrelation Local spatial autocorrelation Lattice data 

Mathematics Subject Classification

62P12 62P20 62P25 



We would like to thank the editors and reviewers for constructive suggestions that we hope have clarified the conclusions of this comparative study. We would also like to thank Shiyang Ruan for assistance with ArcGIS Python programming.


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2018

Authors and Affiliations

  1. 1.Department of EconomicsNorwegian School of EconomicsBergenNorway
  2. 2.Department of Geography and GeoInformation ScienceGeorge Mason UniversityFairfaxUSA

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