Comparing implementations of global and local indicators of spatial association

TEST volume 27, pages716–748(2018)Cite this article

Abstract

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.

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Notes

  1. 1.

    Some free software, like CrimeStat, is closed source.

  2. 2.

    Source code now available from https://github.com/rsbivand/legacy_systat.

  3. 3.

    For an example, see https://community.esri.com/thread/60740.

  4. 4.

    In implementations we also find \(m_2 = (n - 1)^{-1} \sum _{i=1}^{n}z_i^2\), but this does not seem to have support in the original source.

  5. 5.

    Again, division by \((n-1)\) is encountered in implementations.

  6. 6.

    https://nij.gov/topics/technology/maps/pages/crimestat.aspx.

  7. 7.

    https://github.com/GeoDaCenter/geoda/.

  8. 8.

    https://spatial.uchicago.edu/geoda.

  9. 9.

    http://pysal.readthedocs.io/en/latest/.

  10. 10.

    https://github.com/pysal.

  11. 11.

    https://cran.r-project.org/package=spdep.

  12. 12.

    https://github.com/r-spatial/spdep/.

  13. 13.

    https://data.cdrc.ac.uk/tutorial/an-introduction-to-spatial-data-analysis-and-visualisation-in-r.

  14. 14.

    https://github.com/pysal/pysal/issues/970.

  15. 15.

    https://github.com/GeoDaCenter/geoda/blob/master/Explore/GStatCoordinator.cpp, lines 338–342, 526–527.

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Acknowledgements

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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Affiliations

  1. Department of Economics, Norwegian School of Economics, Helleveien 30, 5045, Bergen, Norway

    Roger S. Bivand

  2. Department of Geography and GeoInformation Science, George Mason University, Exploratory Hall, 4400 University Dr., Fairfax, VA, 22030, USA

    David W. S. Wong

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  1. Roger S. Bivand
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Correspondence to Roger S. Bivand.

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Bivand, R.S., Wong, D.W.S. Comparing implementations of global and local indicators of spatial association. TEST 27, 716–748 (2018). https://doi.org/10.1007/s11749-018-0599-x

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Keywords

  • Software implementations
  • Global spatial autocorrelation
  • Local spatial autocorrelation
  • Lattice data

Mathematics Subject Classification

  • 62P12
  • 62P20
  • 62P25