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Comparing implementations of global and local indicators of spatial association

Author

Listed:
  • Roger S. Bivand

    (Norwegian School of Economics)

  • David W. S. Wong

    (George Mason University)

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 $$I_i$$ I i and $$G_i$$ G i , available in a range of software including Crimestat, GeoDa, ArcGIS, PySAL and R contributed packages.

Suggested Citation

  • Roger S. Bivand & David W. S. Wong, 2018. "Comparing implementations of global and local indicators of spatial association," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 716-748, September.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:3:d:10.1007_s11749-018-0599-x
    DOI: 10.1007/s11749-018-0599-x
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    References listed on IDEAS

    as
    1. Bivand, Roger & Piras, Gianfranco, 2015. "Comparing Implementations of Estimation Methods for Spatial Econometrics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i18).
    2. Roger Bivand, 2008. "Implementing Representations Of Space In Economic Geography," Journal of Regional Science, Wiley Blackwell, vol. 48(1), pages 1-27, February.
    3. Roger Bivand & Albrecht Gebhardt, 2000. "Implementing functions for spatial statistical analysis using the language," Journal of Geographical Systems, Springer, vol. 2(3), pages 307-317, September.
    4. Manfred M. Fischer & Arthur Getis (ed.), 2010. "Handbook of Applied Spatial Analysis," Springer Books, Springer, number 978-3-642-03647-7, December.
    5. Bivand, Roger & Müller, Werner G. & Reder, Markus, 2009. "Power calculations for global and local Moran's," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2859-2872, June.
    6. repec:rre:publsh:v:37:y:2007:i:1:p:5-27 is not listed on IDEAS
    7. L W Hepple, 1998. "Exact Testing for Spatial Autocorrelation among Regression Residuals," Environment and Planning A, , vol. 30(1), pages 85-108, January.
    8. Daniel P. McMillen, 2003. "Spatial Autocorrelation Or Model Misspecification?," International Regional Science Review, , vol. 26(2), pages 208-217, April.
    9. J. Ord & Arthur Getis, 2012. "Local spatial heteroscedasticity (LOSH)," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 48(2), pages 529-539, April.
    10. J. Keith Ord & Arthur Getis, 2001. "Testing for Local Spatial Autocorrelation in the Presence of Global Autocorrelation," Journal of Regional Science, Wiley Blackwell, vol. 41(3), pages 411-432, August.
    11. Roger S. Bivand & Boris A. Portnov, 2004. "Exploring Spatial Data Analysis Techniques Using R: The Case of Observations with No Neighbors," Advances in Spatial Science, in: Luc Anselin & Raymond J. G. M. Florax & Sergio J. Rey (ed.), Advances in Spatial Econometrics, chapter 6, pages 121-142, Springer.
    12. Min Xu & Chang-Lin Mei & Na Yan, 2014. "A note on the null distribution of the local spatial heteroscedasticity (LOSH) statistic," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(3), pages 697-710, May.
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