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Power calculations for global and local Moran's


  • Bivand, Roger
  • Müller, Werner G.
  • Reder, Markus


As in any statistical test, a power analysis can help in assessing the outcomes of whether global or local spatial dependencies exist. This point was briefly addressed with respect to global Moran's , but it has not been widely used. One reason may be that the most commonly used spatial analysis and GIS software packages do not support power analysis. Thus, apart from using the code for saddle-point approximation, applications have been restricted to employing normal approximations. An implementation of the exact distributions for global and local Moran's , which are integrated into the R-package spdep, is presented. Furthermore, assuming a simultaneous autoregressive spatial data generating scheme, substantial cases are provided, demonstrating the drawbacks and potential flaws of using the normal approximation in power calculations. The results confirm that, particularly for local Moran's , due to the smallness of sets of neighborhoods, this practice may potentially lead to errors of inference. An example concerned with Upper-Austrian migration, where using the exact distribution leads to different conclusions, is presented as well.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:2859-2872

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    References listed on IDEAS

    1. Daniel Griffith, 2006. "Hidden negative spatial autocorrelation," Journal of Geographical Systems, Springer, vol. 8(4), pages 335-355, October.
    2. 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.
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    4. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
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    6. Luc Anselin, 2003. "Spatial Externalities, Spatial Multipliers, And Spatial Econometrics," International Regional Science Review, , vol. 26(2), pages 153-166, April.
    7. Yee Leung & Chang-Lin Mei & Wen-Xiu Zhang, 2003. "Statistical Test for Local Patterns of Spatial Association," Environment and Planning A, , vol. 35(4), pages 725-744, April.
    8. L W Hepple, 1998. "Exact Testing for Spatial Autocorrelation among Regression Residuals," Environment and Planning A, , vol. 30(1), pages 85-108, January.
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    Cited by:

    1. Arif Wismadi & Mark Zuidgeest & Mark Brussel & Martin Maarseveen, 2014. "Spatial Preference Modelling for equitable infrastructure provision: an application of Sen’s Capability Approach," Journal of Geographical Systems, Springer, vol. 16(1), pages 19-48, January.
    2. Yanguang Chen, 2013. "New Approaches for Calculating Moran’s Index of Spatial Autocorrelation," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
    3. Buil-Gil, David & Moretti, Angelo & Langton, Samuel, 2020. "The integrity of crime statistics: Assessing the impact of police data bias on crime mapping," SocArXiv myfhp, Center for Open Science.
    4. Arbia, Giuseppe & Piras, Gianfranco, 2009. "A new class of spatial concentration measures," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4471-4481, October.
    5. LeSage, James & Banerjee, Sudipto & Fischer, Manfred M. & Congdon, Peter, 2009. "Spatial statistics: Methods, models & computation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2781-2785, June.
    6. Bivand, Roger, 2010. "Exploiting Parallelization in Spatial Statistics: an Applied Survey using R," Discussion Paper Series in Economics 25/2010, Norwegian School of Economics, Department of Economics.
    7. Qing Luo & Daniel A. Griffith & Huayi Wu, 2019. "Spatial autocorrelation for massive spatial data: verification of efficiency and statistical power asymptotics," Journal of Geographical Systems, Springer, vol. 21(2), pages 237-269, June.
    8. 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.
    9. Herrera Gómez, Marcos & Cid, Juan Carlos & Paz, Jorge Augusto, 2012. "Introducción a la econometría espacial: Una aplicación al estudio de la fecundidad en la Argentina usando R [Introduction to Spatial Econometrics: An application to the study of fertility in Argent," MPRA Paper 41138, University Library of Munich, Germany.
    10. 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.
    11. Xuan Yu & Manhong Shen & Weiteng Shen & Xiao Zhang, 2020. "Effects of Land Urbanization on Smog Pollution in China: Estimation of Spatial Autoregressive Panel Data Models," Land, MDPI, Open Access Journal, vol. 9(9), pages 1-1, September.

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