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On Moran’s I coefficient under heterogeneity

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  • Zhang, Tonglin
  • Lin, Ge

Abstract

Moran’s I is the most popular spatial test statistic, but its inability to incorporate heterogeneous populations has been long recognized. This article provides a limiting distribution of the Moran’s I coefficient which can be applied to heterogeneous populations. The method provides a unified framework of testing for spatial autocorrelation for both homogeneous and heterogeneous populations, thereby resolving a long standing issue for Moran’s I. For Poisson count data, a variance adjustment method is provided that solely depends on populations at risk. Simulation results are shown to be consistent with theoretical results. The application of Nebraska breast cancer data shows that the variance adjustment method is simple and effective in reducing type I error rates, which in turn will likely reduce potential misallocation of limited resources.

Suggested Citation

  • Zhang, Tonglin & Lin, Ge, 2016. "On Moran’s I coefficient under heterogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 83-94.
    • Handle: RePEc:eee:csdana:v:95:y:2016:i:c:p:83-94
    DOI: 10.1016/j.csda.2015.09.010
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    1. Mikosch, T., 1991. "Functional limit theorems for random quadratic forms," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 81-98, February.
    2. Denis Mollison & Valerie Isham & Bryan Grenfell, 1994. "Epidemics: Models and Data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 157(1), pages 115-129, January.
    3. Zhang, Tonglin & Lin, Ge, 2007. "A decomposition of Moran's I for clustering detection," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6123-6137, August.
    4. Kelsall J. & Eld J.W., 2002. "Modeling Spatial Variation in Disease Risk: A Geostatistical Approach," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 692-701, September.
    5. Michael F. Goodchild & Luc Anselin & Richard P. Appelbaum & Barbara Herr Harthorn, 2000. "Toward Spatially Integrated Social Science," International Regional Science Review, , vol. 23(2), pages 139-159, April.
    6. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    7. Tonglin Zhang & Ge Lin, 2009. "Cluster Detection Based on Spatial Associations and Iterated Residuals in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 65(2), pages 353-360, June.
    8. Julian Besag & James Newell, 1991. "The Detection of Clusters in Rare Diseases," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 154(1), pages 143-155, January.
    9. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
    10. Green P.J. & Richardson S., 2002. "Hidden Markov Models and Disease Mapping," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1055-1070, December.
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    Cited by:

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    3. Xu, Bin & Lin, Boqiang, 2018. "Do we really understand the development of China's new energy industry?," Energy Economics, Elsevier, vol. 74(C), pages 733-745.
    4. Yongfeng Zhu & Zilong Wang & Shilei Qiu & Lingling Zhu, 2019. "Effects of Environmental Regulations on Technological Innovation Efficiency in China’s Industrial Enterprises: A Spatial Analysis," Sustainability, MDPI, vol. 11(7), pages 1-19, April.

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