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Spatial autocorrelation for massive spatial data: verification of efficiency and statistical power asymptotics

Author

Listed:
  • Qing Luo

    (Wuhan University
    Wuhan University)

  • Daniel A. Griffith

    (The University of Texas at Dallas)

  • Huayi Wu

    (Wuhan University
    Wuhan University)

Abstract

Being a hot topic in recent years, many studies have been conducted with spatial data containing massive numbers of observations. Because initial developments for classical spatial autocorrelation statistics are based on rather small sample sizes, in the context of massive spatial datasets, this paper presents extensions to efficiency and statistical power comparisons between the Moran coefficient and the Geary ratio for different variable distribution assumptions and selected geographic neighborhood definitions. The question addressed asks whether or not earlier results for small n extend to large and massively large n, especially for non-normal variables; implications established are relevant to big spatial data. To achieve these comparisons, this paper summarizes proofs of limiting variances, also called asymptotic variances, to do the efficiency analysis, and derives the relationship function between the two statistics to compare their statistical power at the same scale. Visualization of this statistical power analysis employs an alternative technique that already appears in the literature, furnishing additional understanding and clarity about these spatial autocorrelation statistics. Results include: the Moran coefficient is more efficient than the Geary ratio for most surface partitionings, because this index has a relatively smaller asymptotic as well as exact variance, and the superior power of the Moran coefficient vis-à-vis the Geary ratio for positive spatial autocorrelation depends upon the type of geographic configuration, with this power approaching one as sample sizes become increasingly large. Because spatial analysts usually calculate these two statistics for interval/ration data, this paper also includes comments about the join count statistics used for nominal data.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:jgeosy:v:21:y:2019:i:2:d:10.1007_s10109-019-00293-3
    DOI: 10.1007/s10109-019-00293-3
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    References listed on IDEAS

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    1. Yongwan Chun, 2008. "Modeling network autocorrelation within migration flows by eigenvector spatial filtering," Journal of Geographical Systems, Springer, vol. 10(4), pages 317-344, December.
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    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.
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    10. Bartels, Cornelis P. A. & Hordijk, Leen, 1977. "On the power of the generalized Moran contiguity coefficient in testing for spatial autocorrelation among regression disturbances," Regional Science and Urban Economics, Elsevier, vol. 7(1-2), pages 83-101, March.
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    Cited by:

    1. Daniel A. Griffith & Yongwan Chun, 2022. "Some useful details about the Moran coefficient, the Geary ratio, and the join count indices of spatial autocorrelation," Journal of Spatial Econometrics, Springer, vol. 3(1), pages 1-30, December.
    2. Daniel A. Griffith & Yongwan Chun & Monghyeon Lee, 2020. "Deeper Spatial Statistical Insights into Small Geographic Area Data Uncertainty," IJERPH, MDPI, vol. 18(1), pages 1-16, December.
    3. Ilya V. Naumov & Vladislav M. Sedelnikov, 2021. "Scenario modelling and forecasting of spatial transformation in the Russian catering market," Upravlenets, Ural State University of Economics, vol. 12(4), pages 75-91, September.

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    More about this item

    Keywords

    Moran coefficient; Geary ratio; Efficiency; Power; Geographic configuration; Join count statistics;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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