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New framework of Getis-Ord’s indexes associating spatial autocorrelation with interaction

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  • Yanguang Chen

Abstract

Spatial autocorrelation and spatial interaction are two important analytical processes for geographical analyses. However, the internal relations between the two types of models have not been brought to light. This paper is devoted to integrating spatial autocorrelation analysis and spatial interaction analysis into a logic framework by means of Getis-Ord’s indexes. Based on mathematical derivation and transform, the spatial autocorrelation measurements of Getis-Ord’s indexes are reconstructed in a new and simple form. A finding is that the local Getis-Ord’s indexes of spatial autocorrelation are equivalent to the rescaled potential energy indexes of spatial interaction theory based on power-law distance decay. The normalized scatterplot is introduced into the spatial analysis based on Getis-Ord’s indexes, and the potential energy indexes are proposed as a complementary measurement. The global Getis-Ord’s index proved to be the weighted sum of the potential energy indexes and the direct sum of total potential energy. The empirical analysis of the system of Chinese cities are taken as an example to illustrate the effect of the improved methods and measurements. The mathematical framework newly derived from Getis-Ord’s work is helpful for further developing the methodology of geographical spatial modeling and quantitative analysis.

Suggested Citation

  • Yanguang Chen, 2020. "New framework of Getis-Ord’s indexes associating spatial autocorrelation with interaction," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-25, July.
  • Handle: RePEc:plo:pone00:0236765
    DOI: 10.1371/journal.pone.0236765
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    References listed on IDEAS

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    1. Yanguang Chen, 2015. "A New Methodology of Spatial Cross-Correlation Analysis," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-20, May.
    2. Ethan A Wilson & Patrick J Sullivan & Janis L Dickinson, 2014. "Spatial Distribution of Oak Mistletoe as It Relates to Habits of Oak Woodland Frugivores," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-7, November.
    3. Yanguang Chen, 2012. "On the four types of weight functions for spatial contiguity matrix," Letters in Spatial and Resource Sciences, Springer, vol. 5(2), pages 65-72, July.
    4. Benjamin Koester & Thomas J Rea & Alan R Templeton & Alexander S Szalay & Charles F Sing, 2012. "Long-Range Autocorrelations of CpG Islands in the Human Genome," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-10, January.
    5. Yanguang Chen, 2016. "Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-19, January.
    6. Jan Beck & Andrea Sieber, 2010. "Is the Spatial Distribution of Mankind's Most Basic Economic Traits Determined by Climate and Soil Alone?," PLOS ONE, Public Library of Science, vol. 5(5), pages 1-10, May.
    7. Chandan Kumar & Prashant Kumar Singh & Rajesh Kumar Rai, 2012. "Under-Five Mortality in High Focus States in India: A District Level Geospatial Analysis," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-15, May.
    8. Christopher W K Lai & Helen K W Law, 2015. "Mammographic Breast Density in Chinese Women: Spatial Distribution and Autocorrelation Patterns," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-10, September.
    9. 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.
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    12. Vincent Deblauwe & Pol Kennel & Pierre Couteron, 2012. "Testing Pairwise Association between Spatially Autocorrelated Variables: A New Approach Using Surrogate Lattice Data," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-9, November.
    13. In-Chan Ng & Tzai-Hung Wen & Jann-Yuan Wang & Chi-Tai Fang, 2012. "Spatial Dependency of Tuberculosis Incidence in Taiwan," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-7, November.
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    16. Sebastian Scheuer & Dagmar Haase & Martin Volk, 2016. "On the Nexus of the Spatial Dynamics of Global Urbanization and the Age of the City," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-20, August.
    17. Rene Westerholt & Enrico Steiger & Bernd Resch & Alexander Zipf, 2016. "Abundant Topological Outliers in Social Media Data and Their Effect on Spatial Analysis," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-31, September.
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