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New Approaches for Calculating Moran’s Index of Spatial Autocorrelation

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  • Yanguang Chen

Abstract

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran’s index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran’s index. Moran’s scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran’s index and Geary’s coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran’s index and Geary’s coefficient will be clarified and defined. One of theoretical findings is that Moran’s index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0068336
    DOI: 10.1371/journal.pone.0068336
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    1. 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.
    2. Daniel A. Griffith, 2003. "Spatial Autocorrelation and Spatial Filtering," Advances in Spatial Science, Springer, number 978-3-540-24806-4, Fall.
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    4. Getayeneh Antehunegn Tesema & Tesfaye Hambisa Mekonnen & Achamyeleh Birhanu Teshale, 2020. "Spatial distribution and determinants of abortion among reproductive age women in Ethiopia, evidence from Ethiopian Demographic and Health Survey 2016 data: Spatial and mixed-effect analysis," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-17, June.
    5. Huang, Wei, 2019. "Forest condition change, tenure reform, and government-funded eco-environmental programs in Northeast China," Forest Policy and Economics, Elsevier, vol. 98(C), pages 67-74.
    6. Francesco Tolu & Mario Palermo & Maria Pina Dore & Alessandra Errigo & Ana Canelada & Michel Poulain & Giovanni Mario Pes, 2019. "Association of endemic goitre and exceptional longevity in Sardinia: evidence from an ecological study," European Journal of Ageing, Springer, vol. 16(4), pages 405-414, December.
    7. Rakin Abrar & Showmitra Kumar Sarkar & Kashfia Tasnim Nishtha & Swapan Talukdar & Shahfahad & Atiqur Rahman & Abu Reza Md Towfiqul Islam & Amir Mosavi, 2022. "Assessing the Spatial Mapping of Heat Vulnerability under Urban Heat Island (UHI) Effect in the Dhaka Metropolitan Area," Sustainability, MDPI, vol. 14(9), pages 1-24, April.
    8. Inna MANAEVA & Anna TKACHEVA & Elena CHENTSOVA & Elena ILYICHEVA, 2021. "Assessment Of The Interconnectedness Of Cities In The Russian Far East," Regional Science Inquiry, Hellenic Association of Regional Scientists, vol. 0(2), pages 123-133, June.
    9. 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.
    10. Pinto, Erveton P. & Pires, Marcelo A. & Matos, Robert S. & Zamora, Robert R.M. & Menezes, Rodrigo P. & Araújo, Raquel S. & de Souza, Tiago M., 2021. "Lacunarity exponent and Moran index: A complementary methodology to analyze AFM images and its application to chitosan films," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    11. Gertrudes Saúde Guerreiro & António Bento Caleiro, 2014. "A convergência espacial do conhecimento em Portugal," Economics Working Papers 01_2014, University of Évora, Department of Economics (Portugal).
    12. Ffion Carney, 2021. "Linking Loyalty Card Data to Public Transport Data to Explore Mobility and Social Exclusion in the Older Population," Sustainability, MDPI, vol. 13(11), pages 1-19, May.
    13. Rakhohori Bag & Manoranjan Ghosh & Bapan Biswas & Mitrajit Chatterjee, 2020. "Understanding the spatio‐temporal pattern of COVID‐19 outbreak in India using GIS and India's response in managing the pandemic," Regional Science Policy & Practice, Wiley Blackwell, vol. 12(6), pages 1063-1103, December.
    14. Liu, Yan-Ping & Wang, Lin & Zhang, Feng & Wang, Rui-Wu, 2020. "Diffusion sustains cooperation via forming diverse spatial patterns in prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 375(C).

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