Indicators of spatial association

Indicators of spatial association are statistics that evaluate the existence of clusters in the spatial arrangement of a given variable. For instance, if we are studying cancer rates among census tracts in a given city local clusters in the rates mean that there are areas that have higher or lower rates than is to be expected by chance alone; that is, the values occurring are above or below those of a random distribution in space.

Global indicators

Notable global indicators of spatial association include:[1]

  • Global Moran's I: The most commonly used measure of global spatial autocorrelation or the overall clustering of the spatial data developed by Patrick Alfred Pierce Moran.[2][3]
  • Geary's C (Geary's Contiguity Ratio): A measure of global spatial autocorrelation developed by Geary in 1954.[4][5] It is inversely related to Moran's I, but more sensitive to local autocorrelation than Moran's I.
  • Getis–Ord G (Getis–Ord global G, Geleral G-Statistic): Introduced by Getis and Ord in 1992 to supplement Moran's I.[6]

Local indicators

Notable local indicators of spatial association (LISA) include:[1]

  • Local Moran's I: Derived from Global Moran's I, it was introduced by Luc Anselin in 1995[7] and can be computed using GeoDa.[8]
  • Getis–Ord Gi (local Gi): Developed by Getis and Ord based on their global G.
  • INDICATE's IN: Originally developed to assess the spatial behaviour of stars,[9] can be computed for any discrete 2+D dataset using python-based INDICATE tool available from GitHub.[10]

See also

References
  1. George Grekousis (2020). Spatial Analysis Methods and Practice. Cambridge University Press. p. 210. ISBN 9781108712934.
  2. Moran, P. A. P. (1950). "Notes on Continuous Stochastic Phenomena". Biometrika. 37 (1): 17–23. doi:10.2307/2332142. JSTOR 2332142. PMID 15420245.
  3. Li, Hongfei; Calder, Catherine A.; Cressie, Noel (2007). "Beyond Moran's I: Testing for Spatial Dependence Based on the Spatial Autoregressive Model". Geographical Analysis. 39 (4): 357–375. doi:10.1111/j.1538-4632.2007.00708.x.
  4. Geary, R. C. (1954). "The Contiguity Ratio and Statistical Mapping". The Incorporated Statistician. 5 (3): 115–145. doi:10.2307/2986645. JSTOR 2986645.
  5. J. N. R. Jeffers (1973). "A Basic Subroutine for Geary's Contiguity Ratio". Journal of the Royal Statistical Society, Series D. Wiley. 22 (4): 299–302. doi:10.2307/2986827. JSTOR 2986827.
  6. Getis, Arthur; Ord, J. Keith (1992). "The analysis of spatial association by use of distance statistics". Geographical Analysis. 24 (3): 189–206. doi:10.1111/j.1538-4632.1992.tb00261.x.
  7. Anselin, Luc (1995). "Local Indicators of Spatial Association—LISA". Geographical Analysis. 27 (2): 93–115. doi:10.1111/j.1538-4632.1995.tb00338.x.
  8. Anselin, Luc (2005). "Exploring Spatial Data with GeoDaTM: A Workbook" (PDF). Spatial Analysis Laboratory. p. 138.
  9. Buckner, Anne S. M.; Khorrami, Zeinab; Khalaj, Pouria; Lumsden, Stuart L.; Joncour, Isabelle; Moraux, Estelle; Clark, Paul; Oudmaijer, René D.; Blanco, José Manuel; de la Calle, Ignacio; Herrera-Fernandez, José M.; Motte, Frédérique; Salgado, Jesús J.; Valero-Martín, Luis (2019-02-01). "The spatial evolution of young massive clusters. I. A new tool to quantitatively trace stellar clustering". Astronomy and Astrophysics. 622: A184. arXiv:1901.02371. Bibcode:2019A&A...622A.184B. doi:10.1051/0004-6361/201832936. ISSN 0004-6361. S2CID 119071236.
  10. abuckner89 (2021-07-22), abuckner89/INDICATE, retrieved 2022-09-14

Further reading
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