Indicators of spatial association

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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.

Contents

Global indicators

Notable global indicators of spatial association include: [1]

Local indicators

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

See also

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References

  1. 1 2 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{{citation}}: CS1 maint: numeric names: authors list (link)

Further reading