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 Roy C. 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 Arthur Getis and J. Keith 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 G_i (local G_i): Developed by Getis and Ord based on their global G.
INDICATE's I_N: Originally developed to assess the spatial distribution of stars,^[9] can be computed for any discrete 2+D dataset using python-based INDICATE tool available from GitHub.^[10]

References

^ ^a ^b George Grekousis (2020). Spatial Analysis Methods and Practice. Cambridge University Press. p. 210. ISBN 9781108712934.
^ Moran, P. A. P. (1950). "Notes on Continuous Stochastic Phenomena". Biometrika. 37 (1): 17–23. doi:10.2307/2332142. JSTOR 2332142. PMID 15420245.
^ 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.
^ Geary, R. C. (1954). "The Contiguity Ratio and Statistical Mapping". The Incorporated Statistician. 5 (3): 115–145. doi:10.2307/2986645. JSTOR 2986645.
^ J. N. R. Jeffers (1973). "A Basic Subroutine for Geary's Contiguity Ratio". Journal of the Royal Statistical Society, Series D. 22 (4). Wiley: 299–302. doi:10.2307/2986827. JSTOR 2986827.
^ 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.
^ Anselin, Luc (1995). "Local Indicators of Spatial Association—LISA". Geographical Analysis. 27 (2): 93–115. doi:10.1111/j.1538-4632.1995.tb00338.x.
^ Anselin, Luc (2005). "Exploring Spatial Data with GeoDa: A Workbook" (PDF). Spatial Analysis Laboratory. p. 138.
^ 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.
^ abuckner89 (2021-07-22), abuckner89/INDICATE, retrieved 2022-09-14{{citation}}: CS1 maint: numeric names: authors list (link)

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