Local and Global Spatial Statistics
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Linearization Indexing of Moving Objects, Bx -Tree Space-Filling Curves
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Main Text Moran’s I and Geary’s C are global indices of spatial association that include all the locations in the data. A spatial contiguity matrix W ij , with a zero diagonal, and the offdiagonal non-zero elements indicating contiguity of locations i and j are used to code proximities. The most commonly used global indicators of spatial autocorrelation are Moran’s I and Geary’s C which are defined as: N i j Wij Zi Zj I= (1) 2, i i Wij i Zi (N − 1) i j Wij (xi − xj )2 C= . (2) 2( i j Wij ) i Zi2 Z i is the deviation of the variable of interest xi from the mean x¯ at location i, and N is the number of data points. Getis and Ord (1995) have defined several local measures including G* which is defined as follows: j Wij (d)xj ∗ Gi ∗ = . (3) j xj Anselin (1995) defines a local version of the Moran’s I as well as LISA statistics. These local measures have been used to identify spatial “hot-spots.” The local Moran I i is defined as: Ii = Zi Wij Z j . (4) j
Link-Node Model Road Network Data Model
LISA Statistics Local and Global Spatial Statistics
Local autocorrelation statistics make it possible to assess the spatial association of a variable within a particular distance of each observation. Cross References Spatial Contiguity Matrices
Recommended Reading
Local and Global Spatial Statistics S UMEETA S RINIVASAN School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
Anselin, L.: Local indicators of spatial association – LISA. Geogr. Anal. 27, 93–115 (1995) Ord, J.K., Getis, A.: Local Spatial Autocorrelation Statistics: Distributional Issues and an Application. Geogr. Anal. 27, 286–306 (1995) Cliff, A., Ord, J.K.: Spatial Autocorrelation. Pion, London (1973)
Synonyms Getis-Ord ind
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