Geary's C: A Measure Of Spatial Autocorrelation

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3.8.2 Geary’s C
Another measure of spatial autocorrelation is Geary’s C statistic which ranges from 0 to 2 where 0 signifies maximum positive spatial autocorrelation or clustering, 1 signifies no autocorrelation or randomness and 2 signifies maximum negative autocorrelation or dispersal. If the values of Geary’s C are low it indicates positive spatial autocorrelation and if the values are high it indicates negative spatial autocorrelation. The calculation is similar to Moran’s I but here the cross product is taken on actual values at two locations.
C(d)=((n-1))/(2Σ_i^n Σ_j^n w_(ij ) ).Σ_i^n Σ_j^n w_(ij ) (x_i-x_j )^2/Σ_i^n (x_i-x ̅ )^2 n – number of observations x_i,x_j-values of varaibles in locations i and j x ̅-mean value of x varaible w_(ij )-element of spatial weight matrix W

3.2.2 Geary’s C Pros and Cons
This test for global spatial autocorrelation is also one of the common measures (Gorniak, 2016) and one of the limitations of this is that it is used only for continuous
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“The spatial correlogram describes the way spatial autocorrelation changes with increasing lag distance between the locations (Plant, 2012)”. As can be seen from the Moran’s I equation a spatial weights matrix is calculated based on distance on point or polygon data. Moran correlogram is distance based and as we increase distance between cells we can measure change in correlation structure (Plant,2012).
3.9.2 Moran Scatterplot
This tool is also based on Moran’s I statistic. It is a bivariate plot in which slope of regression line represents the statistic. With the help of this plot we can know about the local structure of the data and visualize the potential outliers. “the Moran scatterplot reveals the extent to which the global I statistic effectively summarize the spatial structure (Plant,

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