Global Moran and Global Geary

# Global Moran and Global Geary - Global Morans I and Global...

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Global Moran’s I and Global Geary’s c Moran’s I and Geary’s c are well known tests for spatial autocorrelation. They represent two special cases of the general cross-product statistic that measures spatial autocorrelation. Moran’s I is produced by standardizing the spatial autocovariance by the variance of the data. Geary’s c uses the sum of the squared differences between pairs of data values as its measure of covariation. Both of these statistics depend on a spatial structural specification such as a spatial weights matrix or a distance related decline function. Input 1. The input data file should contain the X,Y coordinates and the value at each point (x I ). 2. Input whether you have a spatial weights matrix file. 3. If you do not have a spatial weights matrix, you’ll be asked to enter the A and m parameters (see below). 4. You will be asked to enter the maximum distance, the number of steps, and whether you want bands or increments. Analysis The expected value of Moran’s I is -1/(N-1) . Values of I that exceed -1/(N-1) indicate positive spatial autocorrelation, in which similar values, either high values or low values are spatially clustered. Values of I below -1/(N-1) indicate negative spatial autocorrelation, in which neighboring values are dissimilar. The theoretical expected value for Geary’s c is 1. A value of Geary’s c less than 1 indicates positive spatial autocorrelation, while a value larger than 1 points to negative spatial autocorrelation. Formula [1] [2]

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where is the mean of , , , and w(i,j) is the connectivity spatial weight between I and j. The variances of
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Global Moran and Global Geary - Global Morans I and Global...

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