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 crossproduct 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/(N1)
.
Values of
I
that exceed
1/(N1)
indicate
positive spatial autocorrelation, in which similar values, either high values or low values
are spatially clustered. Values of
I
below
1/(N1)
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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is the mean of
,
,
, and
w(i,j)
is the connectivity
spatial weight between I and j.
The variances of
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 Summer '08
 Staff
 Variance, Moran, Geary, spatial autocorrelation, spatial weights matrix

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