Global Versus Local
Global spatial analysis or global spatial autocorrelation analysis yields only one statistic to summarize the whole study area. In other words, global analysis assumes homogeneity. If that assumption does not hold, then having only one statistic does not make sense as the statistic should differ over space.
But if there is no global autocorrelation or no clustering, we can still find clusters at a local level using local spatial autocorrelation. The fact that Moran's I is a summation of individual crossproducts is exploited by the "Local indicators of spatial association" (LISA) to evaluate the clustering in those individual units by calculating Local Moran's I for each spatial unit and evaluating the statistical significance for each Ii. From the previous equation we then obtain:
where:
then,
I is the Moran's I measure of global autocorrelation, Ii is local, and N is the number of analysis units in the map.
LISAs can for example be calculated in GeoDA, which uses the Local Moran's I, proposed by Luc Anselin in 1995.
Read more about this topic: Indicators Of Spatial Association
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