Global Spatial Autocorrelation
Global spatial autocorrelation is a measure of the overall clustering of the data. One of the statistics used to evaluate global spatial autocorrelation is Moran's I, defined by:
where
- is the deviation of the variable of interest with respect to the mean;
- is the matrix of weights that in some cases is equivalent to a binary matrix with ones in position i,j whenever observation i is a neighbor of observation j, and zero otherwise;
- and .
The matrix W is required because in order to address spatial autocorrelation and also model spatial interaction, we need to impose a structure to constrain the number of neighbors to be considered. This is related to Tobler’s first law of geography, which states that Everything depends on everything else, but closer things more so - in other words, the law implies a spatial distance decay function, such that even though all observations have an influence on all other observations, after some distance threshold that influence can be neglected.
Read more about this topic: Indicators Of Spatial Association
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