A demonstration of how the Multilevel Index of Dissimilarity measures spatial clustering as well as unevenness
A criticism of the standard Index of Dissimilarity (ID) is that it only measures one of the two principal dimensions of segregation - unevenness but not spatial clustering. Because of this, very different spatial patterns of segregation can generate the same ID score but the ID is unable to distinguish between them.
In contrast, the multilevel index can detect the differences because different patterns (scales) of segregation change the percentage of the variance due to each level. The demonstation illustrates this using the classic example of a checkerboard. The examples show how the percentage of the total variance (labelled Pvariance) moves up the hierarchy with the increase in spatial clustering at greater geographical cases. However, the ID is always the same.
The 'stray' cell in examples 2-4 is to allow the model to be fitted. With it the model correctly identifies that some of the variation remains at the base level)
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