ABSTRACT
Special cases of the Local Moran are local versions of the Differential Moran's I for observations at two points in time, and the Empirical Bayes Smoothed Moran's I for rates. Both statistics are straightforward applications of the Local Moran principle to specially calculated variables. The Median Local Moran is a cross-product local statistic that uses the median spatial lag to summarize values at neighboring locations instead of the usual average.
The Local Geary is a local version of Geary's c statistic and is based on squared differences instead of cross-products. Its interpretation in terms of types of clusters and spatial outliers is therefore more difficult. In GeoDa, a visualization is used that combines information from the Moran Scatterplot with the locations of significant local statistics to interpret them as “High-High”, “Low-Low”, and “Other.” Spatial outliers cannot be distinguished between their two forms.
Getis-Ord statistics are originally derived from a point pattern logic and designed to detect clusters as hot spots and cold spots, but not spatial outliers. The results are often highly similar to those for the Local Moran (apart from not detecting spatial outliers). In contrast, the indications given by Local Geary and Local Moran often differ.
