A fundamental concern of pattern researchers is to find peculiarities in spatial data that lead to the identification of hot spots or clusters that signify that something out of the ordinary has occurred in one or more regions within the area covered by the data. In fields such as regional science, economic geography, and epidemiology questions are often raised about the number of events in particular subregions of the study area. These include concerns such as the location of migration destinations, the location of specialized economic activity, and the location of infectious diseases. In recent years, a number of papers have been written where the identification of hot spots is the principal concern.
A natural direction for this research has been to develop statistics that can pinpoint the exact location of places that exhibit these special characteristics. Previous to the development of local statistics, one depended on indicators such as the mapped residuals from regression to identify spatial outliers. Well known global statistics such as Moran’s I, Geary’s c, and Matheron’s variogram are not designed to look beyond the general autocorrelation characteristics of a pattern, although they can be made sensitive to directional influences. Cressie (1991), for his pocket plot, while identifying outliers, does not provide a test for statistical significance. The variogram does dissect patterns into their component correlations by distance increments as do the correlograms based on Moran’s and Geary’s statistics, but these do not depend on a single spatial focus as do local statistics.
The local statistics of Ord and Getis (GA: 1992, 1995) and the LISA statistics of Anselin (GA: 1994) are designed to test individual sites for membership into clusters. Both Ord and Getis and Anselin recognize, however, that in the face of global autocorrelation, finding individual centers of clustering becomes a problem. Ord and Getis provide a discussion of the issue with a proof that local statistics must be interpreted differently at different levels of global autocorrelation.
Ord and Getis also addressed the issue of finding appropriate statistical test cutoff values of their local statistics when multiple simultaneous dependent tests are employed. This is an issue of some importance, especially when the technology is moving us in the direction of larger data sets.
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Email: arthur.getis@sdsu.edu