DATA ANALYSIS Part III

The above testing procedures are all motivated by the spatial autoregressive model of residual errors. So before moving on to spatial regression analyses of areal data, it is appropriate to consider certain alternative measures of spatial association that are also based on spatial weights matrices. By far the most important of these for our purposes are the so-called G-statistics, developed by Getis and Ord (1992,1995).1 These statistics focus on direct associations among (nonnegative) spatial attributes rather than spatial residuals from some underlying explanatory model. For any given set of nonnegative data, 1 ( ,.., ) n x x x   , associated with n areal units, together with an appropriate spatial weights matrix, ( : , 1,.., ) ij W w i j n   , the * G statistic for x is defined to be:2