Concluding Comments

The principal emphasis in this book is on visualizing spatial autocorrelation latent in georeferenced data, most often with a map, to promote a better understanding of spatial autocorrelation. When done with razzle-dazzle color, rather than the gray tones utilized throughout this book, such visualization can produce very beautiful maps, but this is a needless artistic touch that does not necessarily increase one’s understanding of spatial autocorrelation. An important feature of maps portraying spatial filter components that captures spatial autocorrelation effects is geographic pattern consisting of local clusters of similar values. As the degree of positive spatial autocorrelation increases, the size of clusters tends to increase while their number tends to decrease. Because eigenvectors of matrix (I - 11T/n)C(I - 11T/n), whose linear combinations constitute spatial filters, are computed to a factor of ±1 , a cluster of values constituting a relative sink or hill can be reversed simply by multiplying an eigenvector by -1. Accordingly, maps of spatial filters—which in fact are synthetic variates measured on an interval scale—most often are described here in terms of increasing darkness of gray tones rather than with a legend. The critical information arises from the map patferrc that Pm erge nnt the artificial numerical values that are manned.