ABSTRACT
Waldo Tobler made famous his “–rst law of geography,” which states that “everything is related to everything else, but near things are more related than distant things” (Tobler, 1970, p. 236), but he was obviously not the –rst person to realize this. Awareness of the need to take into account the effect of temporal and spatial proximity when carrying out statistical analyses goes back at least as far as Student (1914). Nowadays, data that obey the –rst law of geography are said to be spatially autocorrelated. The pre–x “auto” comes from the Greek word αυτo’, meaning “self.” Thus, to say a feature is spatially autocorrelated means etymologically that its attribute values are correlated with attribute values of the same feature at nearby locations. Different authors de–ne the term spatial autocorrelation differently. Anselin and Bera (1998, p. 241) provide a concise verbal de–nition: “spatial autocorrelation can be loosely de–ned as the coincidence of value similarity with locational similarity.” For example, one of the quantities recorded in the Weislander survey illustrated in Figure 1.1 is mean annual precipitation. Nearby locations would probably tend to have similar mean annual precipitation levels. Anselin and Bera (1998) also provide a more formal de–nition as follows: a nonzero spatial autocorrelation exists between attributes of a feature de–ned at locations i and j if the covariance between feature attribute values at those points is nonzero. If this covariance is positive (i.e., if data with attribute values above the mean tend to be near other data with values above the mean), then we say there is positive spatial autocorrelation; if the converse is true, then we say there is negative spatial autocorrelation. Positive autocorrelation is much more common in nature, but negative autocorrelation does exist, for example, in the case of conspeci–c allelopathy, the tendency of some plants to inhibit the nearby growth of other plants of the same species (Rice, 1984). Nevertheless, in this book, whenever we use the term spatial autocorrelation, we will mean positive spatial autocorrelation.
