Local measures of spatial association

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Abstract
A fundamental concern in analyzing a spatial data set is to identify the presence and nature of spatial autocorrelation. Global measures can be used to summarize the typical features of spatial autocorrelation for the entire data set. However, if the data set has large spatial coverage, it is likely that there will be one or more subareas, possibly of variable sizes and shapes, that are different from the typical situation. Further, unless prior information is available, we are unlikely to have strong expectations about the number, locations, sizes, and shapes of such anomalies. Local measures of spatial autocorrelation have been developed to provide a way of revealing such peculiarities. By identifying anomalous subareas, local measures provide information that is useful in modelling the spatial processes that are thought to give rise to the data, especially since they give an indication of the spatial scales at which such processes might be operating. In addition, the information they provide is of potential value in other activities such as identifying patches and delimiting boundaries. This paper reviews the development and use of local measures of spatial autocorrelation and presents a summary of the findings for all existing measures. It also explores unresolved issues in their application and considers likely directions for future work.