ABSTRACT
This chapter introduces the concept of spatial autocorrelation, which is central to the detection of spatial patterns in data. It is situated against the null hypothesis of spatial randomness and the alternatives of positive spatial autocorrelation (clustering of like values) and negative spatial autocorrelation (checkerboard pattern). Attempting to detect spatial clustering by eye is fraught with problems, hence the need for a spatial autocorrelation statistic. Such a statistic combines the notions of locational similarity (expressed in spatial weights) and attribute similarity (or dissimilarity). Different concepts of attribute similarity result in different statistics, the most prominent of which are Moran's I (cross-product) and Geary's c (squared difference).
Inference for these statistics is based either on analytical derivations or on random permutation. The visualization of Moran's I by means of a Moran scatterplot is illustrated, which allows four types of spatial association to be distinguished: positive spatial autocorrelation as high-high and low-low quadrants, and negative spatial autocorrelation (spatial outliers) as high-low and low-high quadrants. It is shown how the slope of a linear fit through the Moran scatterplot is Moran's I. The importance of linking and brushing is again highlighted, with an important distinction between the use of dynamic and static spatial weights.
