ABSTRACT
In a nonparametric approach to spatial autocorrelation, instead of expressing locational similarity by means of a spatial weights matrix, a direct relationship to distance is used. A measure of similarity or dissimilarity between pairs of observations is related to the distance that separates them. The interest lies in determining the range of interaction, a distance beyond which the correlation disappears, and the form of the distance decay (Tobler's law). Two approaches are illustrated in this chapter.
In the spatial correlogram, the cross-product between a pair of standardized observations is related to the distance between them. In GeoDa, this is implemented by grouping the pairs of observations into distance bins. Operational decisions are the number of bins, or, alternatively, their width, and a distance cut-off point, which eliminates pairs of observations from the estimation that are too far apart.
The smoothed distance scatter plot is a simple scatter plot of squared difference between pairs of observations against the distance that separates them. Operational decisions pertain to the choice of the smoothing function, distance cut-off and scaling of the axis.
Whereas the spatial correlogram decreases with distance, the smoothed distance scatter plot increases with distance.
