Chapter 11 Distance-Based Spatial Weights

In this second chapter devoted to spatial weights, the focus is on weights that are derived from a notion of distance. Intrinsically, this is most appropriate for point layers, but it can easily be generalized to polygons as well, through the use of the polygon centroids.

The chapter starts with a brief overview of distance metrics and the fundamental difference between points expressed in projected coordinates and points in latitude-longitude decimal degrees. Whereas for the former the familiar concept of Euclidean distance can be applied, the latter requires the computation of great circle distance or arc distance. In addition, a concept of distance in multivariate attribute space is introduced.

This is followed by a review of spatial weights that are based on distance-bands, k-nearest neighbor weights and the use of generalized concepts of distance.

Next is a discussion of the implementation of the weights functionality in GeoDa, including a broadening of the strict concept of contiguity to apply to points.

The chapter closes with a discussion of set operations on weights, such as intersection, union and making symmetric.

The methods are illustrated with a point data set that contains performance measures for 261 Italian community banks for 2011-2017. This data set was used in an analysis of spatial spillovers in technical efficiency by Algeri et al. (2022). The data are contained in the Italy Community Banks sample data set. The space-time weights are illustrated with the Oaxaca Development data.

As mentioned in the previous chapter, to work most effectively with the spatial weights files, the data sets should first be copied (Save As) to a working directory.