Chapter 10 Contiguity-Based Spatial Weights

A core concept in the exploration of spatial patterns is spatial autocorrelation. It is considered in depth in Parts IV and V. At this point, it suffices to recognize that spatial autocorrelation is essentially a compromise between attribute similarity (the usual notion of correlation) and spatial similarity.

Spatial similarity in this context is typically interpreted as locational or geographical similarity, i.e., the presence of a neighbor relationship between a pair of observations. However, the concept is perfectly general, and pertains to any network structure that represents observations as nodes, connected by edges. The existence of an edge between a pair of observations then becomes the neighbor structure.

The matrix representation of this network structure is the so-called spatial weights matrix. In the current and the next two chapters, this concept is discussed in more detail, although with a particular focus on its implementation in GeoDa. Consequently, only a limited set of aspects of this broad ranging topic will be covered. More extensive and technical discussions as well as further references can be found in Anselin (1988), Bavaud (1998), Getis (2009), R. Harris, Moffat, and Kravtsova (2011), Anselin and Rey (2014), and Anselin (2021), among others.

This chapter deals with spatial weights derived from the presence of a common border between two observations (typically polygons), or contiguity-based weights. It begins with a more formal introduction of the concept of spatial weights, followed by a review of the creation of so-called rook and queen weights, as well as higher order contiguity weights and space-time weights. The chapter closes with a discussion of a range of methods that can be used to analyze and visualize characteristics of the spatial weights.

To illustrate these concepts, I will mostly use the Ceará Zika sample data set, except in the discussion of space-time weights, where Oaxaca Development is employed. Note that to deal efficiently with the resulting spatial weights files, it is preferable to save the sample data sets onto a designated working directory before constructing the weights.66

  1. The sample data sets are contained within a special file attached to the GeoDa software and cannot be changed.↩︎