Contiguity-Based Spatial Weights
Luc Anselin · 2024
Spatial weights are a core concept needed for the treatment of spatial autocorrelation. This chapter introduces the notion and elaborates some basic concepts pertaining to contiguity-based spatial weights. In such weights, a neighbor relation is defined when two spatial units share a common boundary or boundary point. A distinction is made between rook-based contiguity (only a common vertex) and queen-based contiguity (a common edge). Further clarification is offered between the existence of a neighbor relationship as a binary condition and its use in row-standardized form in spatial autocorrelation statistics. Higher order contiguity is defined recursively as first-order contiguity to a lower order. A distinction is made between pure higher order weights (no lower order neighbors included) and cumulative higher order weights (inclusive of lower order neighbors). The implementation of spatial weights is illustrated by means of the Weights Manager in GeoDa. In addition to creating different types of contiguity weights, this also provides a means to analyze the characteristics of spatial weights, such as the connectivity structure or cardinality (in a connectivity histogram), as well as map and graph representations of this structure.