Spatial Weights Matrix

Synonyms

Spatial weighting matrix; Proximity matrix; Continuity matrix

Definition

A spatial weights matrix is an n × n positive symmetric matrix W with element w _ij at location i, j for n locations. The values of w _ij or the weights for each pair of locations are assigned by some preset rules which define the spatial relations among locations and, therefore, determine the spatial autocorrelation statistics. By convention, w _ii   =  0 for the diagonal elements.

Main Text

There are many ways to define the weights, including contiguity weights, distance weights, and other weights. The simplest form of weights is binary weight where w _ij   =  1 for neighboring locations i and j, or when the distance between location i and j is less than a fixed distance, or for the fixed number of locations nearest to location i. Otherwise, w _ij   =  0. Another widely used weight is the distance inverse weight in which w _ij   =  1/d _ij ^α. In this continuous weighting function, the changing rate of...