Neighbor relationships

Neighbor relationships between regions or between events in time underlie statistical methods such as local Moran.

To examine spatial association, you first need to define how ClusterSeer should set neighbor, or contiguity, relationships. Exactly what is next to what? ClusterSeer can set neighbor relationships in two ways: 1) using lists of neighbors for each region from SpaceStat™ sparse ASCII files or 2) based on polygon contiguity from a GIS file.

Contiguity matrix

ClusterSeer uses either data file to create a contiguity matrix holding binary spatial weights. These weights indicate whether regions neighbor each other. The weight between two areas that share a common border is set to 1. The weight between two areas that do not share a common border is set to 0.

The figure below illustrates a simple example of three polygons and their contiguity matrix. The first row in the matrix describes neighbor relationships for polygon 1 (it cannot neighbor itself, so the first value is zero, it neighbors polygon 2, so the second value is 1, and it does not neighbor polygon 3, another zero.). Lower rows describe polygons 2 and 3 in turn.

For local Moran, ClusterSeer row-standardizes spatial weights stored in the contiguity matrix. For example, as polygon 2 has two neighbors, each neighbor is weighted ½, so that the weights on each row sum to 1 and the statistic is not biased by the number of neighboring regions. Row-standardizing the example matrix above leads to:

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