Tips: Defining Contiguity

In spatial autocorrelation analysis some measure of contiguity is required. Contiguity has a rather broad definition depending on the research question, however, most analyses in spatial autocorrelation adhere to a common definition of neighborhood relations. Namely, neighborhood relations are defined as either rooks case, bishops case or queens (kings) case. These are rather simple and intuitive as their names suggest (Fig. 1). Rooks case contiguity is by a neighborhood of 4 locations adjacent to each cell, Bishops only considers the diagonals of the relation and queens or kings case considers a neighborhood of eight cells. These are the most common forms of contiguity used in spatial autocorrelation when considering continuous data in a raster format. Of these three the rooks case is the most commonly used and most programs only will compute this particular case.

However, this type of contiguity is not sufficient for vector data formats or irregularly spaced points. In these cases distances to the four or even n nearest neighbors can be used or distance between a variate X and all neighbors can be used.

Fig. 1

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References

[1] Global Spatial Autocorrelation Indices - Moran's I, Geary's C and the General Cross-Product Statistic, from University of Ottawa.