Spatial Dissimilarity Index

The classic index of dissimilarity measures only how unevenly two groups are distributed across units and ignores where those units sit, so it scores a checkerboard of alternating groups the same as two solid, separated blocks. The spatial index starts from that same value but subtracts an interaction term across shared boundaries, lowering the score wherever neighbouring units resemble each other. As a result it falls below the aspatial value precisely when segregation is spatially clustered, capturing arrangement as well as composition.

The checkerboard problem is the failure of the aspatial dissimilarity index to distinguish spatial patterns that have the same unit compositions but very different geographies. A perfectly alternating checkerboard and a board split into two solid halves both yield maximal aspatial dissimilarity, even though the halves are far more segregated in any meaningful sense. The spatial index solves this by accounting for whether adjacent units are similar, rewarding the mixed borders of the checkerboard with a lower score.

Morrill's 1991 adjustment used a simple binary contiguity matrix: units either share a boundary or they do not. Wong's 1993 refinement made the correction geometric, weighting each pair's interaction by the length of their shared boundary relative to the unit's perimeter, and in fuller versions by unit area and shape. This means two units with a long common edge interact more strongly than two that barely touch, so the index reflects the real intensity of contact between units rather than treating all neighbours equally.