Local Indicators of Spatial Autocorrelation (LISA) Autocorrelation Distance

Conceptualization of Spatial Relationships INVERSE_DISTANCE—Nearby neighboring features have a larger influence on the computations for a target feature than features that are far away. INVERSE_DISTANCE_SQUARED—Same as INVERSE_DISTANCE except that the slope is sharper, so influence drops off more quickly. FIXED_DISTANCE_BAND—Each feature is analyzed within the context of neighboring features. Neighboring features inside the specified critical distance receive a weight of 1. ZONE_OF_INDIFFERENCE—Features within the specified critical distance of a target feature receive a weight of 1 and once the critical distance is exceeded, weights diminish with distance. CONTIGUITY_EDGES_ONLY—Only neighboring polygon features that share a boundary or overlap will influence computations for the target polygon feature. CONTIGUITY_EDGES_CORNERS—Polygon features that share a boundary, share a node, or overlap will influence computations for the target polygon feature. GET_SPATIAL_WEIGHTS_FROM_FILE—Spatial relationships are defined in a spatial weights file. The path to the spatial weights file is specified in the Weights Matrix File

Distance Tools Calculate Distance Band from Neighbor Count Returns the minimum, the maximum, and the average distance to the specified Nth nearest neighbor (N is an input parameter) for a set of features. Incremental Spatial Autocorrelation Measures spatial autocorrelation for a series of distances and optionally creates a line graph of those distances and their corresponding z-scores. Z-scores reflect the intensity of spatial clustering, and statistically significant peak z-scores indicate distances where spatial processes promoting clustering are most pronounced. These peak distances are often appropriate values to use for tools with a Distance Band or Distance Radius parameter.

Random Pottery Example Calculate Distance Band from Neighbor Count Minimum Distance – 200 meters Average Distance – 561 meters Can be used as an interval to determine correlation distances Maximum Distance – 1166 meters The start to determine correlation distances Incremental Spatial Autocorrelation Beginning Distance: 1200 Distance Increment: 600 Euclidean Distance

Random Pottery Example Incremental Spatial Autocorrelation

Hot Spot Analysis (Getis-Ord Gi*)

Tucson Census Tract Data – Fraction of Hispanic Calculate Distance Band from Neighbor Count Minimum Distance: 626 meters Average Distance: 1630 meters Maximum Distance: 6814 meters Incremental Spatial Autocorrelation

High-Low Clustering Fixed Distance Extent Contiguity Edges Corners

Hot Spot Analysis Fixed Distance ExtentContiguity Edges Corners