Calculating Varying Scales of Clustering Among Locations

Abstract

The Nearest Neighbor Index (NNI) is a spatial statistic that detects geographical patterns of clustered or dispersed event locations. Unless the locations are randomly distributed, the distances of either clustered or dispersed nearest neighbors form a skewed distribution that biases the average nearest neighbor distance used in calculating the NNI. If the clustering or dispersion of locations is moderate to extreme, the NNI can be inaccurate if the skew is substantial. Using Housing Choice Voucher program residential locations, we demonstrate in this article the method to derive an NNI based on a median and two quartiles that more accurately represents the midpoint of a set of nearest neighbor distances. We also demonstrate how to use these alternative point estimates to gauge multiple scales of clustering from different positions across the nearest neighbor distance distribution. Finally, we discuss how to use the average and standard deviation distances from the calculation of each NNI to more comprehensively gauge the scale of the geographic patterns. We also include a Python program that creates a randomized set of locations to calculate statistical significance for the median and quartile NNIs.