Local Indicators of Spatial Association (LISA)

LISA statistics, introduced by Luc Anselin in 1995, provide a framework for detecting local patterns of spatial association. While global measures like Moran's IMoran's IMoran's I is the most widely used global measure of spatial autocorrelation, quantifying the degree to which values a... summarize spatial autocorrelationSpatial AutocorrelationSpatial autocorrelation measures the degree to which values at nearby locations are similar (positive) or dissimilar ... across an entire study area with a single value, LISA statistics assess each observation individually, revealing where clusters of similar values (hot spots and cold spots) and spatial outliers (high values surrounded by low, or vice versa) are located.

The most common LISA statistic is Local Moran's IMoran's IMoran's I is the most widely used global measure of spatial autocorrelation, quantifying the degree to which values a..., which computes a spatial autocorrelationSpatial AutocorrelationSpatial autocorrelation measures the degree to which values at nearby locations are similar (positive) or dissimilar ... measure for each feature by comparing its value to those of its neighbors. Each observation is classified into one of four categories based on statistical significance: high-high (a high value surrounded by high values), low-low (a low value surrounded by low values), high-low (a high-value outlier amid low values), or low-high (a low-value outlier amid high values). The sum of all Local Moran's I values is proportional to the Global Moran's I, establishing a clear relationship between local and global spatial patterns.

Urban planners use LISA to identify neighborhoods with significantly clustered socioeconomic characteristics for targeted investment. Public health analysts detect disease hotspots and coldspots, guiding intervention programs. Crime analysts pinpoint statistically significant crime clusters rather than relying on subjective hotspot interpretation. Environmental scientists identify local clusters of pollution or biodiversity that may warrant protection. Real estate analysts locate neighborhoods where property values form significant clusters or outliers.

LISA results are evaluated using permutation-based pseudo p-values, which compare the observed local statistic to a reference distribution generated by randomly reassigning values to locations. Multiple testing corrections (such as Bonferroni or false discovery rate) are applied to control for the increased probability of false positives when testing many locations simultaneously.