Local Spatial Autocorrelation
Local Spatial Autocorrelation Analysis · Also known as: local spatial association, local SA, LISA methods, local spatial clustering
Local Spatial Autocorrelation methods decompose global spatial clustering into location-specific statistics, revealing where in a study area significant clustering or dispersion occurs. Each observation receives its own association score and significance value, enabling the detection of spatial hot spots, cold spots, and spatial outliers rather than reporting a single summary statistic.
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When to use it
Use local spatial autocorrelation when you need to identify where in a study area significant clustering or spatial outliers occur, not just whether clustering exists globally. It is appropriate for continuous or count data distributed across areal units (census tracts, counties) or georeferenced points when aggregated. It is the right tool when spatial heterogeneity is suspected — when some regions cluster strongly while others do not. Do not use it as a substitute for global Moran's I if only a global summary is needed. Avoid it when the spatial weights matrix is poorly defined, when the sample is very small (fewer than ~30 units), or when many units have zero or very few neighbors, as inference becomes unreliable. Multiple-testing inflation is a genuine concern; always apply a correction such as FDR.
Strengths & limitations
- Decomposes spatial association into location-specific measures, enabling precise identification of hot spots, cold spots, and spatial outliers.
- Flexible: multiple statistics (Local Moran's I, Local Geary's C, Gi*) suit different research questions about clustering versus outlier detection.
- Permutation-based inference makes no distributional assumptions about the data.
- Results translate directly into intuitive, policy-relevant cluster maps that communicate spatial inequality or disease burden at a glance.
- Additive decomposition property: the sum of local Moran's I values equals (up to a constant) the global Moran's I, providing a bridge between local and global analyses.
- Results depend heavily on the choice and specification of the spatial weights matrix; different neighbor definitions can yield different cluster maps.
- Conducting a separate significance test for every location inflates the family-wise error rate; multiple-testing corrections reduce power.
- Permutation inference can be computationally intensive for large datasets with many permutations.
- Local statistics assume stationarity within each local neighborhood, which may not hold in highly heterogeneous regions.
- Interpretation of spatial outlier quadrants (High-Low, Low-High) requires caution; they may reflect data quality issues or boundary effects rather than true spatial anomalies.
Frequently asked
How is local spatial autocorrelation different from global Moran's I?
Global Moran's I produces a single number summarizing the overall degree of spatial clustering across the entire study area. Local spatial autocorrelation produces a statistic for every individual location, revealing which specific places form significant clusters or outliers. The local values can sum to reproduce the global statistic, so they are complementary rather than competing measures.
Which local statistic should I choose — Local Moran's I, Local Geary's C, or Gi*?
Local Moran's I is best for detecting clusters and spatial outliers simultaneously and is most widely used. Local Geary's C is more sensitive to local dissimilarity and outliers. Getis-Ord Gi* focuses exclusively on concentration (hot and cold spots) and does not identify spatial outliers; it is preferred when you want to test whether high or low values concentrate locally.
What multiple-testing correction should I apply?
The Benjamini-Hochberg false discovery rate (FDR) correction is now the standard recommendation in spatial analysis because it is less conservative than Bonferroni while still controlling the expected proportion of false discoveries. Some software (e.g., GeoDa) applies FDR by default. Always report the correction used.
How many permutations are needed for reliable inference?
999 permutations is the conventional minimum for p = 0.05 thresholds; 9999 permutations are recommended when working at the p = 0.01 or p = 0.001 level or when precision matters for publication. More permutations increase computation time but improve p-value stability.
Can local spatial autocorrelation be applied to point data?
Yes, but point data must first be aggregated to areal units or a spatial weights matrix must be constructed from distance or k-nearest-neighbor criteria. Kernel density estimation is an alternative for continuous spatial fields; local spatial autocorrelation is most naturally suited to data already organized into discrete spatial units.
Sources
- Anselin, L. (1995). Local indicators of spatial association — LISA. Geographical Analysis, 27(2), 93–115. DOI: 10.1111/j.1538-4632.1995.tb00338.x ↗
- Indicators of spatial association. Wikipedia. link ↗
How to cite this page
ScholarGate. (2026, June 3). Local Spatial Autocorrelation Analysis. ScholarGate. https://scholargate.app/en/spatial-analysis/local-spatial-autocorrelation
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Hot Spot AnalysisSpatial analysis↔ compare
- Local Geary's CSpatial analysis↔ compare
- Local Getis-Ord Gi*Spatial analysis↔ compare
- Local Indicators of Spatial AssociationSpatial analysis↔ compare
- Local Moran's ISpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare