LISA — Local Indicators of Spatial Association (Local Moran's I)
Local Indicators of Spatial Association (Local Moran's I) · Also known as: local Moran's I, local spatial autocorrelation, LISA cluster analysis, LISA — Yerel Uzamsal Otokorelasyon (Local Moran's I)
LISA, introduced by Luc Anselin in 1995, is a local statistic that computes spatial autocorrelation separately for every observation rather than for the map as a whole. It pinpoints where high or low values cluster and where spatial outliers sit, decomposing the global Moran's I into a contribution from each location.
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Method map
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When to use it
Use LISA for cross-sectional, georeferenced continuous data when you want to locate where clusters and outliers occur rather than just confirm clustering exists globally. It requires a defined spatial weight matrix W and coordinate information, works best with at least about 30 observations, and calls for a multiple-testing correction such as Bonferroni or FDR. With small samples the local estimates can be unstable, and without coordinates the local statistic cannot be computed at all.
Strengths & limitations
- Maps exactly where High-High, Low-Low, High-Low, and Low-High patterns occur, not just whether clustering exists.
- Identifies spatial outliers — locations that differ sharply from their neighbours — that a global statistic hides.
- Decomposes global Moran's I into per-location contributions, giving an interpretable cluster map.
- Requires a correctly specified spatial weight matrix W; results depend on this choice.
- Running one test per observation demands multiple-testing correction (Bonferroni or FDR) to control false positives.
- Local estimates can be unstable when the number of observations is small.
Frequently asked
How is LISA different from the global Moran's I?
The global Moran's I gives a single number summarising clustering across the whole map. LISA breaks this into one statistic per location, so it tells you where the clustering and the outliers are. The local statistics sum back to the global value.
What do the four cluster categories mean?
High-High is a high value surrounded by high neighbours, Low-Low is a low value among low neighbours — both indicate clusters. High-Low and Low-High are spatial outliers, where a location differs from its surroundings.
Why do I need to correct for multiple testing?
LISA runs a separate significance test for every observation, so with many locations some will appear significant by chance. A correction such as Bonferroni or FDR keeps the false-positive rate under control.
What should I do if I have no coordinate data?
Local spatial autocorrelation cannot be computed without locations, so LISA does not apply. Use the global Moran's I test instead to check for overall spatial clustering.
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 ↗
How to cite this page
ScholarGate. (2026, June 1). Local Indicators of Spatial Association (Local Moran's I). ScholarGate. https://scholargate.app/en/spatial-analysis/lisa-analysis
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.
- KrigingSpatial analysis↔ compare
- Moran's ISpatial analysis↔ compare
- Spatial Durbin ModelSpatial analysis↔ compare
- Spatial Error ModelSpatial analysis↔ compare
- Spatial Lag ModelSpatial analysis↔ compare