Robust Local Indicators of Spatial Association (Robust LISA)
Robust Local Indicators of Spatial Association · Also known as: Robust LISA, outlier-resistant LISA, robust local spatial autocorrelation, LISA with robust weights
Robust Local Indicators of Spatial Association extend Anselin's LISA framework to handle outliers, extreme values, and spatially heterogeneous populations. By applying outlier-resistant adjustments to the spatial weights or the standardised values, Robust LISA identifies statistically significant local clusters and spatial outliers without the distortions caused by highly influential observations.
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When to use it
Use Robust LISA when your spatial data contain extreme values, rare events with small at-risk populations (e.g., disease rates in small counties), or when preliminary diagnostics show that standard LISA results are dominated by one or a few influential locations. It is particularly appropriate for epidemiological data, crime rates with small population denominators, and socioeconomic variables with heavy-tailed distributions. Do not use it as a routine replacement for standard LISA when the data are well-behaved; the robust adjustments add complexity and the results can be harder to communicate. Also avoid when the sample of spatial units is very small (fewer than ~30 areas), since permutation inference has limited power.
Strengths & limitations
- Reduces distortion from outliers and extreme values that can create artefactual clusters in standard LISA.
- Population-adjusted variants (Assuncao-Reis) provide more reliable inference for spatially heterogeneous denominators.
- Retains the interpretability of the standard LISA cluster map (High-High, Low-Low, spatial outliers).
- Permutation-based inference remains valid without distributional assumptions.
- Can be combined with any spatial weights specification (contiguity, distance-band, k-NN).
- The choice of robust adjustment method is not standardised; different implementations may yield different cluster maps.
- Added complexity makes results harder to explain to non-technical audiences compared with standard LISA.
- If the data are not actually outlier-contaminated, robust adjustments reduce statistical power.
- Does not resolve fundamental issues with the modifiable areal unit problem (MAUP) or edge effects.
Frequently asked
How does Robust LISA differ from standard Local Moran's I?
Standard Local Moran's I standardises the attribute using the global mean and variance, making it sensitive to extreme values. Robust LISA applies outlier-resistant standardisation (e.g., MAD-based scaling, rank transforms, or population adjustment) before computing the same local statistic, so a single extreme observation does not dominate the cluster map.
What is the Assuncao-Reis adjustment and when should I use it?
The Assuncao-Reis (1999) adjustment rescales a spatially varying rate by the square root of the expected count under a null model, stabilising variance across areas with different population sizes. Use it when analysing rates (e.g., deaths per 1,000 residents) across spatial units with very different population denominators.
How many permutations should I use?
At least 999 permutations for a 0.05 significance level and at least 9,999 for a 0.01 threshold. More permutations give more stable pseudo p-values but increase computation time.
Should I use a FDR correction with Robust LISA?
Yes. When testing hundreds of locations simultaneously, the expected number of false positives is large. Benjamini-Hochberg FDR correction or the spatial FDR approach in GeoDa is recommended to control the overall false discovery rate.
Can I apply Robust LISA to point data rather than areal data?
Yes, but you must first define a spatial weights matrix for point locations (e.g., distance-band or k-nearest neighbors). The robust adjustment logic is the same; the cluster map interpretation requires care because point-level results are sensitive to the bandwidth chosen.
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 ↗
- Assuncao, R. M., & Reis, E. A. (1999). A new proposal to adjust Moran's I for population density. Statistics in Medicine, 18(16), 2147–2162. DOI: 10.1002/(SICI)1097-0258(19990830)18:16<2147::AID-SIM179>3.0.CO;2-I ↗
How to cite this page
ScholarGate. (2026, June 3). Robust Local Indicators of Spatial Association. ScholarGate. https://scholargate.app/en/spatial-analysis/robust-local-indicators-of-spatial-association
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.
- 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
- Robust Spatial AutocorrelationSpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare