Local Geary's C
Local Geary's C Contiguity Ratio · Also known as: Local Geary, local spatial contiguity ratio, LISA Geary, local c statistic
Local Geary's C is a local indicator of spatial association (LISA) that measures, for each location, how dissimilar its value is from its immediate neighbours. Unlike Local Moran's I, which detects clustering of similar values, Local Geary's C focuses on squared value differences and is especially sensitive to local spatial outliers and local heterogeneity.
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When to use it
Use Local Geary's C when you need to identify locations that are unusually different from their spatial neighbours — spatial outliers — or to detect fine-grained local clusters that may be missed by global statistics. It is appropriate for continuous georeferenced data with a meaningful spatial weights structure (contiguity or distance-based). Prefer it over Local Moran's I when detecting local heterogeneity or dissimilarity is the primary goal. Do not use it when the spatial weights matrix is poorly defined, when data are not georeferenced, when the sample is very small (fewer than ~30 observations), or when the variable is categorical — for categorical data, use join-count statistics instead.
Strengths & limitations
- Specifically sensitive to local spatial outliers — locations whose values differ markedly from their neighbours.
- Provides a separate diagnostic for each observation, enabling fine-grained mapping of local spatial patterns.
- Complements Global Geary's C and Local Moran's I, giving a fuller picture of spatial dependence.
- Permutation-based inference is assumption-light and robust to non-normality of the attribute.
- Extended to the multivariate case (multivariate Local Geary's C, Anselin 2019), broadening applicability.
- Interpretation is less intuitive than Local Moran's I because it uses squared differences rather than covariance-style products.
- Results depend heavily on the choice of spatial weights matrix; different neighbour definitions can alter conclusions.
- Multiple testing across all locations inflates the Type I error rate; corrections (e.g., false discovery rate) are recommended.
- Does not distinguish between high-high and low-low clusters in the way a Moran scatter plot does.
Frequently asked
How does Local Geary's C differ from Local Moran's I?
Local Moran's I uses the cross-product of each location's deviation from the mean and its neighbours' deviations, making it most powerful for detecting clusters of similarly high or low values. Local Geary's C uses squared differences between raw values, making it more sensitive to dissimilarity and spatial outliers. The two statistics are complementary and are often mapped together.
What does a significant low Local Geary's C indicate?
A significantly low c_i (small squared differences) means the location's value is similar to its neighbours — evidence of a local spatial cluster. A significantly high c_i means the location is dissimilar from its neighbours — a potential spatial outlier.
How many permutations should I use for inference?
At least 999 permutations are recommended for stable p-values at the 0.05 level; 9999 permutations are preferred when testing at 0.001. More permutations reduce Monte Carlo error in the reference distribution.
Should I correct for multiple testing when mapping Local Geary's C?
Yes. When testing n locations simultaneously, the expected number of false positives under H0 grows with n. Apply a false discovery rate (FDR) correction or a Bonferroni correction, or use GeoDa's built-in significance filter which accounts for the effective number of tests.
Can Local Geary's C handle binary or categorical variables?
No. Local Geary's C is designed for continuous variables. For binary outcomes use join-count statistics; for categorical variables consider other local spatial association measures appropriate to the data type.
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 ↗
- Anselin, L. (2019). A local indicator of multivariate spatial association: extending Geary's C. Geographical Analysis, 51(2), 133–150. DOI: 10.1111/gean.12164 ↗
How to cite this page
ScholarGate. (2026, June 3). Local Geary's C Contiguity Ratio. ScholarGate. https://scholargate.app/en/spatial-analysis/local-gearys-c
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.
- 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
- Moran's ISpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare