Space-Time Geary's C
Space-Time Geary's Contiguity Ratio · Also known as: ST-Geary's C, spatiotemporal Geary C, space-time contiguity ratio, space-time local spatial autocorrelation
Space-Time Geary's C extends the classical Geary contiguity ratio to panel or longitudinal spatial data, measuring autocorrelation across both geographic neighbors and adjacent time periods simultaneously. Values below 1 indicate positive space-time clustering; values above 1 indicate dispersion, and a value near 1 suggests random arrangement across the space-time lattice.
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When to use it
Use Space-Time Geary's C when you have repeated measurements of a variable across geographic units over multiple time periods and want to test whether similar values cluster in both space and time simultaneously. It is well-suited for epidemiological surveillance (disease spread), environmental monitoring, socioeconomic panel data, and criminology. Do not use it if you have only a single cross-section (use standard Geary's C instead), if your panel is severely unbalanced with many missing periods, or if you need a local decomposition — in that case prefer local space-time LISA or local Geary's C approaches.
Strengths & limitations
- Captures both spatial and temporal dimensions of autocorrelation in a single statistic, avoiding the need for separate cross-sectional tests per period.
- More sensitive to local clustering than Moran's I because it uses squared local differences rather than deviations from the global mean.
- Permutation-based inference does not require distributional assumptions about the attribute values.
- Can accommodate flexible space-time weight structures, including purely spatial, purely temporal, or combined neighborhood definitions.
- Directly interpretable scale: values below 1 are positive autocorrelation, above 1 are dispersion.
- A single global statistic; it cannot identify where in the space-time domain clustering occurs — use local decompositions for that.
- Choice of the space-time weight matrix (spatial bandwidth, temporal lag window, standardization scheme) strongly influences results and lacks a universal default.
- Assumes stationarity of the autocorrelation process over space and time, which may not hold for long panels or heterogeneous regions.
- Computationally intensive for large panels because permutation tests require many recalculations of the full statistic.
- Less commonly implemented in standard software than Moran's I, which may require custom scripting in R (spdep) or Python (esda).
Frequently asked
How does Space-Time Geary's C differ from standard Geary's C?
Standard Geary's C operates on a single cross-section, linking observations only through geographic contiguity. Space-Time Geary's C uses a weight matrix that also connects each observation to the same unit in adjacent time periods, so it measures clustering across both dimensions simultaneously.
How does Space-Time Geary's C differ from Space-Time Moran's I?
Both measure global space-time autocorrelation, but Moran's I uses covariances (products of mean-deviation values), whereas Geary's C uses squared differences between neighboring pairs. Geary's C is more sensitive to local heterogeneity; Moran's I reflects global covariance structure. They are not simply monotone transforms of each other.
How do I choose the temporal lag for the space-time weight matrix?
Start with one period (t-1 and t+1) as the temporal neighborhood, which captures short-run diffusion. Inspect temporal autocorrelation functions (ACF) of the spatially filtered residuals to see whether extending to two or three lags is empirically justified. Sensitivity analyses across different lag windows are recommended.
What software can compute Space-Time Geary's C?
The R package spdep and the Python library esda (part of PySAL) support space-time autocorrelation statistics including space-time extensions of Geary's C. GeoDa provides a graphical interface for some space-time LISA methods. Custom implementation is sometimes needed for fully flexible space-time weight matrices.
Can I use Space-Time Geary's C with irregularly spaced time points?
Yes, but with caution. If the temporal gaps between observations vary, the temporal weights should reflect proximity in real time rather than just adjacency in the observation sequence. Inverse-distance temporal weights (based on actual time elapsed) are more appropriate than simple contiguity for irregular panels.
Sources
- Geary, R. C. (1954). The Contiguity Ratio and Statistical Mapping. The Incorporated Statistician, 5(3), 115-145. DOI: 10.2307/2986645 ↗
- 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). Space-Time Geary's Contiguity Ratio. ScholarGate. https://scholargate.app/en/spatial-analysis/space-time-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 Geary's CSpatial analysis↔ compare
- Moran's ISpatial analysis↔ compare
- Space-Time Local Indicators of Spatial AssociationSpatial analysis↔ compare
- Space-Time Moran's ISpatial analysis↔ compare
- Space-Time Spatial AutocorrelationSpatial analysis↔ compare