Multiscale Getis-Ord Gi* Hot Spot Analysis
Also known as: multi-distance Gi*, multiscale hot spot analysis, multi-bandwidth Getis-Ord, scale-varying Gi*
Multiscale Getis-Ord Gi* extends the classic local hot spot statistic by computing Gi* z-scores across a range of spatial distance bands or neighborhood sizes. This reveals whether clusters of high or low values are scale-dependent — appearing only at fine local scales, only at broad regional scales, or persistently across all scales — providing richer spatial intelligence than a single-bandwidth analysis.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use Multiscale Gi* when the scale at which clustering occurs is uncertain or theoretically important — for example, in epidemiology (disease cluster radius), criminology (patrol zone sizing), ecology (habitat patch size), or regional economics (market area delineation). It is particularly valuable when a single bandwidth has been difficult to justify, or when prior studies have used different bandwidths and results are contradictory. Prefer it over single-scale Gi* whenever policy decisions depend on the spatial extent of hotspots. Do not use it when sample size is very small (fewer than 30 areal units), when the attribute is binary without continuous variation, or when a confirmatory test at a theoretically prescribed scale is required — in those cases standard single-bandwidth Gi* is more appropriate and easier to interpret.
Strengths & limitations
- Reveals whether spatial clusters are scale-dependent or robust, information unavailable from any single-bandwidth analysis.
- Guards against the arbitrary-bandwidth problem by making the analyst's scale choice empirically informed.
- Produces the same familiar Gi* z-scores and p-values at each scale, so results are interpretable without new statistical training.
- Directly identifies the operationally relevant scale for interventions such as patrol zones, buffer areas, or resource allocation regions.
- Compatible with both fixed-distance and adaptive-bandwidth weight matrices, giving flexibility for irregular point patterns.
- Computational cost grows linearly with the number of distance bands tested, which can be substantial for large datasets and fine-grained scale sweeps.
- Multiple-comparison correction is mandatory but can be conservative, potentially masking genuine clusters when many scales and locations are tested simultaneously.
- Interpretation of the scale-profile matrix requires spatial analysis expertise; naive users may over-interpret scale-specific significance as evidence of distinct processes.
- Results depend on the set of distance bands chosen; an ill-chosen scale range can miss the relevant clustering scale entirely.
- Edge effects at study-area boundaries affect Gi* at all scales and may be more pronounced at larger distance bands where many border locations lack complete neighborhoods.
Frequently asked
How do I choose the distance bands for the scale sweep?
Ground choices in domain knowledge or process theory — for example, average travel time, administrative boundaries, or ecologically meaningful patch sizes. A practical starting point is to test a geometric sequence from the minimum inter-location distance to roughly one-third of the study area's diameter, covering at least five to eight bands. Sensitivity analysis comparing outputs at adjacent bands helps confirm that results are not artefacts of a specific cut-point.
What is the difference between Multiscale Gi* and standard Gi*?
Standard Gi* is computed at a single, fixed bandwidth and produces one z-score per location. Multiscale Gi* repeats the computation for a sequence of bandwidths, producing a z-score profile per location. This reveals whether a location's cluster status is robust to bandwidth choice or specific to a narrow scale range.
How should I correct for multiple comparisons in a multiscale analysis?
Because each location is tested across multiple distance bands, the family-wise error rate inflates. The false discovery rate (FDR) correction (Benjamini-Hochberg) is generally preferred over Bonferroni because it is less conservative while still controlling the expected proportion of false discoveries. Apply correction jointly across all location-by-scale combinations.
Can I use adaptive rather than fixed-distance bandwidths?
Yes. Adaptive bandwidths (k-nearest neighbors) expand in sparse areas and contract in dense areas to maintain a fixed number of neighbors rather than a fixed distance. A multiscale sweep over a range of k values is the adaptive-bandwidth analogue and is especially useful for irregular or clustered point patterns.
What does it mean if a hotspot disappears at larger scales?
It suggests the clustering is a fine-scale, localised phenomenon — perhaps a single dense cluster of events on one block that averages out when a larger neighborhood is considered. This is often ecologically meaningful: the process driving the cluster operates at the local scale and is diluted by unrelated variation at broader scales.
Sources
- Ord, J. K., & Getis, A. (1995). Local spatial autocorrelation statistics: Distributional issues and an application. Geographical Analysis, 27(4), 286-306. DOI: 10.1111/j.1538-4632.1995.tb00912.x ↗
- Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley. ISBN: 978-0471496168
How to cite this page
ScholarGate. (2026, June 3). Multiscale Getis-Ord Gi* Hot Spot Analysis. ScholarGate. https://scholargate.app/en/spatial-analysis/multiscale-getis-ord-gi
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 Getis-Ord Gi*Spatial analysis↔ compare
- Local Moran's ISpatial analysis↔ compare
- Multiscale Geographically Weighted RegressionSpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare