Local Geographically Weighted Regression (GWR)
Local Geographically Weighted Regression · Also known as: GWR, geographically weighted regression, local spatial regression, spatially varying coefficient model
Local Geographically Weighted Regression (GWR) estimates a separate regression model at each location in the study area, allowing every coefficient to vary spatially. By weighting nearby observations more heavily than distant ones, GWR reveals how predictor-outcome relationships shift across geographic space rather than forcing a single global estimate on heterogeneous data.
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When to use it
Use GWR when theory or exploratory analysis suggests that predictor effects differ across locations — for example, that the influence of employment on commuting times varies between urban and rural areas. It is appropriate when you have at least 50-100 georeferenced observations, a continuous outcome, and a research question centered on spatial heterogeneity. Do not use GWR when relationships are genuinely stationary across space (a global model is simpler and more efficient), when the sample is small (local subsets may have too few observations for stable estimation), when predictors are strongly collinear (local multicollinearity is worse than global), or when only a global average effect is needed.
Strengths & limitations
- Explicitly models spatial nonstationarity, revealing how relationships vary across a study area.
- Produces interpretable local coefficient maps that communicate geographic patterns to non-technical audiences.
- Handles heterogeneous datasets where a single global regression would mask important regional differences.
- Adaptive bandwidth option accommodates irregular data density without researcher judgment.
- AICc-based bandwidth selection is principled and comparable across competing model specifications.
- Local multicollinearity is often more severe than global multicollinearity and can destabilise coefficient estimates at data-sparse locations.
- Computationally expensive for large datasets because a separate weighted regression is solved at every location.
- Results are sensitive to bandwidth choice; a poorly chosen bandwidth can over-smooth (losing local detail) or under-smooth (producing noisy maps).
- Standard significance tests for local coefficients require correction for multiple comparisons across locations.
- Cannot be directly applied to binary or count outcomes without generalised GWR extensions.
Frequently asked
How does GWR differ from a global spatial regression model?
A global spatial lag or spatial error model adds spatial structure to a single set of coefficients to account for spatial dependence in the error or outcome. GWR instead estimates a different set of coefficients at every location to capture spatial heterogeneity in the relationships themselves. The two approaches address different spatial problems and can be combined in a spatially varying coefficient spatial lag model.
What bandwidth should I choose?
Let the data decide: minimise AICc (preferred) or cross-validation prediction error over a grid of candidate bandwidths. Use an adaptive bandwidth (fixed number of neighbours, e.g., 40-60) when observation density is uneven, and a fixed distance bandwidth when density is roughly uniform.
Are local coefficient t-values reliable for hypothesis testing?
Not without correction. Because GWR estimates hundreds or thousands of local models, applying a 5% significance threshold to each individual t-value will produce many false positives. Apply a Bonferroni correction, the false discovery rate procedure, or the Monte Carlo permutation test provided by standard GWR software.
How many observations do I need?
As a rough guide, at least 50-100 georeferenced points for the full dataset, and each local regression should have at least 20-30 effective observations (controlled by the bandwidth). With fewer data, local estimates become unstable and unreliable.
What software runs GWR?
The GWmodel package in R and the mgwr Python library are the most commonly used open-source implementations. ArcGIS Spatial Statistics and GeoDa also provide GWR toolboxes accessible to non-programmers.
Sources
- Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley. ISBN: 978-0471496168
- Brunsdon, C., Fotheringham, A. S., & Charlton, M. E. (1996). Geographically weighted regression: a method for exploring spatial nonstationarity. Geographical Analysis, 28(4), 281-298. DOI: 10.1111/j.1538-4632.1996.tb00936.x ↗
How to cite this page
ScholarGate. (2026, June 3). Local Geographically Weighted Regression. ScholarGate. https://scholargate.app/en/spatial-analysis/local-geographically-weighted-regression
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.
- Geographically Weighted RegressionSpatial analysis↔ compare
- Local Spatial AutocorrelationSpatial analysis↔ compare
- Multiscale Geographically Weighted RegressionSpatial analysis↔ compare
- Spatial Error ModelSpatial analysis↔ compare
- Spatial Lag ModelSpatial analysis↔ compare