Local Spatial Regression
Also known as: locally weighted spatial regression, spatially varying coefficient model, local spatial model, place-based regression
Local Spatial Regression fits a separate regression model at each location in a study area, allowing regression coefficients to vary continuously across space. Rather than forcing one global slope on all observations, it reveals where and how the relationship between predictors and an outcome changes geographically — producing a map of coefficients rather than a single number.
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When to use it
Use Local Spatial Regression when you suspect that the relationship between predictors and the outcome differs by location — a condition called spatial non-stationarity. It is appropriate for georeferenced cross-sectional data where a global model's residuals show spatial autocorrelation or where theory predicts place-specific mechanisms (e.g., housing markets, health outcomes, ecological gradients). Do not use it when the sample size is small (fewer than ~100 observations), when you have no meaningful coordinate information, or when you only need a single average effect. It is also inappropriate if the scientific question is whether spatial heterogeneity exists (use a global model plus diagnostics first) rather than how it manifests.
Strengths & limitations
- Reveals spatial non-stationarity: shows how and where predictor effects vary across the study area.
- Produces interpretable coefficient maps that communicate spatial patterns to non-technical audiences.
- Naturally accounts for spatial context without requiring a pre-specified spatial weights matrix.
- Flexible kernel choice (Gaussian, bisquare, fixed or adaptive bandwidth) adapts to data density.
- Can be extended to generalised linear model families (logistic, Poisson) for non-continuous outcomes.
- Computationally intensive: a separate regression is fitted at every location, scaling poorly with very large datasets.
- Local estimates can be unstable and highly collinear when predictors covary similarly across space, inflating local standard errors.
- Bandwidth selection via cross-validation or AIC can be sensitive to outliers and may over-smooth or under-smooth the coefficient surface.
- Local coefficient surfaces are difficult to summarise in a single table; visualisation and interpretation require GIS expertise.
- Does not directly model spatial dependence in the error term; residual autocorrelation may remain.
Frequently asked
How does Local Spatial Regression differ from ordinary spatial regression models?
Global spatial models (spatial lag, spatial error, Durbin) fit a single coefficient for each predictor across the entire study area but account for spatial dependence through a weights matrix. Local Spatial Regression instead allows each coefficient to vary continuously by location, prioritising the detection of spatial non-stationarity. The two approaches address different spatial problems and can be combined.
How do I choose the bandwidth?
The most common automatic approach minimises a leave-one-out cross-validation score or an AIC over a range of candidate bandwidths. Adaptive bandwidths (defined by a number of nearest neighbours rather than a fixed distance) are preferred when observation density is uneven across the study area.
Are the local coefficients statistically significant?
Local pseudo-t statistics can be computed, but because a coefficient surface consists of many correlated estimates, individual p-values overstate significance. Monte Carlo permutation tests and corrections for multiple testing (e.g., the Benjamini-Hochberg procedure) are recommended before concluding that a local effect is significant.
Can I use Local Spatial Regression with a binary or count outcome?
Yes. Geographically Weighted Generalised Linear Models extend the framework to logistic regression (binary outcomes) and Poisson regression (count outcomes) by applying a locally weighted maximum likelihood estimator instead of weighted least squares.
What software supports Local Spatial Regression?
The mgwr Python package (multiscale GWR), the GWR4 standalone application, and the spdep/GWmodel packages in R are the principal tools. StatWise provides a guided workflow for standard GWR with automatic bandwidth selection and coefficient map export.
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. (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 Spatial Regression. ScholarGate. https://scholargate.app/en/spatial-analysis/local-spatial-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 Lag ModelSpatial analysis↔ compare
- Multiscale Geographically Weighted RegressionSpatial analysis↔ compare
- Spatial Durbin ModelSpatial analysis↔ compare
- Spatial Error ModelSpatial analysis↔ compare
- Spatial Lag ModelSpatial analysis↔ compare