Local Spatial Lag Model
Also known as: local SLM, geographically weighted spatial lag model, GW-SLM, spatially varying lag model
The Local Spatial Lag Model extends the classical spatial lag model by allowing both the spatial autocorrelation parameter and the regression coefficients to vary across geographic locations. Instead of one global estimate of how neighboring outcomes influence each observation, the model fits location-specific parameters using kernel-weighted local estimation, revealing spatial heterogeneity in spatial dependence.
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When to use it
Use the Local Spatial Lag Model when you expect that the strength of spatial spillovers varies across your study region and you want to map that heterogeneity. It is appropriate when the global spatial lag model fits poorly or when residuals from a standard SLM show spatial clustering of coefficient magnitude. Suitable data include georeferenced cross-sectional observations with a continuous outcome and meaningful spatial dependence. Avoid it when the sample is small (fewer than ~100 observations per bandwidth neighborhood), when the spatial process is genuinely stationary across the region, or when a simpler global model already fits well — the additional complexity yields unstable local estimates in those cases.
Strengths & limitations
- Captures spatially varying spatial dependence, revealing where neighborhood spillovers are strong versus weak.
- Combines the inferential power of spatial lag modeling with the flexibility of geographically weighted regression.
- Produces interpretable local coefficient maps that communicate heterogeneity to non-technical audiences.
- More realistic than a global SLM when the study region spans diverse urban-rural or environmental gradients.
- Local estimates can guide targeted policy or intervention at specific geographic subregions.
- Computationally intensive: requires fitting a separate (or iterative) model at every location, especially for large datasets.
- Bandwidth selection is non-trivial and strongly influences results; different criteria (CV, AIC) can yield different bandwidths.
- Local estimates have inflated variance compared to the global SLM, and standard inferential theory is approximate.
- Simultaneous estimation of a local rho and local betas is technically demanding and may not converge for thin data.
- Results can be difficult to publish in journals that expect a single parsimonious spatial model.
Frequently asked
How is the Local Spatial Lag Model different from Geographically Weighted Regression?
Standard GWR allows regression coefficients to vary locally but ignores spatial lag dependence. The Local Spatial Lag Model additionally lets the spatial autocorrelation parameter rho vary by location, accounting for the fact that the outcome is itself spatially lagged. This makes it more appropriate when spatial spillovers are present alongside spatially varying covariate effects.
Is the local rho always statistically meaningful?
Not necessarily. In some regions of the study area rho may be near zero and statistically insignificant, while in others it is large and significant. Mapping local rho with its pseudo-p-values reveals this heterogeneity; areas with non-significant local rho may be adequately described by a simpler local OLS or GWR model.
What software can estimate a Local Spatial Lag Model?
R packages such as spatialreg and GWmodel provide building blocks; some researchers combine the two manually. Python's PySAL ecosystem also supports spatially varying regression extensions. Dedicated plug-and-play implementations are less standardized than for global SLM or GWR alone.
How do I choose the bandwidth?
Bandwidth is typically selected by minimizing AIC or leave-one-out cross-validation error over a grid of candidate values. A smaller bandwidth gives more local, more volatile estimates; a larger one smooths toward the global model. The optimal bandwidth balances flexibility and variance.
Can the Local Spatial Lag Model handle panel data?
Extensions to panel settings exist but are considerably more complex, requiring assumptions about whether the spatial and temporal heterogeneity are separable. For panel data with spatial dependence, a spatial panel model or space-time GWR is often a more tractable starting point.
Sources
- Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers. ISBN: 978-9024737215
- 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). Local Spatial Lag Model. ScholarGate. https://scholargate.app/en/spatial-analysis/local-spatial-lag-model
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 Durbin ModelSpatial analysis↔ compare
- Multiscale Geographically Weighted RegressionSpatial analysis↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare
- Spatial Lag ModelSpatial analysis↔ compare