Local Spatial Durbin Model
Also known as: local SDM, geographically weighted Spatial Durbin Model, GW-SDM, spatially varying Durbin model
The Local Spatial Durbin Model (Local SDM) extends the global Spatial Durbin Model by allowing regression coefficients to vary across geographic space. It combines the SDM's ability to capture both spatial lag of the dependent variable and spatial lags of covariates with a geographically weighted estimation framework, producing location-specific direct and indirect spillover effects.
Key highlights
- Captures spatially varying direct effects, indirect spillovers, and cross-variable spillovers simultaneously.
- Reveals spatial non-stationarity in both the outcome-lag parameter and the covariate-lag parameters.
- More complete than local spatial lag or error models because it includes both Wy and WX terms.
- Produces interpretable maps of how spillover strength shifts across the study region.
- Subsumes both the local spatial lag model and local OLS/GWR as special cases, providing a flexible diagnostic.
Intuition
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How it works
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When to use it
Use the Local Spatial Durbin Model when theory suggests that both the outcome and the covariates exhibit spatial spillovers, and when those spillovers are unlikely to be spatially stationary. It is well-suited to regional economics, urban policy evaluation, and environmental studies where cross-border or neighborhood spillover mechanisms differ across the study area. Require georeferenced areal or point data with a sufficient number of observations (generally n > 100) to support local estimation. Do not use when the study area is small or homogeneous (a global SDM suffices), when spatial spillover effects are absent (OLS or GWR is simpler), when panel depth is the primary concern without cross-sectional spatial variation, or when computational resources are limited for large grids.
Strengths & limitations
- Captures spatially varying direct effects, indirect spillovers, and cross-variable spillovers simultaneously.
- Reveals spatial non-stationarity in both the outcome-lag parameter and the covariate-lag parameters.
- More complete than local spatial lag or error models because it includes both Wy and WX terms.
- Produces interpretable maps of how spillover strength shifts across the study region.
- Subsumes both the local spatial lag model and local OLS/GWR as special cases, providing a flexible diagnostic.
- Computationally intensive: a full local SDM requires iterative estimation at every location, multiplying the cost of a global SDM.
- Bandwidth selection is non-trivial and can strongly influence results; misspecification leads to over- or under-smoothing of coefficient surfaces.
- Local estimation with small effective sample sizes at each location inflates standard errors and reduces reliability of local inference.
- Identifying rho(i) locally is more prone to identification problems than in a global model, especially with sparse or irregular spatial weights matrices.
- No single widely adopted software package implements the full local SDM; analysts often approximate with GWR-based wrappers or Monte Carlo approaches.
Common pitfalls
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Applications
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Frequently asked
How does the Local SDM differ from Geographically Weighted Regression?
GWR localizes a standard OLS model and ignores spatial dependence between observations. The Local SDM localizes a Spatial Durbin Model, so it explicitly models spatial lag dependence (Wy) and cross-variable spillovers (WX) in addition to allowing coefficients to vary geographically. GWR residuals often retain spatial autocorrelation that the Local SDM absorbs into the model structure.
When should I prefer the global SDM over the local version?
If a Moran's I test on GWR or local SDM residuals shows no remaining spatial autocorrelation, and if coefficient maps appear smooth and statistically uniform, the global SDM is more parsimonious and gives more precise estimates. The local version is warranted only when there is evidence of spatial non-stationarity in the spillover parameters.
How do I choose the spatial weights matrix W for the Local SDM?
Standard practice is to test queen or rook contiguity for areal data and distance-band or k-nearest-neighbor weights for point data. Sensitivity analysis across two or three candidate W matrices is advisable; if conclusions change substantially, report results for each matrix.
Can the Local SDM be applied to panel data?
Yes, but it requires additional care: the local estimation must account for temporal as well as geographic weighting, or a two-step approach can be used (spatial panel for global parameters, then residual analysis for local variation). Dedicated spatial panel local models are an active research area.
How do I interpret negative indirect effects in the Local SDM?
A negative indirect effect at location i means that an increase in a covariate in neighboring locations j actually reduces the outcome at i. This can indicate competitive displacement — for example, a new business in a neighboring area drawing customers away — and whether this holds uniformly or only in specific zones is precisely what the local model reveals.
Sources
- 1.LeSage, J. P., & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press / Taylor & Francis.ISBN 978-1420064247
- 2.Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley.ISBN 978-0471496168
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Cite this page
ScholarGate. (2026, June 3). Local Spatial Durbin Model. ScholarGate. https://scholargate.app/spatial-analysis/local-spatial-durbin-model