Global Spatial Durbin Model (SDM)
Global Spatial Durbin Model · Also known as: SDM, Spatial Durbin Model, global SDM, spatially lagged X model with spatial lag
The Global Spatial Durbin Model extends the spatial lag model by including not only a spatially lagged dependent variable but also spatially lagged independent variables (WX). A single set of global coefficients applies uniformly across all locations, making it suitable for estimating average spillover effects when spatial dependence is pervasive throughout the study region.
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When to use it
Use the Global SDM when theory or exploratory analysis suggests that both neighboring outcomes and neighboring covariate values influence a unit's outcome — for example, income spillovers across regions, disease transmission where both case counts and population density of neighbors matter, or housing prices affected by neighboring amenities. It is the preferred default spatial model when the researcher is uncertain whether the true data-generating process is SAR or SEM, because SDM nests both. Do not use it when spatial relationships vary strongly by location (prefer GWR or MGWR), when the sample is too small for ML estimation to be stable, or when the theoretical mechanism involves only error-based spatial dependence (use SEM instead).
Strengths & limitations
- Nests the Spatial Autoregressive (SAR) and Spatial Error Model (SEM) as special cases, offering flexibility when the true model is uncertain.
- Captures both endogenous (outcome-to-outcome) and exogenous (covariate-to-outcome) spatial spillovers in a single framework.
- Produces interpretable direct, indirect, and total impact measures that correctly account for spatial feedback loops.
- Global parameterisation provides efficiency gains over local models when spillover effects are truly homogeneous across space.
- Well-supported by established ML and GMM estimators implemented in GeoDa, R (spatialreg), and Stata (spregress).
- The global assumption — uniform spillover effects across all locations — is often violated in heterogeneous study regions.
- Requires a correctly specified spatial weights matrix; results can be sensitive to W choice (contiguity vs. distance-based).
- Interpretation of coefficients is non-trivial: raw β and θ estimates must be transformed into impact measures before reporting.
- ML estimation can be computationally demanding for very large datasets (n > 10,000 without sparse matrix optimisations).
- Adding WX increases the number of parameters, reducing degrees of freedom and risking multicollinearity when X variables are highly correlated.
Frequently asked
How does the Global SDM differ from the Spatial Lag Model (SAR)?
The SAR model includes only a spatially lagged dependent variable (ρWy). The SDM adds spatially lagged independent variables (WXθ), allowing neighbor covariate values to directly influence the outcome. SDM nests SAR as the special case θ = 0.
Why must I compute impact measures instead of reading the coefficients directly?
Because of the spatial lag ρWy, a shock to one unit ripples through the network, affecting all other units and feeding back. The raw coefficients capture only direct local effects and miss these feedback loops. LeSage & Pace (2009) impact decomposition correctly aggregates all direct and spillover effects.
How do I choose between SDM and SEM?
If the constraint θ + ρβ = 0 is not rejected by a likelihood ratio test, the SEM is a valid restriction of SDM. If θ = 0 is not rejected, SAR suffices. When both restrictions are rejected, retain SDM. Robust LM tests from the diagnostics for spatial dependence can guide the initial direction.
Does the 'global' label mean the model covers the entire world?
No. 'Global' means the estimated coefficients apply uniformly to every spatial unit — a single global parameter set rather than location-specific parameters. It contrasts with 'local' spatial models like GWR, which allow coefficients to vary by location.
Can I apply the Global SDM to panel data?
Yes. The spatial panel extension of SDM adds fixed or random effects for units and time periods, allowing control for unobserved heterogeneity. Elhorst (2014) provides full treatment of the spatial panel Durbin model with ML and GMM estimators.
Sources
- LeSage, J. P., & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press / Taylor & Francis. ISBN: 978-1420064247
- Elhorst, J. P. (2014). Spatial Econometrics: From Cross-Sectional Data to Spatial Panels. Springer. ISBN: 978-3642403392
How to cite this page
ScholarGate. (2026, June 3). Global Spatial Durbin Model. ScholarGate. https://scholargate.app/en/spatial-analysis/global-spatial-durbin-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
- Global Spatial Error ModelSpatial analysis↔ compare
- Multiscale Geographically Weighted RegressionSpatial analysis↔ compare
- Spatial Error ModelSpatial analysis↔ compare
- Spatial Lag ModelSpatial analysis↔ compare