Spatial Durbin Model (SDM)
Also known as: SDM, spatial mixed model, uzamsal durbin modeli
The Spatial Durbin Model is a general spatial regression model that includes a spatial lag of both the dependent variable (ρWy) and the explanatory variables (WXθ). Introduced as the recommended starting point by LeSage and Pace (2009), it nests the spatial autoregressive (SAR) and spatial error (SEM) models as special cases.
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When to use it
Use the Spatial Durbin Model with cross-sectional data that carry geographic coordinates, when the outcome is continuous and you suspect spatial dependence in both the outcome and the predictors. It suits prediction, relationship, and explanatory aims and needs a reasonable sample (at least about 80 units). It is appropriate when the spatial weight matrix W can be treated as exogenous, when spatial dependence in both the dependent and independent variables should be tested, when direct and indirect effects must be separated as LeSage and Pace recommend, and when maximum-likelihood estimation (or Bayesian MCMC for small samples) is feasible. Without geographic coordinates the model cannot be applied and standard OLS regression is preferred.
Strengths & limitations
- Nests SAR and SEM as special cases, so it serves as a safe general starting model that can be reduced via a likelihood-ratio test.
- Captures spillovers from both neighbouring outcomes (ρWy) and neighbouring characteristics (WXθ).
- Separates effects into interpretable direct and indirect (spillover) impacts following LeSage and Pace (2009).
- Cannot be applied without geographic coordinates; falls back to ordinary OLS regression.
- Requires a reasonable sample size (at least about 80 units) and a correctly specified, exogenous spatial weight matrix W.
- Maximum-likelihood estimation can be demanding, and small samples may need a Bayesian MCMC alternative.
Frequently asked
How does SDM differ from the SAR and SEM models?
SDM includes a spatial lag of the outcome (ρWy) and a spatial lag of the predictors (WXθ). The SAR model is the special case with θ = 0, and the SEM model corresponds to the constraint θ = -ρβ. Because both are nested inside SDM, LeSage and Pace (2009) suggest starting from SDM and testing down with a likelihood-ratio test.
Why can't I just read the coefficients directly?
Because the outcome depends on neighbouring outcomes through ρWy, a change in one unit's predictor feeds back through the spatial system. Effects are therefore summarised as direct impacts (on the unit itself) and indirect impacts (spillovers to others), as recommended by LeSage and Pace (2009).
How is the model estimated?
Maximum likelihood is the common estimator, maximising the log-likelihood of the outcomes given the predictors and the spatial weight matrix W. For small samples a Bayesian MCMC approach is a frequently used alternative.
What if my data have no geographic coordinates?
The Spatial Durbin Model cannot be applied without coordinates, since it relies on a spatial weight matrix. In that case standard OLS regression is the recommended choice.
Sources
- LeSage, J. & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press. DOI: 10.1201/9781420064254 ↗
- Elhorst, J. P. (2010). Applied Spatial Econometrics: Raising the Bar. Spatial Economic Analysis, 5(1), 9–28. DOI: 10.1080/17421770903541772 ↗
How to cite this page
ScholarGate. (2026, June 1). Spatial Durbin Model (SDM). ScholarGate. https://scholargate.app/en/spatial-analysis/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.
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