Global Spatial Error Model (SEM)
Global Spatial Error Model · Also known as: SEM, spatial error model, spatial error regression, global SEM
The Global Spatial Error Model (SEM) is a spatial regression technique that accounts for spatially autocorrelated error terms using a single, globally constant spatial parameter. It separates genuine predictor effects from spatial nuisance dependence in the residuals, yielding unbiased and efficient coefficient estimates when spatial error correlation is present across all observations.
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When to use it
Use the Global SEM when a Lagrange Multiplier test (LM-Error) on OLS residuals is significant and the LM-Lag test is not, signalling that spatial dependence is concentrated in the error rather than in the dependent variable itself. It is well-suited to cross-sectional geographic data where omitted spatially correlated variables — not substantive spillovers — drive the dependence. Do not use SEM when the theory implies that the outcome in one location genuinely causes the outcome in neighbours (use the Spatial Lag Model instead). Avoid it when spatial heterogeneity is the primary concern (use Geographically Weighted Regression instead), or when lambda varies across regions (consider local spatial regression variants).
Strengths & limitations
- Corrects standard errors and inference when spatially correlated omitted variables contaminate OLS residuals.
- Coefficient estimates remain unbiased and efficient under spatial error dependence that would otherwise inflate OLS standard errors.
- Uses a single global lambda parameter, making the model parsimonious and straightforward to interpret.
- Maximum likelihood estimation provides well-calibrated test statistics and AIC/BIC for model comparison.
- Widely implemented in open-source tools (PySAL, R spdep, GeoDa) with established diagnostic workflows.
- Assumes that the spatial error autocorrelation parameter lambda is constant across all regions; heterogeneous spatial processes require local models.
- Results are sensitive to the choice and specification of the spatial weights matrix W, which must be determined before estimation.
- Maximum likelihood estimation can be slow for very large datasets due to repeated computation of the log-determinant of (I - lambda*W).
- Cannot capture substantive spatial spillovers in the outcome variable; misspecification as SEM when SEM is wrong distorts inference.
- Does not address spatial heteroscedasticity or non-stationarity in regression coefficients.
Frequently asked
How is the Global SEM different from the Spatial Lag Model?
The Spatial Lag Model (SLM) places spatial dependence in the outcome variable itself — the outcome in one location is directly influenced by outcomes in neighbours. The SEM places spatial dependence only in the error term, capturing unmeasured spatially correlated influences without asserting that y causes y in neighbours. The Lagrange Multiplier diagnostics on OLS residuals guide which is more appropriate.
Why is the model called 'Global'?
The prefix 'global' signals that the spatial error parameter lambda is a single constant estimated over all observations. This contrasts with local spatial regression approaches (e.g., geographically weighted variants) where the parameter is allowed to vary across locations. If you believe the spatial error structure differs substantially by sub-region, a local model may be more appropriate.
Does SEM estimate the effect of neighbouring outcomes on my outcome?
No. SEM models spatially correlated errors, not spillovers in the dependent variable. If you want to estimate how the outcome in neighbouring units feeds back into the focal unit's outcome, use the Spatial Lag Model instead.
How do I choose the spatial weights matrix?
Contiguity matrices (queen or rook) are standard for polygon data like administrative areas. Distance-based matrices (k-nearest neighbours or inverse distance) suit point data. The choice should reflect the theoretical mechanism of spatial dependence. Row-standardise W so that lambda is interpretable as a proportion. Sensitivity analysis across different W specifications is good practice.
Can I use SEM with panel data?
The basic SEM is designed for cross-sectional data. For repeated-measures spatial data, use spatial panel models that jointly handle fixed or random individual effects and spatial error autocorrelation, available in R packages such as splm.
Sources
- Anselin, L. (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers. ISBN: 978-9024737322
- Anselin, L., & Bera, A. K. (1998). Spatial dependence in linear regression models with an introduction to spatial econometrics. In A. Ullah & D. E. A. Giles (Eds.), Handbook of Applied Economic Statistics (pp. 237-289). Marcel Dekker. link ↗
How to cite this page
ScholarGate. (2026, June 3). Global Spatial Error Model. ScholarGate. https://scholargate.app/en/spatial-analysis/global-spatial-error-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 Durbin ModelSpatial analysis↔ compare
- Moran's ISpatial analysis↔ compare
- OLS RegressionEconometrics↔ compare
- Spatial AutocorrelationSpatial analysis↔ compare