Spatial Error Model

The spatial error model is a spatial regression in which the error terms of neighboring locations are correlated through a spatial autoregressive process defined by a spatial weights matrix.

공간오차모형은 공간가중행렬로 정의되는 공간자기회귀 과정을 통해 인접 지역의 오차항이 서로 상관되도록 한 공간회귀모형이다.

How do I run a regression when residuals are spatially correlated?

회귀분석 잔차에 공간적 자기상관이 있을 때 어떻게 분석하나요?

The spatial error model adds a spatially autoregressive error term, so unmeasured factors shared by nearby areas are accounted for while estimating regression coefficients. It fits areal data such as counties or districts when residuals from an ordinary regression show spatial autocorrelation but there is no substantive spillover in the outcome itself.

When to use Spatial Error Model

• Areal units such as districts or counties with spatially clustered residuals
• Lagrange multiplier tests favor the error model over the lag model
• Unmeasured spatially structured variables are suspected

When to use something else

• The outcome in one area directly affects neighboring areas (spillover): use the spatial lag model or spatial Durbin model
• Relationships themselves vary across space: use geographically weighted regression

Assumptions and requirements

• A spatial weights matrix that reflects the neighborhood structure
• Correctly specified mean model
• Normally distributed errors for maximum likelihood estimation
• Spatial dependence confined to the error term

What the analysis reports

• Regression coefficients with standard errors
• Spatial error parameter (lambda) with test
• Log-likelihood and AIC compared with OLS
• Moran's I of residuals before and after modeling
• Lagrange multiplier diagnostics

How to report it

The spatial error model indicated significant spatial dependence in the errors, λ = [value], p = [value]; [predictor] remained associated with [outcome], b = [value], p = [value].

Related methods

• Spatial Lag Model
• Spatial Durbin Model
• Moran's I

Run Spatial Error Model on Quorant