Spatial Lag Model

The spatial lag model is a spatial regression that includes a spatially weighted average of neighboring areas' outcomes as a predictor, capturing spillovers in which one area's outcome depends on outcomes nearby.

공간시차모형은 이웃 지역 결과변수의 공간가중평균을 예측변수로 포함하여, 한 지역의 결과가 인근 지역의 결과에 의존하는 파급효과를 포착하는 공간회귀모형입니다.

How do I run a regression when outcomes in one area are influenced by outcomes in neighboring areas?

한 지역의 결과가 이웃 지역의 결과에 영향을 받을 때 회귀분석은 어떻게 하나요?

The spatial lag model adds a spatially lagged outcome to a regression, so the estimated coefficient rho measures how strongly an area's outcome depends on its neighbors' outcomes. It fits areal data with substantive spillovers, and because of feedback between neighbors, effects are interpreted through direct, indirect, and total impacts rather than raw coefficients.

When to use Spatial Lag Model

• Regional, county, or neighborhood data with outcomes that spill across borders
• OLS residuals showing significant spatial autocorrelation with LM tests favoring a lag
• Questions about diffusion or contagion of outcomes between areas

When to use something else

• Spatial dependence lies only in unmeasured factors: use the spatial error model
• Relationships vary across locations: use geographically weighted regression (GWR)

Assumptions and requirements

• Spatial weights matrix defined for neighboring units
• Estimation by maximum likelihood or instrumental variables, not OLS
• Approximately normal errors for maximum likelihood inference
• Spatial units and weights appropriate to the process studied

What the analysis reports

• Spatial autoregressive coefficient (rho) with p-value
• Regression coefficients
• Direct, indirect, and total impacts
• Log-likelihood and AIC compared with OLS
• Moran's I of residuals

How to report it

The spatial lag model showed significant spatial dependence, ρ = [value], p = [value], and the total impact of [predictor] on [outcome] was [value] (direct = [value], indirect = [value]).

Related methods

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

Run Spatial Lag Model on Quorant