Geographically Weighted Regression (GWR)

Geographically weighted regression (GWR) is a local regression method that estimates a separate set of coefficients at each location, weighting nearby observations more heavily, to show how relationships vary across space.

지리가중회귀(GWR)는 가까운 관측치에 더 큰 가중치를 두어 위치마다 별도의 계수를 추정함으로써 변수 간 관계가 공간에 따라 어떻게 달라지는지 보여주는 국지 회귀 방법이다.

How do I check whether the relationship between variables differs from place to place?

변수 간의 관계가 장소마다 다른지 어떻게 확인하나요?

Geographically weighted regression fits a weighted regression at each location using a kernel and bandwidth, so coefficients can vary across the study area. It fits spatial data where a single global regression may hide regional differences, and multiscale GWR allows each predictor its own bandwidth.

When to use Geographically Weighted Regression (GWR)

• Spatial units with coordinates and an outcome explained by several predictors
• Testing whether coefficients vary across regions
• Mapping local coefficient estimates and local R²

When to use something else

• Relationships are stable but residuals are spatially dependent: use a spatial lag or spatial error model
• Predictors operate at different spatial scales: use multiscale GWR (MGWR)

Assumptions and requirements

• Coordinates or a spatial distance measure for each observation
• An appropriate kernel and bandwidth (chosen by AICc or cross-validation)
• No strong local multicollinearity
• Enough observations for stable local estimates

What the analysis reports

• Local coefficients and t-values for each location
• Optimal bandwidth
• Local R²
• AICc compared with a global OLS model
• Coefficient maps

How to report it

The GWR model (adaptive bandwidth = [value] neighbors) improved fit over global OLS (AICc = [value] vs. [value]), and the coefficient for [predictor] ranged from [min] to [max].

Related methods

• Multiscale GWR (MGWR)
• Spatial Lag Model
• Local Indicators of Spatial Association (LISA)

Run Geographically Weighted Regression (GWR) on Quorant