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Geographic Weighted Regression

Definition

Geographic Weighted Regression, often called Geographically Weighted Regression, is a local modeling technique that estimates how relationships between a dependent variable and predictors vary across space. Instead of one global coefficient per predictor, GWR fits a separate regression at each location using nearby observations weighted by a kernel and a bandwidth. The result is a surface of coefficients, residuals, and diagnostics that reveal spatial nonstationarity. Analysts can see where income strongly predicts sales, where air pollution is more sensitive to traffic, or where housing prices respond to school quality. The method complements global models by exposing local context.

Application

Practitioners use GWR for real estate valuation, health outcomes, environmental exposure, retail demand, and transportation safety. It helps planners understand local drivers and design place specific policies. GWR outputs coefficient rasters and local R squared maps that communicate where models fit well and where other variables may be missing. When combined with cross validation and careful diagnostics, GWR becomes a powerful exploratory and explanatory tool.

FAQ

What is Geographic Weighted Regression in GIS and when should you choose it over ordinary least squares?

GWR is a spatially varying regression that calibrates a local model at each location using distance weighted neighbors. Choose it when you suspect that relationships change over space, for example when market behavior differs by neighborhood or environmental response varies with terrain. Use ordinary least squares when a single global relationship is appropriate and when simplicity is a priority.

How do you run GWR correctly, choose bandwidth, and interpret coefficient maps?

Prepare predictors with similar scales and check multicollinearity. Select a kernel type and calibrate the bandwidth using cross validation or AICc. Fit the model, then map local coefficients, standard errors, and residuals. Look for meaningful spatial structure and compare to domain knowledge. Areas with poor fit may require new variables or a different scale of analysis.

What pitfalls can lead to misleading GWR results and how can analysts avoid them?

Common pitfalls include overfitting with too small a bandwidth, multicollinearity that inflates local variance, ignoring multiple testing when interpreting many local coefficients, and confusing correlation with causation. Avoid problems by standardizing variables, testing several bandwidths, applying corrections for multiple comparisons, and validating against held out data or an independent period.

What are practical examples where GWR produced actionable insights for policy or business?

A city used GWR to find that traffic speed explained crash severity in outer suburbs while intersection density mattered downtown, which informed targeted interventions. A retailer learned that proximity to transit predicted sales in urban markets but parking supply dominated in exurban markets. A health agency discovered that asthma hospitalizations correlated with older housing only in a subset of neighborhoods, which guided home retrofit programs.