Multiscale Geographically Weighted Regression (MGWR)
Multiscale Geographically Weighted Regression · Also known as: multiscale GWR, multi-scale geographically weighted regression, Çok Ölçekli Coğrafi Ağırlıklı Regresyon (MGWR)
Multiscale Geographically Weighted Regression, introduced by Fotheringham, Yang and Kang in 2017, is a spatial regression model that lets each coefficient vary across space at its own spatial scale. It generalises Geographically Weighted Regression by giving every predictor its own bandwidth, so some relationships can act locally while others act almost globally.
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When to use it
MGWR fits cross-sectional data that carry geographic coordinates, a continuous outcome, and at least roughly 80 observations, when you suspect that different predictors operate at different spatial scales. It is the right choice when GWR's single bandwidth seems too restrictive — some effects clearly local, others broadly stable. Each coefficient may settle at its own scale, and a globally constant coefficient is a valid outcome. It demands geographic coordinates and is more computationally expensive than GWR, so very large samples (n > 500) can run slowly, and local multicollinearity may intensify.
Strengths & limitations
- Allows each coefficient to vary at its own spatial scale, often yielding more accurate estimates than GWR when some effects are local and others global.
- Reveals the scale at which each predictor operates, turning bandwidth itself into an interpretable result.
- Reduces to a near-global (constant) coefficient automatically when a relationship does not vary across space.
- Requires geographic coordinates for every observation; without them the model cannot be fitted.
- Computationally heavier than GWR because of back-fitting and per-coefficient bandwidth search; it can be slow for n > 500.
- Local multicollinearity can be more severe than in a global model, destabilising local coefficient estimates.
Frequently asked
How is MGWR different from GWR?
GWR uses a single bandwidth, forcing every coefficient to vary at the same spatial scale. MGWR estimates a separate bandwidth for each predictor, so each relationship can act at its own scale — some local, some nearly global.
Do I need geographic coordinates?
Yes. MGWR weights observations by spatial proximity, so each record must carry coordinates. Without them, use standard GWR or OLS instead.
Why is MGWR slow on large datasets?
It uses a back-fitting algorithm that repeatedly re-estimates each coefficient surface and searches for a separate optimal bandwidth per predictor. The cost grows quickly, so samples above about 500 observations can take a long time.
What does a large bandwidth for a predictor mean?
A very large (near-global) bandwidth means that predictor's effect is essentially constant across the study area, while a small bandwidth means the effect is strongly local and varies from place to place.
Sources
- Fotheringham, A. S., Yang, W. & Kang, W. (2017). Multiscale Geographically Weighted Regression (MGWR). Annals of the American Association of Geographers, 107(6), 1247–1265. DOI: 10.1080/24694452.2017.1352480 ↗
- Oshan, T. M., Li, Z., Kang, W., Wolf, L. J. & Fotheringham, A. S. (2019). mgwr: A Python Implementation of Multiscale Geographically Weighted Regression. Journal of Open Source Software, 4(42), 1670. link ↗
How to cite this page
ScholarGate. (2026, June 1). Multiscale Geographically Weighted Regression. ScholarGate. https://scholargate.app/en/spatial-analysis/mgwr-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.
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