Spatial Interaction (Gravity) Models
Also known as: gravity model, spatial interaction model, competing destinations model, mekânsal etkileşim modeli
Spatial interaction models predict the volume of flows — migrants, commuters, shoppers, trade, trips — between origins and destinations as a function of the size of each place and the distance or cost separating them. By analogy to Newton's gravity, interaction rises with the 'mass' of origin and destination and falls with separation, and Wilson's 1971 entropy-maximizing family put these models on a rigorous footing for transport, migration, and retail analysis.
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When to use it
Use spatial interaction models to estimate or forecast flows between zones — commuting and trip distribution in transport planning, migration between regions, retail catchment and store revenue, trade between countries, and patient/student flows. They are the standard tool when you have origin and destination sizes and a separation measure and want to predict or redistribute flows, including under scenarios (new road, new store). Calibrate the distance-decay and use the constrained form that matches what is known (origin totals, destination totals, or both). Estimating with Poisson regression respects the count nature of flows; ordinary log-linear regression mishandles zeros and heteroskedasticity. Be aware of spatial-structure bias (addressed by competing-destinations specifications) and that the gravity analogy is descriptive, not behavioural — discrete-choice (logit) models offer a utility-based alternative.
Strengths & limitations
- Simple, interpretable framework for predicting origin-destination flows.
- Constrained forms reproduce known marginal totals (transport-planning standard).
- Calibratable distance-decay captures how interaction falls with separation.
- Estimable by Poisson/log-linear regression with covariates.
- The gravity analogy is descriptive, not grounded in individual behaviour.
- Basic form suffers spatial-structure bias (needs competing-destinations terms).
- Sensitive to the chosen deterrence function and zoning (MAUP).
- Log-linear estimation mishandles zero flows; Poisson is preferable.
Frequently asked
Why is it called a gravity model?
By analogy to Newton's law of gravitation: interaction between two places is proportional to the product of their 'masses' (size/attractiveness) and inversely related to the distance between them. The analogy is descriptive — it summarizes flow patterns well but is not derived from individual decision-making.
What does 'doubly constrained' mean?
A doubly-constrained model forces the predicted flows to sum to the known total leaving each origin AND arriving at each destination, using balancing factors. It is used in transport planning when both production and attraction totals are known; singly-constrained variants fix only one side.
How should the model be estimated?
Because flows are counts (often with zeros), Poisson regression is the appropriate estimator and is equivalent to the entropy-maximizing model. Taking logs and using OLS forces dropping zeros and assumes constant variance, which biases results; Poisson handles both correctly.
Sources
- Wilson, A. G. (1971). A family of spatial interaction models, and associated developments. Environment and Planning A, 3(1), 1–32. DOI: 10.1068/a030001 ↗
- Fotheringham, A. S. (1983). A new set of spatial-interaction models: the theory of competing destinations. Environment and Planning A, 15(1), 15–36. DOI: 10.1068/a150015 ↗
How to cite this page
ScholarGate. (2026, June 2). Spatial Interaction (Gravity) Models. ScholarGate. https://scholargate.app/en/spatial-analysis/spatial-interaction-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.
- GIS-MCDASpatial analysis↔ compare
- Location-AllocationSpatial analysis↔ compare
- Multinomial LogitEconometrics↔ compare
- Poisson RegressionEconometrics↔ compare