Tobler's “An Alternative Formulation for Spatial-Interaction Modeling”: An Observation

1983 ◽  
Vol 15 (5) ◽  
pp. 705-706 ◽  
Author(s):  
A G Wilson
Keyword(s):  
Spatial Interaction ◽  
Interaction Model ◽  
Alternative Formulation ◽  
Spatial Interaction Model ◽  
Interaction Modeling ◽  
Kullback Entropy ◽  
Spatial Interaction Modeling

It is shown that there is a possible relationship between the maximand used to produce To bier's spatial interaction model and Kullback entropy.

Parameter Estimation in Spatial Interaction Modeling

1973 ◽  
Vol 5 (4) ◽  
pp. 503-518 ◽  
Author(s):  
F J Cesario
Keyword(s):  
Parameter Estimation ◽  
Growth Factor ◽  
Structural Characteristics ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Solution Properties ◽  
Spatial Interaction Model ◽  
Interaction Modeling ◽  
Constrained Model ◽  
Spatial Interaction Modeling

New ways of estimating the parameters of the so-called ‘doubly-constrained’ spatial interaction model are developed and tested against contemporary procedures. Two variations of the doubly-constrained model—growth-factor and interactance (that is, gravity and entropy) models—are considered: The structural characteristics of these models are specified and several new solution properties are established. Then alternative parameter-estimation strategies are formulated and tested. The proposed techniques (which solve problems that are equivalent to existing models) are shown to be inferior to current methodology with respect to all criteria related to solution speed. However, it is shown that the proposed methods are more flexible than current approaches since a wider range of assumptions can be incorporated into the analysis.

An Alternative Formulation for Spatial-Interaction Modeling

1983 ◽  
Vol 15 (5) ◽  
pp. 693-703 ◽  
Author(s):  
W Tobler
Keyword(s):  
Spatial Competition ◽  
Spatial Interaction ◽  
Linear Equations ◽  
Interaction Model ◽  
Neumann Boundary ◽  
The United States ◽  
Alternative Formulation ◽  
Continuous Version ◽  
Movement Rates ◽  
Interaction Modeling

Elementary geometric assumptions are used to derive a spatial-interaction model in which places are related to each other through a set of simultaneous linear equations. The system has simple properties with respect to aggregation and turnover, yet incorporates spatial competition, adjacency, and effects of geographic shadowing. The objective function satisfied by the model reduces congestion and minimizes the per capita work; solves a quadratic transportation-problem and fulfils in-sum and out-sum constraints. The associated Lagrangians can be interpreted as pushes and pulls, or as shadow prices. A spatially continuous version of the model consists of coupled elliptical partial differential equations with Neumann boundary conditions, solvable by numerical methods. With migration data from the United States of America the model yields an amazingly good fit, better than existing models and with fewer free parameters. Inversion of the model yields an estimate of distances between regions. In-movement rates are predicted from out-movement rates in the model.

Equilibrium and Nonequilibrium Statistical Thermodynamical Approaches to Modeling Spatial Interaction Dynamics

1992 ◽  
Vol 24 (3) ◽  
pp. 441-446 ◽  
Author(s):  
P B Slater
Keyword(s):  
Nonequilibrium Thermodynamics ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Human Movement ◽  
Evolutionary Processes ◽  
Spatial Interaction Model ◽  
Interaction Dynamics ◽  
Interaction Modeling ◽  
Migratory Population ◽  
Over Time

Spatial interaction modeling can be embedded in the framework of statistical thermodynamics. This has been shown in part by Wilson and by Erlander, in particular. However, to complete the embedding, it is necessary to ask the dynamic question of how a migratory population evolves over time from one (observed) distribution at time t0 to another (observed) distribution at time t1, rather than just the question of how many people who started in one area at t0 ended in another at t1—with no regard to the intermediate locations of the migrants. The manner in which such evolutionary processes are addressed in the context of equilibrium and nonequilibrium thermodynamics serves as a basis for extending the spatial interaction model of human movement.

Comments on the Urban Spatial-Interaction Model Based on the Intervening-Opportunities Principle

1979 ◽  
Vol 11 (5) ◽  
pp. 527-539 ◽  
Author(s):  
Irena Chudzyńska ◽  
Z Słodkowski
Keyword(s):  
Mathematical Model ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Spatial Interaction Model ◽  
Model Based ◽  
Number Of Equilibria ◽  
Intervening Opportunities

A mathematical model of urban spatial interaction based on the intervening-opportunities principle is discussed and its equilibria are studied. It is shown that, under natural assumptions, the number of equilibria is finite, and a mathematical criterion for distinguishing the equilibrium corresponding to reality is given.

scholarly journals A primer for working with the Spatial Interaction modeling (SpInt) module in the python spatial analysis library (PySAL)

REGION ◽  
2016 ◽  
Vol 3 (2) ◽  
pp. 11 ◽  
Author(s):  
Taylor M Oshan
Keyword(s):  
Spatial Analysis ◽  
Spatial Interaction ◽  
Practical Guide ◽  
Interaction Modeling ◽  
Spatial Interaction Modeling

This primer provides a practical guide to get started with spatial interaction modeling using the SpInt module in the python spatial analysis library (PySAL).

Sign in / Sign up

Export Citation Format

Share Document