An Examination of the Equivalence of Three Alternative Mechanisms for Establishing the Equilibrium Solutions of the Production-Constrained Spatial Interaction Model

1987 ◽  
Vol 19 (7) ◽  
pp. 861-874 ◽  
Author(s):  
R Crouchley
Keyword(s):  
Spatial Interaction ◽  
Equilibrium Points ◽  
Interaction Model ◽  
Equilibrium Solutions ◽  
Differential Topology ◽  
Entropy Maximization ◽  
Spatial Interaction Model ◽  
Comparison Of The Results

In this paper, three methods for determining the equilibrium points of the production-constrained spatial interaction model are reviewed; these are a balancing mechanism, differential topology, and entropy maximization. Harris and Wilson's examination of the equivalence of the three methods is summarized, and then the conditions under which equivalence can break down are established. A comparison of the results obtained from an application of each method to an often-used two-zone example is also presented.

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 Spatial Interaction Model for Healthcare Accessibility: What Scale Has to Do with It

2020 ◽  
Vol 12 (10) ◽  
pp. 4324
Author(s):  
Felipa de Mello-Sampayo
Keyword(s):  
Spatial Autocorrelation ◽  
Multilevel Modeling ◽  
Regression Models ◽  
Spatial Interaction ◽  
Healthcare Providers ◽  
Interaction Model ◽  
Local Variation ◽  
Spatial Interaction Model ◽  
Healthcare Accessibility ◽  
Spatial Autoregressive

This manuscript develops a theoretical spatial interaction model using the entropy approach to relax the assumption of the deterministic utility function. The spatial healthcare accessibility improves as the demand for healthcare increases or the opportunity cost of traveling to and from healthcare providers decreases. The empirical application used different spatial econometric techniques and multilevel modeling to evaluate the spatial distribution of existing hospitals in Texas and their social and economic correlates. To control for spatial autocorrelation, spatial autoregressive regression models were estimated, and geographically weighted regression models examined potential spatial non-stationarity. The multilevel modeling controlled for spatial autocorrelation and also allowed local variation and spatial non-stationarity. The empirical analysis showed that healthcare accessibility was not stationary in Texas in 2015, with areas of poor accessibility in rural and peripheral areas in Texas, when using hospitals’ location and county data. The model of spatial interaction applied to healthcare accessibility can be used to evaluate policies aiming at the provision of health services, such as closures of hospitals and capacity increases.

Economies of Scale and the Existence of Supply-Side Equilibria in a Production-Constrained Spatial-Interaction Model

1982 ◽  
Vol 14 (6) ◽  
pp. 823-837 ◽  
Author(s):  
B Harris ◽  
J-M Choukroun ◽  
A G Wilson
Keyword(s):  
Spatial Patterns ◽  
Critical Points ◽  
Economies Of Scale ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Supply Side ◽  
Spatial Interaction Model ◽  
Population Distributions ◽  
The Given

In previous research it has been shown that discrete changes in spatial patterns of supply in the production-constrained spatial-interaction model arise from changes in parameters such as α and β In this case, pattern changes are explored as a function of the given population distributions. This shows the existence of new kinds of critical points.

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