Empirically Derived Deterrence Functions for Maximum Performance Spatial Interaction Models

1977 ◽  
Vol 9 (9) ◽  
pp. 1067-1079 ◽  
Author(s):  
S Openshaw ◽  
C J Connolly
Keyword(s):  
Goodness Of Fit ◽  
Spatial Interaction ◽  
Model Performance ◽  
Interaction Model ◽  
Theoretical Research ◽  
Maximum Performance ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
The Relationship ◽  
Descriptive Models

The relationship between the choice of deterrence function and the goodness of fit of a singly constrained spatial interaction model is examined as a basis for improving model performance. The results show that there is no significant improvement in model goodness of fit until a deterrence-function characterisation is used which is based on a family of functions, with the spatial domain of each function being determined in an approximately optimal manner. These findings are consistent with theoretical research on microlevel trip behaviour and can be used to identify descriptive models which possess maximum levels of performance.

Effects of Spatial System Design on Spatial Interaction Models. 1: The Spatial System Definition Problem

1989 ◽  
Vol 21 (1) ◽  
pp. 27-46 ◽  
Author(s):  
S H Putman ◽  
S-H Chung
Keyword(s):  
Goodness Of Fit ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Spatial Aggregation ◽  
Model Parameters ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
Aggregation Methods ◽  
Future Paper ◽  
Spatial System

Rather little has been published about systematic empirical research on the problem of spatial aggregation and its effects on spatial interaction models. Of the work which has been published, all of it has dealt almost exclusively with single-parameter spatial interaction models. In this article five different aggregation procedures are examined. The experiments were based on the use of a multivariate multiparametric spatial interaction model. A first set of hypotheses tests was performed with respect to the sensitivity of model parameters to spatial aggregation methods. A second set was performed with respect to the sensitivity of model goodness-of-fit to the five spatial aggregation methods. Although questions remain, the results clearly show that the multiparametric model responds well to different aggregation algorithms. Some parameters showed substantial response, as they should, to different zonal aggregations, whereas others are shown to be much less responsive. Further, the results clearly indicate that systematic aggregation procedures generally produce better results than do random procedures. A future paper will continue with a discussion of zone definition criteria, and recommendations will be made with regard to aggregation algorithms.

A Note on the Calibration of Maximum-Performance Spatial-Interaction Models

1978 ◽  
Vol 10 (10) ◽  
pp. 1151-1154
Author(s):  
M J Baxter
Keyword(s):  
Spatial Interaction ◽  
Model Performance ◽  
Maximum Performance ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
The Family

Evidence is presented to show that the improvement in model performance achieved by the family of maximum-performance spatial-interaction models developed by Openshaw and Connolly (1977) may be explicable solely for statistical reasons and that there is no need for a geographical or behavioural explanation, as was suggested.

On the Relationship between Alonso's Theory of Movement and Wilson's Family of Spatial-Interaction Models

1981 ◽  
Vol 13 (2) ◽  
pp. 217-224 ◽  
Author(s):  
J Ledent
Keyword(s):  
Input Data ◽  
Spatial Interaction ◽  
System Of Equations ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
Standard Family ◽  
Original Contribution ◽  
Standard Models ◽  
The Relationship

This paper compares the system of equations underlying Alonso's theory of movement with that of Wilson's standard family of spatial-interaction models. It is shown that the Alonso model is equivalent to one of Wilson's four standard models depending on the assumption at the outset about which of the total outflows and/or inflows are known. This result turns out to supersede earlier findings—inconsistent only in appearance—which were derived independently by Wilson and Ledent. In addition to this, an original contribution of this paper—obtained as a byproduct of the process leading to the aforementioned result—is to provide an exact methodology permitting one to solve the Alonso model for each possible choice of the input data.

Optimal Zoning Systems for Spatial Interaction Models

1977 ◽  
Vol 9 (2) ◽  
pp. 169-184 ◽  
Author(s):  
S Openshaw
Keyword(s):  
Spatial Model ◽  
Model Building ◽  
Spatial Interaction ◽  
Empirical Studies ◽  
Model Performance ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
Parameter Values ◽  
Zoning Systems

The design of zoning systems for spatial interaction models is a major problem which affects both the interpretation and acceptability of these models. This paper demonstrates that zoning-system effects on parameter values and model performance are nontrivial, and that their magnitude is far larger than was previously thought likely. An approach which is most appropriate in an applied context, where there is also the problem of poor model performance, is to identify a zoning system which will approximately optimise model performance. The paper gives details of how this may be achieved. This method is demonstrated by a series of empirical studies. Finally, there is a brief discussion of the general implications for spatial model building.

Dynamic Spatial Interaction Models: New Directions

1988 ◽  
Vol 20 (11) ◽  
pp. 1449-1460 ◽  
Author(s):  
P Nijkamp ◽  
A Reggiani
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Interaction Models ◽  
Shopping Centre ◽  
Spatial Interaction Models ◽  
New Directions ◽  
Interaction Research

Spatial interaction models have received a great deal of attention in the past decade. In recent years, various approaches have also been developed to take into account dynamic aspects of spatial interaction models, by means of, for instance, optimal control theory, bifurcation theory, or catastrophe theory. The present paper deals with new directions in dynamic spatial interaction research. The focus is on a general dynamic interaction model analyzed in the framework of optimal control theory. The objective function used is a bicriterion utility model, to be maximized subject to a set of differential equations which bear some resemblance to those used by Wilson in a shopping-centre context. The link between the model presented and a catastrophe type of model is investigated. It is demonstrated that catastrophe behaviour may emerge as a particular case of this optimal control model. Finally, it is shown how external influences (for example, stochastic impacts of the Brownian motion type) affect the optimal trajectory.

Spatial Aggregation in Gravity Models: 3. Two-Dimensional Trip Distribution and Location Models

1982 ◽  
Vol 14 (5) ◽  
pp. 629-658 ◽  
Author(s):  
M Batty ◽  
P K Sikdar
Keyword(s):  
Spatial Interaction ◽  
Model Performance ◽  
Spatial Aggregation ◽  
Gravity Models ◽  
Canonical Forms ◽  
Two Dimensional ◽  
Variable Model ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
Spatial Entropy

This is the third of four papers and in it the methodology for analysing spatial aggregation in gravity models outlined in the first paper is further elaborated. In the second paper, the methodology was applied to one-dimensional spatial interaction models of the population density type, with some success; and here it is proposed to apply the methodology to two-dimensional spatial interaction models using the same data base, the Reading (UK) region. Accordingly, the methodology is first stated for linking information in data measured by spatial entropy to the parameters of models generated from spatial entropy. The family of four spatial interaction models due to Cordey-Hayes and Wilson is then derived, the canonical forms of their associated spatial entropy functions presented, and the analytic properties of such models explored. These four models are then fitted to spatial aggregations of the Reading region, and various empirical relationships between their entropies and parameters described. The results are not as regular as those of the models in the second paper because of more variable model performance, but nevertheless a means of approximating scale parameters from data based on the work of Kirby is outlined. This enables estimates of the dispersion parameters to be made through the canonical forms. Although the results are poor because of model performance, the methodology outlined here serves as a basis for the more fully fledged application to be discussed in the final paper.

Intransitivity, the Spatial Interaction Model, and US Migration Streams

1980 ◽  
Vol 12 (10) ◽  
pp. 1131-1144 ◽  
Author(s):  
M F Goodchild ◽  
T R Smith
Keyword(s):  
Error Term ◽  
Sampling Error ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Interstate Migration ◽  
Interaction Models ◽  
Spatial Interaction Model ◽  
Spatial Interaction Models ◽  
Large Numbers ◽  
Migration Flows

The flows predicted by a large class of spatial interaction models are transitive, yet US migration tables have been shown to contain large numbers of intransitivities. This paper investigates a number of possible conditions under which flows regulated by the spatial interaction model might be observed to be intransitive. A singly constrained gravity model is calibrated for a number of flow tables, and distorted by sampling error, by aggregation over strata, and by an independently distributed error term. Only the last distortion gives the correct bias in the relative abundance of intransitivities in numerical flows and flow probabilities. This conclusion is supported by further simulations using random spatial interaction models. The results of the calibrations of the spatial interaction model using US interstate migration flows, 1935–1970, are given and compared with others previously published.

Interzonal Migration: Some Historical Tests of Spatial-Interaction Models

1978 ◽  
Vol 10 (10) ◽  
pp. 1187-1200 ◽  
Author(s):  
J C H Stillwell
Keyword(s):  
Spatial Variation ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Regional Variations ◽  
Interaction Models ◽  
Spatial Interaction Model ◽  
Spatial Interaction Models ◽  
Disaggregated Data ◽  
Migration Flows ◽  
Decay Parameters

Observed migration and survival flows between counties and between standard regions are used to test alternative calibrations of a doubly constrained spatial-interaction model. Spatial variation in the propensity to migrate over distance is examined in an analysis of zone-specific decay parameters, and two methods of splitting aggregate migration flows according to reason for move are investigated. The results of the model tests for age/sex-disaggregated data underline regional variations in propensities to migrate and in mean distances migrated.

Effects of scale in spatial interaction models

2013 ◽  
Vol 15 (3) ◽  
pp. 249-264 ◽  
Author(s):  
Giuseppe Arbia ◽  
Francesca Petrarca
Keyword(s):  
Spatial Interaction ◽  
Interaction Models ◽  
Spatial Interaction Models
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