Hierarchical Destination Choice and Spatial Interaction Modelling: A Simulation Experiment

2001 ◽  
Vol 33 (5) ◽  
pp. 901-920 ◽  
Author(s):  
A Stewart Fotheringham ◽  
Tomoki Nakaya ◽  
Keiji Yano ◽  
Stan Openshaw ◽  
Yoshitaka Ishikawa
Keyword(s):  
Simulation Experiment ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Destination Choice ◽  
Spatial Choice ◽  
Spatial Interaction Models ◽  
Interaction Modelling ◽  
Spatial Hierarchy ◽  
Different Levels

A simulation experiment is proposed and undertaken to extend our understanding of the role of the competing destinations spatial interaction model in capturing the effects of hierarchical destination choice. In doing so, we make explicit the linkage between spatial choice behaviour at different levels of a spatial hierarchy. We also make explicit the way in which decisions made at one level of the hierarchy can lead to biased measurements of behaviour at a lower one. This is shown when conventional spatial interaction models are calibrated with interaction data that result from hierarchical destination choice.

Spatial Uncertainty and Spatial Dominance in Interaction Modelling: A Theoretical Perspective on Spatial Competition

1992 ◽  
Vol 24 (7) ◽  
pp. 995-1008 ◽  
Author(s):  
J Pooler
Keyword(s):  
Spatial Competition ◽  
Spatial Interaction ◽  
Theoretical Perspective ◽  
Model Performance ◽  
Interaction Model ◽  
Spatial Uncertainty ◽  
Destination Choice ◽  
Relative Location ◽  
Interaction Modelling ◽  
The Empirical Analysis

In this paper a theoretical index of spatial uncertainty is defined, which measures the degree of diversity faced by potential movers in a destination choice set. As a result of variations in attractiveness and distance, destinations are considered to exert varying degrees of spatial dominance on origins and to compete on that basis for the attention of would-be movers. It is hypothesized that at origins where dominances are more uniform, there is ‘less to choose’ among destinations and it is more difficult to predict accurately spatial interaction (and vice versa). The basic concept put forth is that spatial uncertainty and the spatial interaction-model performance are related to the relative location of origins with respect to destinations. The empirical analysis employs data on recreational day travel and population migration.

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.

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.

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.

scholarly journals Stochastic modelling of urban structure

2018 ◽  
Vol 474 (2213) ◽  
pp. 20170700 ◽  
Author(s):  
L. Ellam ◽  
M. Girolami ◽  
G. A. Pavliotis ◽  
A. Wilson
Keyword(s):  
Spatial Interaction ◽  
Structural Evolution ◽  
Interaction Model ◽  
Stochastic Modelling ◽  
Urban Structure ◽  
Spatial Interaction Models ◽  
The Core ◽  
Structural Variables ◽  
Core Elements

The building of mathematical and computer models of cities has a long history. The core elements are models of flows (spatial interaction) and the dynamics of structural evolution. In this article, we develop a stochastic model of urban structure to formally account for uncertainty arising from less predictable events. Standard practice has been to calibrate the spatial interaction models independently and to explore the dynamics through simulation. We present two significant results that will be transformative for both elements. First, we represent the structural variables through a single potential function and develop stochastic differential equations to model the evolution. Second, we show that the parameters of the spatial interaction model can be estimated from the structure alone, independently of flow data, using the Bayesian inferential framework. The posterior distribution is doubly intractable and poses significant computational challenges that we overcome using Markov chain Monte Carlo methods. We demonstrate our methodology with a case study on the London, UK, retail system.

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.

scholarly journals Regional division of Czechia on the basis of spatial interaction modelling

Geografie ◽  
2010 ◽  
Vol 115 (2) ◽  
pp. 144-160 ◽  
Author(s):  
Marián Halás ◽  
Pavel Klapka
Keyword(s):  
Spatial Interaction ◽  
Spatial Interactions ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
Administrative Division ◽  
Hierarchical Levels ◽  
Interaction Modelling ◽  
Formal Relations ◽  
Mutual Relations ◽  
Spatial Interaction Modelling

Spatial interactions represent mutual relations between geographic areas or regions at different hierarchical levels. The Reilly’s law is one of the spatial interaction models which was originally constructed for survey of retail gravitation and was based on purely formal relations. The article aims at closer presentation of the Reilly’s law and proposes possible applications of the model in regional delineation tasks and in formation of the administrative division of Czechia. Comparisons with other regional and administrative divisions are included as well.

scholarly journals The spatial structure debate in spatial interaction modeling: 50 years on

2020 ◽  
pp. 030913252096813
Author(s):  
Taylor M Oshan
Keyword(s):  
Spatial Structure ◽  
Spatial Interaction ◽  
Ongoing Debate ◽  
Spatial Interaction Models ◽  
The Past ◽  
Interaction Modeling ◽  
Methodological Approaches ◽  
Structure Debate ◽  
Spatial Interaction Modeling

Spatial interaction and spatial structure are foundational geographical abstractions, though there is often variation in how they are conceptualized and deployed in quantitative models. In particular, the last five decades have produced an exceptional diversity regarding the role of spatial structure within spatial interaction models. This is explored by outlining the initiation and development of the notion of spatial structure within spatial interaction modeling and critically reviewing four methodological approaches that emerged from ongoing debate about the topic. The outcome is a comprehensive coverage of the past and a sketch of one potential path forward for advancing this long-standing inquiry.

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