Interzonal Migration: Some Historical Tests of Spatial-Interaction Models

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.

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Intransitivity, the Spatial Interaction Model, and US Migration Streams

Environment and Planning A Economy and Space ◽

10.1068/a121131 ◽

1980 ◽

Vol 12 (10) ◽

pp. 1131-1144 ◽

Cited By ~ 14

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.

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Empirically Derived Deterrence Functions for Maximum Performance Spatial Interaction Models

Environment and Planning A Economy and Space ◽

10.1068/a091067 ◽

1977 ◽

Vol 9 (9) ◽

pp. 1067-1079 ◽

Cited By ~ 18

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.

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Dynamic Spatial Interaction Models: New Directions

Environment and Planning A Economy and Space ◽

10.1068/a201449 ◽

1988 ◽

Vol 20 (11) ◽

pp. 1449-1460 ◽

Cited By ~ 14

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.

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

Environment and Planning A Economy and Space ◽

10.1068/a210027 ◽

1989 ◽

Vol 21 (1) ◽

pp. 27-46 ◽

Cited By ~ 36

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.

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Trade, migration, and the dynamics of spatial interaction

10.31235/osf.io/trbf8 ◽

2019 ◽

Author(s):

Nicolas Gauthier

Keyword(s):

Social Interaction ◽

Settlement Patterns ◽

Large Scale ◽

Spatial Interaction ◽

Interaction Model ◽

Structural Features ◽

Small Scale ◽

Interaction Models ◽

Road Map ◽

Migration Flows

Archaeological settlement patterns are the physical remains of complex webs of human decision-making and social interaction. Entropy-maximizing spatial interaction models are a means of building parsimonious models that average over much of this small-scale complexity, while maintaining key large-scale structural features. Dynamic social interaction models extend this approach by allowing archaeologists to explore the co-evolution of human settlement systems and the networks of interaction that drive them. Yet, such models are often imprecise, relying on generalized notions of settlement "influence" and "attractiveness" rather than concrete material flows of goods and people. Here, I present a dis-aggregated spatial interaction model that explicitly resolves trade and migration flows and their combined influence on settlement growth and decline. I explore how the balance of costs and benefits of each type of interaction influence long-term settlement patterns. I find trade flows are the strongest determinant of equilibrium settlement structure, and that migration flows play a more transient role in balancing site hierarchies. This model illustrates how the broad toolkit for spatial interaction modeling developed in geography and economics can increase the precision of quantitative theory building in archaeology, and provides a road-map for connecting mechanistic models to the empirical archaeological record.

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A New Set of Spatial-Interaction Models: The Theory of Competing Destinations

Environment and Planning A Economy and Space ◽

10.1177/0308518x8301500103 ◽

1983 ◽

Vol 15 (1) ◽

pp. 15-36 ◽

Cited By ~ 133

Author(s):

A S Fotheringham

Keyword(s):

Spatial Interaction ◽

Model Misspecification ◽

Distance Decay ◽

Gravity Models ◽

Parameter Estimates ◽

Interaction Models ◽

Spatial Interaction Models ◽

The Family ◽

Decay Parameters ◽

Alternative Set

Members of the family of spatial-interaction models commonly referred to as gravity models are shown to be misspecified. One result of this misspecification is the occurrence of an undesirable ‘spatial-structure effect’ in estimated distance-decay parameters and this effect is examined in detail. An alternative set of spatial-interaction models is formulated from which more accurate predictions of interactions and more accurate parameter estimates can be obtained. These new interaction models are termed competing destinations models, and estimated distance-decay parameters obtained in their calibration are shown to have a purely behavioural interpretation. The implications of gravity-model misspecification are discussed.

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Modelling population flows using spatial interaction models

Australian Population Studies ◽

10.37970/aps.v2i2.38 ◽

2018 ◽

Vol 2 (2) ◽

pp. 33-58

Author(s):

Adam Dennett

Keyword(s):

Programming Languages ◽

Internal Migration ◽

Spatial Interaction ◽

Capital City ◽

Factors Affecting ◽

Interaction Models ◽

Spatial Interaction Models ◽

Migration Data ◽

Interaction Modelling ◽

Migration Flows

Background Spatial Interaction Models have been used for decades to explain and predict flows (of migrants, capital, traffic, trade etc.) between geographic locations.Aims This paper will guide users through the process of fitting and calibrating spatial interaction models in order to understand, explain and predict internal migration flows in Australia. Data and methods Internal migration data from the Australian 2011 Census of Population and Housing, which records people who have moved between Greater Capital City Statistical Areas over 5-year periods, is used to exemplify the modelling process. The R statistical software is used to process and visualise the data as well as run the models. Results The full suite of Wilson’s family of spatial interaction models is fitted to the internal migration data, revealing that distance and origin/destination populations are some of the most important influencing factors affecting internal migration flows. We see whether constraining the model to known flows about origins and/or destinations will improve the fits and model estimates. Conclusions Spatial interaction modelling has been a tool in the box of some population geographers for a number of decades. However, recent advances in more forgiving programming languages such as R and Python now mean that this powerful modelling methodology is no longer only available to those who also possess advanced computer programming skills. This guide has exemplified the process of fitting and calibrating spatial interaction models on Australian internal migration data, but the methods could easily be applied to other flow data sets in other contexts.

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

Environment and Planning A Economy and Space ◽

10.1068/a130217 ◽

1981 ◽

Vol 13 (2) ◽

pp. 217-224 ◽

Cited By ~ 15

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.

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