scholarly journals Modelling population flows using spatial interaction models

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.

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.

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.

Transitivity, Spatially Separable Utility Functions, and United States Migration Streams, 1935–1970

1978 ◽  
Vol 10 (4) ◽  
pp. 399-414 ◽  
Author(s):  
T R Smith ◽  
C Clayton
Keyword(s):  
United States ◽  
Spatial Interaction ◽  
Spatial Scales ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
Migration Data ◽  
Weak Evidence ◽  
Expected Utility Maximization ◽  
Gross Flows ◽  
Spatial Separability

The predictions of spatial-interaction models applied to migration systems may be viewed as the outcome of expected-utility maximization in which the average beliefs and preferences at a given origin are spatially separable. This theory indicates that a test of the spatial separability of the utilities may be performed by examining the degree of transitivity in probabilities and gross flows that is predicted by the spatial-interaction models. United States migration data for four periods between 1935 and 1970 were examined for transitivity at three spatial scales of resolution. These flows all exhibited significantly high degrees of transitivity, although for no period or scale of resolution were migration flows completely without some statistically significant intransitivities in either the probabilities or gross flows. The regions involved in intransitivities varied greatly from period to period, and only weak evidence indicated lower degrees of intransitivity for local aggregates of regions. The hypothesis of spatially separable utilities must be rejected for the migration data examined. Theoretical discussion indicates that several causes may lead to intransitivities, which in turn lead to problems in applying spatial-interaction models to migration data.

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.

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

Some Supply and Demand Considerations in Urban Spatial Interaction Models

1984 ◽  
Vol 16 (9) ◽  
pp. 1137-1147 ◽  
Author(s):  
J R Roy ◽  
J F Brotchie
Keyword(s):  
Spatial Interaction ◽  
Supply And Demand ◽  
Interaction Models ◽  
Spatial Interaction Models
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