Transitivity and United States Migration Streams: A Comment

1980 ◽  
Vol 12 (4) ◽  
pp. 381-384 ◽  
Author(s):  
P B Slater
Keyword(s):  
United States ◽  
Null Hypothesis ◽  
Spatial Interaction ◽  
Interstate Migration ◽  
Random Assignment ◽  
Spatial Interaction Models ◽  
Linear Assignment Problem ◽  
Single Entry ◽  
Migration Flows ◽  
Linear Assignment

The conclusion of Smith and Clayton (1978) that United States migration streams contain ‘significant’ numbers of intransitivities—thus undermining the applicability to migration of spatial-interaction models—is contraindicated. Fewer intransitivities than could be expected under a null hypothesis of randomness are found in the solution of a linear assignment problem. The solution consists of a single entry from each row and column of a generalized tournament model of 1965–1970 interstate migration. Three cycles are formed by the entries. Three is less than 4–519, the amount expected in a random assignment. Under the constraint that the entries ( fij) selected are greater than 0·5, indicative that more people move from i to j than from j to i, five intransitivities—still an insignificant number—are found. However, a highly significant number, fourteen, of intransitivities are found if the migration flows themselves—not a generalized tournament model of them—are studied.

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.

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.

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.

scholarly journals Rate effects on the growth of centres

2016 ◽  
Vol 28 (2) ◽  
pp. 221-242
Author(s):  
H. M. FRY ◽  
F. T. SMITH
Keyword(s):  
Spatial Interaction ◽  
Mathematical Problem ◽  
Phase Changes ◽  
Archaeological Sites ◽  
Discrete Version ◽  
Spatial Interaction Models ◽  
Rate Effects ◽  
Evolving System ◽  
Migration Flows ◽  
And Migration

Entropy maximising spatial interaction models have been widely exploited in a range of disciplines and applications: from trade and migration flows to the spread of riots and the understanding of spatial patterns in archaeological sites of interest. When embedded into a dynamic system and framed in the context of a retail model, the dynamics of centre growth poses an interesting mathematical problem, with bifurcations and phase changes, which may be addressed analytically. In this paper, we present some analysis of the continuous retail model and the corresponding discrete version, which yields insights into the effect of space on the evolving system, and an understanding of why certain retail centres are more successful than others. The slowly developing growths and the fast explosive growths that are of particular concern are explained in detail.

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.

scholarly journals Debt Relief and Debtor Outcomes: Measuring the Effects of Consumer Bankruptcy Protection

2015 ◽  
Vol 105 (3) ◽  
pp. 1272-1311 ◽  
Author(s):  
Will Dobbie ◽  
Jae Song
Keyword(s):  
United States ◽  
Social Insurance ◽  
The United States ◽  
Debt Relief ◽  
Random Assignment ◽  
Percentage Points ◽  
Consumer Bankruptcy ◽  
Annual Earnings ◽  
The Impact

Consumer bankruptcy is one of the largest social insurance programs in the United States, but little is known about its impact on debtors. We use 500,000 bankruptcy filings matched to administrative tax and foreclosure data to estimate the impact of Chapter 13 bankruptcy protection on subsequent outcomes. Exploiting the random assignment of bankruptcy filings to judges, we find that Chapter 13 protection increases annual earnings by $5,562, decreases five-year mortality by 1.2 percentage points, and decreases five-year foreclo-sure rates by 19.1 percentage points. These results come primarily from the deterioration of outcomes among dismissed filers, not gains by granted filers. (JEL D14, I12, J22, J31, K35)

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
Sign in / Sign up

Export Citation Format

Share Document