A Note on the Treatment of Flows across System Boundaries in Spatial-Interaction Models

1979 ◽  
Vol 11 (4) ◽  
pp. 447-454 ◽  
Author(s):  
I Masser
Keyword(s):  
Spatial Interaction ◽  
System Boundaries ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
The Family ◽  
Constrained Model

Some problems that must be resolved by the analyst in connection with the treatment of flows across system boundaries to and from external zones are discussed in this paper. These problems make it necessary to make modifications to the conventional formulations both of the doubly and of the singly constrained members of the family of spatial-interaction models. None of the possible modifications wholly satisfies theoretical requirements in terms of the doubly constrained model, and the advantages and limitations of various approaches can only be assessed in an operational situation. For this reason some of the findings from a study of the Amersfoort region are presented which help to throw light on this problem.

The Calibration of Gravity, Entropy, and Related Models of Spatial Interaction

1972 ◽  
Vol 4 (2) ◽  
pp. 205-233 ◽  
Author(s):  
M Batty ◽  
S Mackie
Keyword(s):  
Maximum Likelihood ◽  
Spatial Interaction ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
Calibration Methods ◽  
The Family ◽  
Newton Raphson ◽  
Best Parameter ◽  
Parameter Values ◽  
Raphson Method

This paper presents a methodology for deriving best statistics for the calibration of spatial interaction models, and several procedures for finding best parameter values are described. The family of spatial interaction models due to Wilson is first outlined, and then some existing calibration methods are briefly reviewed. A procedure for deriving best statistics based on the principle of maximum-likelihood is then developed from the work of Hyman and Evans, and the methodology is illustrated using the example of a retail gravity model. Five methods for solving the maximum-likelihood equations are outlined: procedures based on a simple first-order iterative process, the Newton—Raphson method for several variables, multivariate Fibonacci search, search using the Simplex method, and search based on quadratic convergence, are all tested and compared. It appears that the Newton—Raphson method is the most efficient, and this is further tested in the calibration of disaggregated residential location models.

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

1983 ◽  
Vol 15 (1) ◽  
pp. 15-36 ◽  
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.

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.

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