Model Misspecification and Spatial Structure in Spatial-Interaction Models

1983 ◽  
Vol 15 (3) ◽  
pp. 319-327 ◽  
Author(s):  
M Baxter
Keyword(s):  
Spatial Structure ◽  
Spatial Interaction ◽  
Model Misspecification ◽  
Parameter Estimates ◽  
Interaction Models ◽  
Misspecified Models ◽  
Spatial Interaction Models ◽  
Misspecified Model ◽  
Special Cases ◽  
Explicit Expressions

Concern has been expressed about the effects of spatial structure on parameter estimates from spatial-interaction models. The problem is essentially one of model misspecification. With a correctly specified model assumed, in which destination attraction depends on whether it is near to an origin or not, the consequences of using a misspecified model are examined. Explicit expressions for bias in the parameter estimates are derived; these are complex, but depend on terms that can be clearly interpreted in terms of aspects of spatial structure, such as scale, compactness, shape, remoteness of destinations, etc. Some simple special cases show how, with misspecified models, estimates from different systems will almost certainly differ. Extensions of the analysis and problems of estimation and interpretation are discussed.

Misspecification in Spatial Interaction Models: Further Results

1985 ◽  
Vol 17 (5) ◽  
pp. 673-678 ◽  
Author(s):  
M J Baxter
Keyword(s):  
Spatial Structure ◽  
Spatial Interaction ◽  
Parameter Estimates ◽  
Interaction Models ◽  
Spatial Interaction Models

Commonly used models for data on flows between sets of origins and destinations may often be misspecified because of a failure to account for the influence of spatial structure and other factors that affect flows. General expressions for the bias in parameter estimates that arises from such misspecification are derived for the most usual methods of estimation.

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.

Spatial Flows and Spatial Patterns

1984 ◽  
Vol 16 (4) ◽  
pp. 529-543 ◽  
Author(s):  
A S Fotheringham
Keyword(s):  
Spatial Structure ◽  
Spatial Patterns ◽  
Spatial Interaction ◽  
A Priori ◽  
Parameter Estimates ◽  
Spatial Interaction Models ◽  
Significant Bias ◽  
Spatial System ◽  
Decay Parameters ◽  
Spatial Flows

The misspecification of gravity spatial interaction models has recently been described by the author. The bias in parameter estimates that results from such misspecification appears to produce the ‘map pattern effect’ or ‘spatial structure bias’ in estimated distance-decay parameters. A further aspect of the misspecification bias in gravity parameter estimates is explored here. The severity of the bias is shown to vary in a predictable manner with variations in spatial structure. In particular, the bias is shown to be dependent upon the pattern of accessibility that exists within a spatial system. The relevant aspects of this pattern are discussed for intraurban and interurban (or interregional) flow matrices. It is shown that from an examination of the spatial structure of centres in a spatial system it is possible, a priori, to identify whether significant bias will arise in the calibration of a gravity model. Certain configurations of centres are shown theoretically to produce maximal bias. The author thus answers the question, “why do gravity parameter estimates appear to be biased in some systems but not in others?”

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
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