Spatial Structure and the Parameters of 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.

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Model Misspecification and Spatial Structure in Spatial-Interaction Models

Environment and Planning A Economy and Space ◽

10.1068/a150319 ◽

1983 ◽

Vol 15 (3) ◽

pp. 319-327 ◽

Cited By ~ 18

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.

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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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