Spatial aggregation in gravity models: 3. Two-dimensional trip distribution and location models

This is the third of four papers and in it the methodology for analysing spatial aggregation in gravity models outlined in the first paper is further elaborated. In the second paper, the methodology was applied to one-dimensional spatial interaction models of the population density type, with some success; and here it is proposed to apply the methodology to two-dimensional spatial interaction models using the same data base, the Reading (UK) region. Accordingly, the methodology is first stated for linking information in data measured by spatial entropy to the parameters of models generated from spatial entropy. The family of four spatial interaction models due to Cordey-Hayes and Wilson is then derived, the canonical forms of their associated spatial entropy functions presented, and the analytic properties of such models explored. These four models are then fitted to spatial aggregations of the Reading region, and various empirical relationships between their entropies and parameters described. The results are not as regular as those of the models in the second paper because of more variable model performance, but nevertheless a means of approximating scale parameters from data based on the work of Kirby is outlined. This enables estimates of the dispersion parameters to be made through the canonical forms. Although the results are poor because of model performance, the methodology outlined here serves as a basis for the more fully fledged application to be discussed in the final paper.