Spatial aggregation in gravity models: 2. One-dimensional population density models

This paper, the second of four, is concerned with applying a methodology for analysing the spatial aggregation problem in gravity models outlined in the first paper. The methodology is based on a consistent framework for linking measures of pattern in interaction data to the derivation and estimation of related interaction models using spatial information theory. In this quest, a link is forged between information in data and the parameters of an associated model, and in part 1 it was suggested that if this link could be formalised then a means would be available for predicting changes in model parameters from different aggregations of the data, prior to the actual estimation of the models themselves. This relationship can be formalised for the case of the continuous one-dimensional interaction model such as the population density model, and this paper is concerned with demonstrating such an application to aggregations of zones in the Reading region. The framework is first described and two continuous models are presented. Then, the discrete model is estimated by means both of regression and of entropy techniques applied to various aggregations of the region, and the resulting parameters are related to the predicted and observed informations. Finally, the parameters approximated from observed information by use of the theoretical models are compared with the estimated parameters, and the approximation is deemed good, thus providing some confidence in the general concepts developed to handle these types of problem.