Spatial Aggregation in Gravity Models. 1. An Information-Theoretic Framework

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Abstract
This is the first of four papers concerned with developing a comprehensive approach to the spatial aggregation problem in gravity models. A framework for exploring the problem is outlined in this paper, and will be applied to one-dimensional and two-dimensional spatial interaction models in the subsequent papers. Appropriate statistics for measuring changes in spatial variation due to spatial aggregation in data sets and in model predictions of spatial interaction are derived by use of information theory; and these statistics, such as spatial entropy, have excellent decomposition properties which can be readily exploited in the study of aggregation effects in data and models. These properties involve information components associated with density, level of detail or average zone size, dimension, and level of resolution. Use of the spatial entropy function, in particular, enables consistent relationships to be developed between information components and model parameters, and these relationships are examined in detail in subsequent papers.