Constraints as factors reducing the entropy of distributions: an entropy-maximizing spatial interaction model as an example = Ograniczenia jako czynniki redukujące entropię rozkładów: przykład modelu maksymalizacji entropii przestrzennej interakcji

Abstract

Abstract. The aim of this paper is to provide empirical evidence for the statement that the constraints imposed on an objective function are able to reduce the entropy of the corresponding distributions produced by entropy-maximizing models. This idea is evaluated via an application to an entropy-maximizing spatial interaction model, as a typical representative of the family of entropy-maximizing models used in geography. Eleven versions of this spatial interaction model are fitted separately to six sets of data concerning interregional migration in Slovakia. For each model, the predicted flow distribution is derived, prior to calculation of the corresponding predicted entropy, and then comparison of the entropy values relating to all the models. The results obtained indicate very clearly that constraints imposed on an objective function reduce the initial maximum entropy successively, with this reduction depending on the number and nature of the constraints incorporated.