Object

Title: 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

Creator:

Paulov, Ján ; Bezák, Anton

Date issued/created:

2017

Resource Type:

Article

Subtitle:

Przegląd Geograficzny T. 89 z. 4 (2017)

Publisher:

IGiPZ PAN

Place of publishing:

Warszawa

Description:

24 cm

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.

References:

1. Batty M., 2010, Space, scale, and scaling in entropy maximizing, Geographical Analysis, 42, 4, pp. 395-421. ; - ; 2. Batty M., Mackie S., 1972, The calibration of gravity, entropy, and related models of spatial interaction, Environment and Planning, 4, 2, pp. 205-233. ; - ; 3. Bell M., Blake M., Boyle P., Duke-Williams O., Rees P., Stillwell J., Hugo G., 2002, Cross-national comparison of internal migration: issues and measures, Journal of the Royal Statistical Society, Series A, 165, 3, pp. 435-464. ; - ; 4. Bezák A., 2000, Funkčné mestské regióny na Slovensku (Functional urban regions in Slovakia), Geographia Slovaca, 15, Slovak Academy of Sciences, Institute of Geography, Bratislava. ; 5. Bezák A., 2000, Interregional migration in Slovakia: some tests of spatial interaction models, Geografický časopis, 52, 1, pp. 15-32. ; 6. Fotheringham A.S., O'Kelly M.E., 1989, Spatial Interaction Models: Formulations and Applications, Kluwer, Dordrecht. ; 7. Garrett A.J.M., 1991, Macroirreversibility and microreversibility reconciled: the second law, [in:] B. Buck, V.A. Macaulay (eds.), Maximum Entropy in Action, Clarendon Press, Oxford, pp. 139-170. ; 8. Jaynes E.T., 1957, Information theory and statistical mechanics, Physical Review, 106, 4, pp. 620-630. ; - ; 9. Masser I., Scheurwater J., 1978, The specification of multi-level systems for spatial analysis, [in:] I. Masser, P.J.B. Brown (eds.), Spatial Representation and Spatial Interaction, Martinus Nijhoff, Leiden, pp. 151-172. ; - ; 10. Pohyb obyvatelstva v České a Slovenské Federatívní Republice v roce 1991, 1993, Český statistický úřad, Praha. ; 11. Pohyb obyvatelstva v Československé socialistické republice v roce … [1981, 1982, 1983, 1984, 1985], 1982-1986, Federální statistický úřad, Praha. ; 12. Pohyb obyvateľstva v Slovenskej republike v roku … [1992, 1993, 1994, 1995], 1993-1996, Štatistický úrad Slovenskej republiky, Bratislava. ; 13. Rogerson P.A., 1990, Buffon's needle and the estimation of migration distances, Mathematical Population Studies, 2, 3, pp. 229-238. ; - ; 14. Roy J.R., Thill J.-C., 2004, Spatial interaction modelling, Papers in Regional Science, 83, 1, pp. 339-361. ; - ; 15. Stillwell J.C.H., 1983, SPAINT: A Computer Program for Spatial Interaction Model Calibration and Analysis, Computer Manual, 14, University of Leeds, School of Geography, Leeds. ; 16. Wilson A.G., 1967, A statistical theory of spatial distribution models, Transportation Research, 1, 3, pp. 253-269. ; - ; 17. Wilson A.G., 1970, Entropy in Urban and Regional Modelling, Pion, London. ; 18. Wilson A.G., 1974, Urban and Regional Models in Geography and Planning, Wiley, Chichester. ; 19. Yaglom A.M., Yaglom I.M., 1983, Probability and Information [Translated from the Russian (1973) by V. K. Jain], D. Reidel, Dordrecht.

Relation:

Przegląd Geograficzny

Volume:

89

Issue:

4

Start page:

517

End page:

533

Format:

File size 0,6 MB ; application/pdf

Resource Identifier:

oai:rcin.org.pl:64378 ; 0033-2143 (print) ; 2300-8466 (on-line) ; 10.7163/PrzG.2017.4.1

Source:

CBGiOS. IGiPZ PAN, sygn.: Cz.181, Cz.3136, Cz.4187 ; click here to follow the link

Language:

eng

Language of abstract:

pol

Rights:

Creative Commons Attribution BY 3.0 PL license

Terms of use:

Copyright-protected material. [CC BY 3.0 PL] May be used within the scope specified in Creative Commons Attribution BY 3.0 PL license, full text available at: ; -

Digitizing institution:

Institute of Geography and Spatial Organization of the Polish Academy of Sciences

Original in:

Central Library of Geography and Environmental Protection. Institute of Geography and Spatial Organization PAS

Projects co-financed by:

Programme Innovative Economy, 2010-2014, Priority Axis 2. R&D infrastructure ; European Union. European Regional Development Fund

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