Testing spatial autocorrelation in weighted networks: the modes permutation test

In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spati...

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Bibliographic Details
Published inJournal of geographical systems Vol. 15; no. 3; pp. 233 - 247
Main Author Bavaud, François
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.07.2013
Springer
Springer Nature B.V
Subjects
Accessibility
Autocorrelation
Bootstrap method
Computer Appl. in Social and Behavioral Sciences
Connectivity
Decomposition
Econometrics
Economics
Economics and Finance
Eigenvectors
Exchange
Formalism
Geographical Information Systems/Cartography
Hypotheses
Landscape/Regional and Urban Planning
Markov analysis
Markov chains
Matrix
Networks
Original Article
Permutations
Regional/Spatial Science
Regions
Spatial filtering
Spectra
Urban Economics
C31
Weighted networks
Permutation test
C12
Local variance
Moran’s
C15
Bootstrap
Markov and semi-Markov processes
Spatial filtering
Spatial autocorrelation
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Summary:In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardized exchange matrix appearing in spectral clustering and generalize to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an accessibility matrix into an exchange matrix with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1435-5930
1435-5949
DOI:10.1007/s10109-013-0179-2