Open Access
December 2011 Revisiting Guerry’s data: Introducing spatial constraints in multivariate analysis
Stéphane Dray, Thibaut Jombart
Ann. Appl. Stat. 5(4): 2278-2299 (December 2011). DOI: 10.1214/10-AOAS356


Standard multivariate analysis methods aim to identify and summarize the main structures in large data sets containing the description of a number of observations by several variables. In many cases, spatial information is also available for each observation, so that a map can be associated to the multivariate data set. Two main objectives are relevant in the analysis of spatial multivariate data: summarizing covariation structures and identifying spatial patterns. In practice, achieving both goals simultaneously is a statistical challenge, and a range of methods have been developed that offer trade-offs between these two objectives. In an applied context, this methodological question has been and remains a major issue in community ecology, where species assemblages (i.e., covariation between species abundances) are often driven by spatial processes (and thus exhibit spatial patterns).

In this paper we review a variety of methods developed in community ecology to investigate multivariate spatial patterns. We present different ways of incorporating spatial constraints in multivariate analysis and illustrate these different approaches using the famous data set on moral statistics in France published by André-Michel Guerry in 1833. We discuss and compare the properties of these different approaches both from a practical and theoretical viewpoint.


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Stéphane Dray. Thibaut Jombart. "Revisiting Guerry’s data: Introducing spatial constraints in multivariate analysis." Ann. Appl. Stat. 5 (4) 2278 - 2299, December 2011.


Published: December 2011
First available in Project Euclid: 20 December 2011

zbMATH: 1234.62092
MathSciNet: MR2907115
Digital Object Identifier: 10.1214/10-AOAS356

Keywords: Autocorrelation , duality diagram , Multivariate analysis , spatial weighting matrix

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.5 • No. 4 • December 2011
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