Revisiting Guerry’s data: introducing spatial constraints in multivariate analysis. (English) Zbl 1234.62092

Dray, Stéphane; Jombart, Thibaut

Ann. Appl. Stat. 5, No. 4, 2278-2299 (2011).

Summary: 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).
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.

MSC:

62H25	Factor analysis and principal components; correspondence analysis
62P12	Applications of statistics to environmental and related topics
62H11	Directional data; spatial statistics
62A09	Graphical methods in statistics

Keywords:

autocorrelation; duality diagram; spatial weighting matrix

Software:

sedaR; ade4; Guerry

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