The Annals of Applied Statistics

Revisiting Guerry’s data: Introducing spatial constraints in multivariate analysis

Stéphane Dray and Thibaut Jombart

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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.

Article information

Ann. Appl. Stat., Volume 5, Number 4 (2011), 2278-2299.

First available in Project Euclid: 20 December 2011

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Autocorrelation duality diagram multivariate analysis spatial weighting matrix


Dray, Stéphane; Jombart, Thibaut. Revisiting Guerry’s data: Introducing spatial constraints in multivariate analysis. Ann. Appl. Stat. 5 (2011), no. 4, 2278--2299. doi:10.1214/10-AOAS356.

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Supplemental materials

  • Supplementary material: Implementation in R. This website hosts an R package (Guerry) containing the Guerry’s data set (maps and data). The package contains also a tutorial (vignette) showing how to reproduce the analyses and the graphics presented in this paper using mainly the package ade4 [Dray and Dufour (2007)]. The package Guerry is also available on CRAN and can be installed using the install.packages(“Guerry”) command in a R session.