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

Details Revisiting Guerry's data: Introducing spatial constraints in multivariate analysis Revisiting Guerry's data: Introducing spatial constraints in multivariate analysis

2012-02-29

arxiv.org/abs/1202.6485v1

Annals of Applied Statistics 2011, Vol. 5, No. 4, 2278-2299

Statistics

Applications

Published in at http://dx.doi.org/10.1214/10-AOAS356 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

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 Andr\'{e}-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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