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

Abstract

Standard multivariate analysis methods aim to identify and summarize the main\nstructures in large data sets containing the description of a number of\nobservations by several variables. In many cases, spatial information is also\navailable for each observation, so that a map can be associated to the\nmultivariate data set. Two main objectives are relevant in the analysis of\nspatial multivariate data: summarizing covariation structures and identifying\nspatial patterns. In practice, achieving both goals simultaneously is a\nstatistical challenge, and a range of methods have been developed that offer\ntrade-offs between these two objectives. In an applied context, this\nmethodological question has been and remains a major issue in community\necology, where species assemblages (i.e., covariation between species\nabundances) are often driven by spatial processes (and thus exhibit spatial\npatterns). In this paper we review a variety of methods developed in community\necology to investigate multivariate spatial patterns. We present different ways\nof incorporating spatial constraints in multivariate analysis and illustrate\nthese different approaches using the famous data set on moral statistics in\nFrance published by Andr\\'{e}-Michel Guerry in 1833. We discuss and compare the\nproperties of these different approaches both from a practical and theoretical\nviewpoint.\n