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

TL;DR

This paper reviews methods for incorporating spatial constraints into multivariate analysis, illustrating their application and properties using Guerry's historical data on moral statistics in France.

Contribution

It introduces and compares various approaches to integrate spatial information into multivariate analysis, highlighting their practical and theoretical differences.

Findings

Different methods effectively reveal spatial patterns in multivariate data.

Spatial constraints improve the interpretation of covariation structures.

Comparison clarifies trade-offs between summarization and pattern detection.

Abstract

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.