Chapter 11 - Canonical analysis

Abstract

The chapter examines the simultaneous analysis of two, or possibly several data tables by direct or indirect comparisons, also called direct and indirect gradient analyses. Canonical analysis may be asymmetric (i.e. redundancy analysis, canonical correspondence analysis, and linear discriminant analysis) or symmetric (i.e. canonical correlation analysis, co-inertia analysis, and Procrustes analysis. The chapter includes discussion of the following topics: redundancy analysis (RDA, simple RDA, statistics in simple RDA, redundancy statistic, algebra of simple RDA, biplot, triplot, partial RDA, statistics in partial RDA, tests of significance in partial RDA, and variation partitioning by RDA), canonical correspondence analysis (CCA, algebra of CCA, and partial CCA), analysis of community composition data with RDA and CCA (classical RDA, classical CCA, transformation-based RDA, tb-RDA, and distance-based RDA, db-RDA), linear discriminant analysis (LDA, discriminant functions, identification function, algebra of LDA, confusion table, classification table, and statistics in LDA), canonical correlation analysis (CCorA, algebra of CCorA, and statistics in CCorA), co-inertia analysis (CoIA, algebra of CoIA, multiple factor analysis), Procrustes analysis (Proc, orthogonal Proc, asymmetric Proc, symmetric Proc, and generalized Proc), uses of canonical correlation, Procrustes and co-inertia analyses, and canonical analysis of community composition data. Numerical methods are illustrated with real ecological applications, drawn from the literature. The chapter ends on a description of relevant software implemented in the R language; it also cites some commercially available statistical packages and programs from researchers.