Procrustean co-inertia analysis for the linking of multivariate datasets

Procrustes analysis is a method for fitting a set of points to another. These two sets of points are often defined by the measurements of two sets of variables for the same individuals (e.g., measurements of species abundances and environmental variables at the same sites). We present a solution for graphical representation of the results of procrustes analysis when the number of variables in each of the two datasets exceeds two. This method is named procrustean co-inertia analysis because it is based on the joint use of procrustes analysis and co-inertia analysis, which is a coupling method for finding linear combinations of two sets of variables of maximal covariance. It provides better graphical representation of the concordance between the two datasets than classical co-inertia analysis. Moreover, distance matrices can be introduced in the analysis to improve its ecological meaning. Lastly, a randomization test equivalent to-PROTEST is proposed as an alternative to the Mantel test. An ecological example is presented to illustrate the method.