The interpretation of Generalized Procrustes Analysis and allied methods

Abstract

We discuss various issues surrounding the use and interpretation of Generalized Procrustes Analysis and related methods. Included are considerations that have to be made before starting an analysis, how to handle different dimensionalities of data, when to consider fitting scaling factors and when not to, and the distinction between the number of dimensions that are needed to give an adequate fit and the number of dimensions needed for graphical representation. The distinction between signal and noise plays an important part in explaining how different methods are suitable for exploring different aspects of the data, rather than being viewed as competing methods with the same general objectives. Explanations are largely set in a geometrical context, thus keeping technical mathematics to a minimum; a common Analysis of Variance framework allows all the methods to be considered in a unified way and suggests some new ways in which these kinds of data may be analysed. The whole is illustrated by example analyses.