Multiple group principal component analysis and population differentiation

Abstract

This paper explores the requirements and advantages of multiple group principal component analysis (MGPCA) when it is used to investigate population differentiation. A distinction is drawn between equality of orientation of the within‐group axes and equality of variance along these axes. Several examples of the use of MGPCA are discussed and it is shown that MGPCA per se does not require equality of variance along the axes although it may be a requirement of some of the techniques subsequently used to analyse the component scores. MGPCA is simple and direct, being based on the mathematically well defined eigenvector analysis of a symmetric positive definite (pooled within‐group covariance) matrix and it can be thought of as a step in the computation of canonical variate analysis (CVA). It can be used with CVA (which is the most popular method of biometrically assessing population affinities) to assess the contribution of within‐group components to among‐group discrimination. It is also one of a range of appropriate techniques that can be used to define (and delete if required) within‐group growth effects and is particularly suitable when CVA is being used to assess the population affinities. When used in this way it has the advantage of being more influenced by the groups with the greatest growth range.