Principal component analysis for grouped data—a case study

Abstract

Two of the most popular descriptive multivariate methods currently employed are the principal component analysis and canonical variate analysis methods. Canonical variate analysis is the most appropriate technique to use whenever the multivariate data are grouped and to discriminate group differences using multiple variables. Principal component analysis, on the other hand, is used to develop linear combinations that successively maximize the total variance of a sample where there is no known group structure. However, when there are more variables than within‐group degrees of freedom, due to the singularity of the within‐group covariance matrix, canonical variates cannot be derived. The main aim of this paper is to explore such situations with an example from a biodiversity study and a further computer simulation; principal component analysis can be a viable substitute, if the between‐group differences are prominent.