RANKING PRINCIPAL COMPONENTS TO REFLECT GROUP-STRUCTURE

Canonical variate analysis is the appropriate descriptive technique for multivariate data which have an a priori group structure, but problems arise with this technique when there cases it is shown through within-group degrees of freedom because of singularity of matrices. In such cases it is shown through illustrative examples that principal component analysis is a viable substitute provided that the principal components are ranked according to the canonical variate criterion (ratio of between- to within-group variances) rather than the usual criterion of total variance. This ranking can also be used to select components for subsequent discriminant analysis.