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 are more variables than 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.