Ordination in the presence of group structure, for general multivariate data

A low-dimensional representation of multivariate data is often sought when the individuals belong to a set ofa-priori groups and the objective is to highlight between-group variation relative to that within groups. If all the data are continuous then this objective can be achieved by means of canonical variate analysis, but no corresponding technique exists when the data are categorical or mixed continuous and categorical. On the other hand, if there is noa-priori grouping of the individuals, then ordination of any form of data can be achieved by use of metric scaling (principal coordinate analysis). In this paper we consider a simple extension of the latter approach to incorporate grouped data, and discuss to what extent this method can be viewed as a generalization of canonical variate analysis. Some illustrative examples are also provided.