Canonical variate analysis

In studies of dependency it is often useful to distinguish between studies of relationship and studies of structure. The term structure is used here to refer to the way in which the sample is organized or constructed. In studies of relationship it is the connections between two sets of observed or measured variables which are of interest. In structural investigations, on the other hand, it is affinities among subsamples making up a sample with respect to p response variables considered simultaneously which are of interest. For this purpose a set of q artificial variables may be created to account for the design characteristics of the survey or experiment which gave rise to the data, or to embody hypotheses concerning structural relationships among subsamples. In this chapter we shall be concerned with the use of canonical analysis in structural investigations of these kinds. The topic is a large one and we cannot hope to do more than touch upon a few selected aspects. Many of the theoretical results presented are illustrated by worked, numerical examples in Chaps. 10 and 11.