ABSTRACT
It is frequently the case that two data sets are available on the same set of individuals and we are interested in relationships between them. The previous chapter dealt with one such situation, where sets of biological and environmental variables were observed at the same sampling points, and the idea was to look for the principal gradients (dimensions) of the biological variables that were directly related to the environmental variables. There was an asymmetry in the way these two sets were considered: the biological variables as responses and the environmental variables as predictors. In this chapter we will look at a general framework for analysing two data matrices, where the set of rows, usually individuals or sampling units, are common to both. Each data set implies a configuration of the individuals in the space of its respective variables. We will be mainly interested in symmetric measures of relationship between the two data sets, answering such questions as: What is the concordance between the two configurations? What are the structures common to both data sets? What are the common dimensions? As specific examples we will concentrate on categorical and count data in the correspondence analysis context.
