ABSTRACT
The objective of correspondence anaysis (CA) is to visualize a table of data in a low-dimensional subspace with optimal explanation of inertia. When additional external information is available for the rows or columns, these can be displayed as supplementary points that do not play any role at all in determining the solution (see Chapter 12). By contrast, we may actually want the CA solution to be directly related to some external variables, in an active rather than a passive way. The context where this often occurs is in environmental research, where information on both biological species composition and environmental parameters are available at the same sampling locations. Here the low-dimensional subspace is required that best explains the biological data but with the condition that the space is forced to be related to the environmental data. This adaptation of CA to the situation where the dimensions are assumed to be responses in a regression-like relationship with external variables is called canonical correspondence analysis, or CCA for short.
