Biplots in correspondence analysis

Conditions under which correspondence analysis maps are biplots are discussed, as well as the interpretation of such biplots. It is shown that the asymmetric map which jointly displays the profiles and the vertices which define the unit vectors in the profile space is a biplot. A number of different ways of interpreting this joint plot are discussed, some of these being dependent on the choice of the x2 metric in the profile space. Biplot axes can be defined and calibrated on the zero-to-one profile scale in the usual way to recover approximations to the individual profile elements. Finally, the biplot interpretation in the context of multiple correspondence analysis is discussed. It is pointed out that joint correspondence analysis leads to a joint display of several variables which can be calibrated in a similar fashion to recover profile elements of the subtables of the Burt matrix.