6.5.5 Supplementary elements

The most distinguishing feature of correspondence analysis is the possibility of introducing supplementary elements (variables or objects) into factor graphics. The supplementary elements do not contribute to the orientation of the factorial axis, but their relative contributions to the factorial axes and their coordinates are computed by the correspondence analysis. A simple way to think of such points is that they have a position in the full space, but no mass.

Supplementary points are additional rows and columns of a contingency table, which have meaningful profiles and which exist in the full space of row and column profiles. They can be projected onto the low-dimensional subspace and their positions relative to the active elements can be determined.


The relative contribution of a supplementary point to the eccentricity of an axis (i.e., COS2 j) can be used to judge whether the supplementary point lies to a larger or lesser extent in the plot rather than out of it. This procedure is used: