Correspondence analysis

Correspondence analysis is a graphical technique for representing the information included in a two-way contingency table containing frequency counts. For example, Table 15.2 lists the number of times an attribute (crispy, sugar-free, good with coffee, etc.) is used by consumers to describe a snack (cookies, candies, muffins, etc.).⁵ The method deals with two categorical or discrete quantitative variables and aims at visualizing how row and column profiles relate to each other, by developing indexes that are used as coordinates for depicting row and column categories on a plane. Again, this can be used for assessing product positioning, among other things. Correspondence analysis is another exploratory–interdependence method, which can be considered as a factorial decomposition of a contingency table.

This cursory and superficial overview should illustrate well the richness of multivariate analysis and its potential for applications. We should also mention that:

• The boundaries between multivariate analysis tools are not quite sharp, as some methods can be considered as specific cases of other methods.
• Methods can be combined in practice. For instance, in order to ease the task of a cluster analysis algorithm, we may first reduce problem dimensionality by principal component analysis.