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In-Depth Information
7
Two-way tables: biplots
associated with
correspondence analysis
7.1 Introduction
Previous chapters have been concerned with biplots for a variety of forms of data matrix
where, typically, the rows refer to
n
samples and the columns to
p
variables. As we
have seen, samples and variables are very different concepts entailing different kinds of
statistical treatment. In the previous chapter we looked at two-way tables with
p
rows
and
q
columns which refer to similar entities. There, the body of the table consists of
numerical values of a single variable playing the role of a dependent variable, while
the two variables represented by the rows and columns have the role of independent
variables. In this chapter, the body of the table is still regarded as a dependent variable
with the rows and column classifiers treated as independent variables. The difference is
that the dependent variable is no longer restricted to be a numerical variable measured
on an interval or ratio scale but is available in the form of counts or frequencies, thus
defining a contingency table. Correspondence analysis (CA) is concerned with the anal-
ysis and visualization of contingency tables, especially two-way contingency tables, and
is discussed in this chapter. Our primary aim will be to understand the several variant
forms of biplot related to CA without going into great detail about the methodology.
Nevertheless, for a proper understanding, some methodological underpinning cannot be
avoided. A CA biplot is very similar visually to the biplots discussed in Chapters 3
(PCA) and 6 (biadditive models). To get a preliminary feeling for the kind of visual-
izations involved, the reader may glance at the examples in Section 7.6 below. CA is
unusual among the methods discussed in this topic in having several variant forms, and
