Information Technology Reference
In-Depth Information
6
Two-way tables:
biadditive biplots
6.1 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 this chapter we shall be concerned with two-way tables with
p
rows and
q
columns which refer to similar entities - hence our change of notation. The
body of the table may contain
(i) the numerical values of a single variable or
(ii) counts, so defining a contingency table, or
(iii) the values of a single categorical variable.
This chapter concerns problem (i); contingency tables are covered by Chapter 7, while
issue (iii) is covered in Chapter 8. Crucially, in these chapters the body of the table
is regarded as a dependent variable, with the rows and column classifiers treated as
independent variables. In case (i) we shall see that additive or biadditive models may
be fitted and, of particular interest for biplots, additional multiplicative terms included.
Case (iii) may be handled by replacing the categories with optimal scores and then
treated as in (i), but can also be handled by multiple correspondence analysis with three
variables - that labelling the rows, that labelling the columns and, thirdly, the categorical
variable in the body of the table - but then the dependency relationship is ignored (see
Chapter 8).
