ABSTRACT
This chapter deals with quantification of categorical data, another area in which
R.P.McDonald’s contribution is well known (e.g., McDonald, 1983; McDonald, Torii, &
Nishisato, 1979).
Under the umbrella of quantification theory, many names have been proposed,
including optimal scaling, dual scaling, correspondence analysis, biplot, the Gifi system
of quantification, and Hayashi’s theory of quantification. These methods are all closely
related to one another or basically the same. They were proposed for most economical
multidimensional decomposition of categorical data, which turned out to be nothing but
singular value decomposition (SVD) (Beltrami, 1873; Eckart & Young, 1936; Jordan,
1874; Schmidt, 1907) applied to categorical data. Before introducing SVD, let us look at
some familiar problems in which SVD is used.