Correspondence Analysis: Theory, Practice and New Strategies

Chapter 3Methods of Decomposition

3.1 Introduction

At the heart of correspondence analysis is the need to reduce a multidimensional space to a low-dimensional space while capturing as much of the association structure as possible. As we have seen in Chapter 2, measurement of this association can be made in a number of different ways and lies at the heart of much that defines what categorical data analysis is. The history of the development of techniques for categorical data analysis has been described by, for example, Agresti (2002, pp. 619–631), Bishop et al. (1975), Imrey et al. (1981) and Fienberg and Rinaldo (2007). Much of the history on the latter developments involve the quantitative aspects (such as the impact log-linear models have had), and only a few consider the graphical analysis of categorical data analysis, which has developed over the last 50 years and blossomed only relatively recently. Since correspondence analysis deals extensively with contingency tables, the interested reader should also refer to Killion and Zahn (1976) who provide an impressive bibliography on the history and development of contingency tables up to 1974.

For now, we shall turn our attention to concepts other than the quantification of association in categorical data. We shall consider the issue of dimension reduction.

3.2 Reducing Multidimensional Space

Space, traditionally, exists in three dimensions. However, the early twentieth century saw this view changed to four dimensions with ...