Correspondence Analysis: Theory, Practice and New Strategies

8External Stability and Confidence Regions

8.1 Introduction

Correspondence analysis and its variants provide the analyst with statistical tools to graphically depict the symmetric or asymmetric association between two or more nominal or ordinal categorical variables. One issue that needs consideration is whether these graphical displays are reliable in representing the association. By reliable we mean if we draw samples of size n where the same two categorical variables are cross-classified to form a contingency table, will the association between these variable categories from a sample be similar or wildly different to the association from another sample?

When discussing the theory and application underlying the correspondence analysis of a two-way contingency table, our attention has so far been on quantifying this association and visually depicting it; there has been no inferential aspect introduced to our discussion. In this chapter we shall be introducing an inferential paradigm into correspondence analysis by considering the sampling variation of the configuration of points. This shall be achieved by using parametric and non-parametric approaches. In much of the literature on correspondence analysis, the focus has been on the reliability of a point's proximity from another point and from the origin. Here, we shall only consider the proximity of a point from the origin by describing confidence regions for each point in a low-dimensional correspondence plot or biplot.