Correspondence Analysis: Theory, Practice and New Strategies

9Variants of Correspondence Analysis

9.1 Introduction

The techniques described so far are the classical approaches to simple correspondence analysis and non-symmetrical correspondence analysis and their ordinal variations. Despite the differences in the scaling of the singular values that provide varying graphical representations of the association between the variables, a key difference between these techniques are the different measures of association that is considered. Recall that classical correspondence analysis relies on the partition of Pearson's chi-squared statistic, while non-symmetrical correspondence analysis considers the Goodman–Kruskal tau index. This suggests that depending on the structure of the data, other measures of association may be considered. Here we shall highlight three alternative variants of these classical approaches that use alternative measures of association. Of course, one may also consider variants of the scaling of the singular values to obtain, for example, any one of the biplot displays. We also discuss other variants that have established themselves as important branches of the correspondence analysis family tree.

9.2 Correspondence Analysis Using Adjusted Standardised Residuals

We have discussed that simple correspondence analysis can be performed by applying a singular value decomposition to the Pearson residuals:

Haberman (1973) and ...