Correspondence Analysis: Theory, Practice and New Strategies

5Non-Symmetrical Correspondence Analysis

5.1 Introduction

In the previous chapters, we have discussed that the origins of ‘modern’ correspondence analysis lay in France during the 1960s. Two decades later, in Italy, a variant of correspondence analysis called non-symmetrical correspondence analysis was developed by Carlo Lauro and Luigi D'Ambra at the University of Naples (Lauro and D'Ambra, 1984; D'Ambra and Lauro, 1989, 1992). While the classical approach to the simple correspondence analysis technique described in Chapter 4 considers variables that are symmetrically associated, non-symmetrical correspondence analysis involves graphically depicting the asymmetric association between two categorical variables in a contingency table.

At this point, it is worth distinguishing what is meant by a symmetric association structure and an asymmetric association structure between the variables of a contingency table. Both terms describe the nature of the dependence between the two categorical variables. For an analysis of categorical variables, we often focus on the study of the interdependence, mutual dependence or symmetric dependence of these variables. That is, a symmetric association structure is one where both variables are effectively treated as predictor variables and neither is considered to be a response variable. This type of association structure has certainly been widely considered in correspondence analysis. However, when one variable can be treated as a response of a ...