Correspondence Analysis: Theory, Practice and New Strategies

Chapter 11Symmetrical and Non-Symmetrical Three-Way Correspondence Analysis

11.1 Introduction

In this chapter, we present the correspondence analysis variants for three-way contingency tables, bearing in mind that three-way contingency tables are different from multiple contingency tables because the associated data folders are different.

The data collected from a number of subjects based on three categorical variables Y , X and Z are classified using three different modes and are organised into a three-way contingency table that consists of I row, J column and K tube categories, respectively; the row categories are associated with variable Y, the column categories are associated with variable X and the tube categories are associated with variable Z. Extending this idea to multi-way data, one may add new variables, but for the sake of brevity, we confine our attention to three-way contingency tables.

The word way is commonly used to indicate a collection of indices by which the data can be classified, while the word mode is used to indicate the entities that constitute one form of the data array (Kroonenberg 2008, p. 28). Therefore, a three-way contingency tables has three ways and three modes, which are different from correlation or similarity three-way tables, where there are only two modes. See, for example, Figure 11.1 that shows the structure of a three-way contingency table and variable specifications under consideration.

Pieter M. Kroonenberg

Figure 11.1 (a) Example ...