Correspondence Analysis: Theory, Practice and New Strategies

6Ordered Correspondence Analysis

6.1 Introduction

In the previous chapters we described some of the key features of simple correspondence analysis and non-symmetrical correspondence analysis. However, without some prior amendment, these techniques are unable to capture certain complex association structures that may exist in the contingency table. Nor do they take into consideration the structure of variables with ordered categories. For this reason, we shall discuss in this chapter an approach to simple correspondence analysis that considers the ordered structure of the categories and is able to detect and provide a meaningful quantification of complex association structures that may exist in the data.

Before we discuss this approach to ordered simple correspondence analysis, we shall first consider the application of the classical approach to simple correspondence analysis to an artificial contingency table with a very apparent non-linear association structure. Suppose we have selected a random sample of 574 adults and categorised them according to their general knowledge level (rated on a seven-point scale) and the age bracket to which they belong. These artificial data are summarised as Table 6.1 and are given the R object name knowledge.dat. We can see from these data that the general knowledge of those who are in the oldest category are either extremely poor or excellent, while most of the young adults aged between 18 and 24 have an adequate general knowledge.

Table 6.1 ...