The generalization of simple correspondence analysis, for two categorical variables, to multiple correspondence analysis where they may be three or more variables, is not straighforward, both from a mathematical and computational point of view. In this paper we detail the exact computational...

We compare two methods for visualising contingency tables and develop a method called the ratio map which combines the good properties of both. The first is a biplot based on the logratio approach to compositional data analysis. This approach is founded on the principle of subcompositional...

The use of simple and multiple correspondence analysis is well-established in social science research for understanding relationships between two or more categorical variables. By contrast, canonical correspondence analysis, which is a correspondence analysis with linear restrictions on the...

Correspondence analysis is introduced in the brand association literature as an alternative tool to measure dominance, for the particular case of free choice data. The method is also used to analyse differences, or asymmetries, between brand-attribute associations where attributes are associated...

Subcompositional coherence is a fundamental property of Aitchison’s approach to compositional data analysis, and is the principal justification for using ratios of components. We maintain, however, that lack of subcompositional coherence, that is incoherence, can be measured in an attempt to...

Although correspondence analysis is now widely available in statistical software packages and applied in a variety of contexts, notably the social and environmental sciences, there are still some misconceptions about this method as well as unresolved issues which remain controversial to this...

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of...

Many multivariate methods that are apparently distinct can be linked by introducing one or more parameters in their definition. Methods that can be linked in this way are correspondence analysis, unweighted or weighted logratio analysis (the latter also known as "spectral mapping"), nonsymmetric...

We consider the joint visualization of two matrices which have common rows and columns, for example multivariate data observed at two time points or split accord-ing to a dichotomous variable. Methods of interest include principal components analysis for interval-scaled data, or correspondence...

The case of two transition tables is considered, that is two square asymmetric matrices of frequencies where the rows and columns of the matrices are the same objects observed at three different time points. Different ways of visualizing the tables, either separately or jointly, are examined. We...