Simple correspondence analysis of nominal-ordinal contingency tables

Abstract

The correspondence analysis of a two-way contingency table is now accepted as a very versatile tool for helping users to understand the structure of the association in their data. In cases where the variables consist of ordered categories, there are a number of approaches that can be employed and these generally involve an adaptation of singular value decomposition. Over the last few years, an alternative decomposition method has been used for cases where the row and column variables of a two-way contingency table have an ordinal structure. A version of this approach is also available for a two-way table where one variable has a nominal structure and the other variable has an ordinal structure. However, such an approach does not take into consideration the presence of the nominal variable. This paper explores an approach to correspondence analysis using an amalgamation of singular value decomposition and bivariate moment decomposition. A benefit of this technique is that it combines the classical technique with the ordinal analysis by determining the structure of the variables in terms of singular values and location, dispersion and higher-order moments.