Scaling of order dependent categorical variables with correspondence analysis : Preprint

In this paper we introduce successively stronger forms of ordinal dependence between categorical variables, corresponding to orderings over the categories of the variables. In our main theorem it is proved that if these forms of dependence are present in contingency tables, then the orderings are reflected in the correspondence analysis solution, whatever a priori ordering may have been given to the categories. This explains two important order phenomena which frequently occur in practice. Furthermore a multivariate generalization of the main theorem is given. The results in this paper support the use of (multi-) correspondence analysis as a scaling technique for categorical variables.