Scaling of Order Dependent Categorical Variables with Correspondence Analysis

摘要

Forms of dependence between categorical variables are introduced which induce successively stronger orderings over the categories of the variables. It is proved that if these forms of dependence are present in contingency tables, the orderings are reflected in the correspondence analysis solution. This explains two important order phenomena which frequently occur in practice. Furthermore a multivariate generalization of the main theorem is given. The results support the use of (multi-) correspondence analysis as a scaling technique for categorical variables.