Studying the dependence between ordinal-nominal categorical variables via orthogonal polynomials

Abstract

In situations where the structure of one of the variables of a contingency table is ordered recent theory involving the augmentation of singular vectors and orthogonal polynomials has shown to be applicable for performing symmetric and non-symmetric correspondence analysis. Such an approach has the advantage of allowing the user to identify the source of variation between the categories in terms of components that reflect linear, quadratic and higher-order trends. The purpose of this paper is to focus on the study of two asymmetrically related variables cross-classified to form a two-way contingency table where only one of the variables has an ordinal structure.

Keywords:

• ordered categorical variables
• non-symmetric correspondence analysis
• bivariate moment decomposition
• singular value decomposition
• orthogonal polynomials