Dimensionality Reduction Methods for Contingency Tables with Ordinal Variables (original) (raw)

Several extensions of correspondence analysis have been introduced in literature coping with the possible ordinal structure of the variables. They usually obtain a graphical representation of the interdependence between the rows and columns of a contingency table, by using several tools for the dimensionality reduction of the involved spaces. These tools are able to enrich the interpretation of the graphical planes, providing also additional information, with respect to the usual singular value decomposition. The main aim of this paper is to suggest an unified theoretical framework of several methods of correspondence analysis coping with ordinal variables. Keywords Ordinal variables ⋅ Single and double cumulative correspondence analysis ⋅ Orthogonal polynomials ⋅ Generalized singular value decomposition 1 Introduction Correspondence Analysis (CA) is a widely used tool for obtaining a graphical representation of the interdependence between the rows and columns of a contingency table, and it is usually performed by applying a generalized singular value decomposition to the standardised residuals of a two-way contingency table obtaining a