Dimensionality reduction methods for contingency tables with ordinal variables

Correspondence analysis is a widely used tool for obtaining a graphical representation of the interdependence between the rows and columns of a contingency table, by using a dimensionality reduction of the spaces. The maximum information regarding the association between the two categorical variables is then visualized allowing to understand its nature. Several extensions of this method take directly into account the possible ordinal structure of the variables by using different dimensionality reduction tools. Aim of this paper is to present an unified theoretical framework of several methods of correspondence analysis with ordinal variables.