The association in two-way ordinal contingency tables through global odds ratios

Hirotsu’s statistic is a suitable measure for studying the association between two variables on an ordinal scale. For visualizing the nature of the association, such a statistic can be decomposed by performing doubly ordered cumulative correspondence analysis. An alternative measure for describing the association between two ordered variables could be global odds ratios. In this paper we consider a generalization of the doubly ordered cumulative correspondence analysis in order to represent the global odds ratios in the two-dimensional plot.