Cumulative Correspondence Analysis using Orthogonal Polynomials

Taguchi's statistic has long been known to be a more appropriate measure of association the dependence for ordinal variables than the Pearson chi-squared statistic. Therefore, there is some advantage in using Taguchi's statistic in the correspondence analysis context when a two-way contingency table consists at least an ordinal categorical variable. The aim of this paper, considering contingency table with two ordinal categorical variables, is to show a decomposition of Taguchi's index into linear, quadratic and higher order components. This decomposition has been developed using Emerson's orthogonal polynomials. Moreover two cases study to explain the methodology has been analyzed.