Weighted cumulative correspondence analysis based on a particular cumulative power divergence family

Abstract

AbstractThe Pearson’s $$X^2$$ X 2 statistic and the likelihood ratio statistic $$G^2$$ G 2 are most frequently used for testing independence or homogeneity, in two-way contingency table. These indexes are members of a continuous family of Power Divergence (PD) statistics, but they perform badly in studying the association between ordinal categorical variables. Taguchi’s and Nair’s statistics have been introduced in the literature as simple alternatives to Pearson’s index for contingency tables with ordered categorical variables. It’s possible to show, using a parameter, how to link Taguchi’s and Nair’s statistics obtaining a new class called Weighted Cumulative Chi-Squared (WCCS-type tests). Therefore, the main aim of this paper is to introduce a new divergence family based on cumulative frequencies called Weighted Cumulative Power Divergence. Moreover, an extension of Cumulative Correspondence Analysis based on WCCS and further properties are shown.