Weighted cumulative correspondence analysis based on a particular cumulative power divergence family
本文提出一种基于累积频率的加权累积幂散度族，并扩展了加权累积卡方型检验的对应分析方法，用于改进有序分类变量关联性的研究。
Abstract The Pearson’s $$X^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>X</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> statistic and the likelihood ratio statistic $$G^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>G</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> 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.