Teresa Kowalczyk, Alicja Ciok,
Elzbieta Pleszczynska, Wieslaw Szczesny

Grade Dependence in Bivariate Mixed Data.
A Uniform Approach Based on Concentration Curve

815

Abstract

A particular system of bivariate dependence measures is suggested. It consists of function-valued measures and the corresponding numerical measures. Dependence of Y on X is distinguished from that of X on Y. The numerical as well as function-valued measures of Y on X form hierarchical structures. Each structure consists of a measure of monotone dependence (when both variables are treated as ordinal) and of two measures of absolute dependence (one where Y is treated as ordinal and X as nominal, and another where both variables are treated as nominal). The measures are universally applicable for pairs freely formed from continuous, discrete, or discrete-continuous variables. This is possible due to randomized grade transformations applied to both variables. Non-randomized grade transformations are also investigated. The system introduces a unified approach to bivariate dependence and forms the background of the grade version of the bivariate correspondence analysis. The so-called Citation Data is used as an example of exceptionally irregular pattern of dependence in a contingency table.