Lorenz Zonoids and Dependence Measures: A Proposal

Abstract

Recently, the analysis of ordered and non-ordered categorical variables has assumed a relevant role, especially with regard to the evaluation of customer satisfaction, health and educational effectiveness. In such real contexts, the study of dependence relations among the involved variables represents an attractive research field. However, the categorical nature of variables does not always successfully allow the application of the existing standard dependence measures, since categorical data are not specified according to a metric scale. In fact, the aforementioned statistical methods are more appropriate in a purely quantitative setting, because based on the Euclidean distance. Our purpose aims at overcoming these restrictions by extending the dependence study in a quali–quantitative perspective. The idea is focused on employing specific statistical tools, such as the Lorenz curves and the so-called Lorenz zonoids. A novel Lorenz zonoids-based relative dependence measure is proposed as an alternative to the partial correlation coefficient to establish each categorical covariate contribution in a multiple linear regression model.