Defining the subjects distance in hierarchical cluster analysis by copula approach

We aim to propose a new measure of the distance to evaluate the dissimilarity between rankings in a hierarchical cluster analysis to segment subjects expressing their preferences by rankings. The proposed index builds upon the Spearman grade correlation coefficient on a transformation of the ordinal variables that describes the rankings of the subjects, calculated by the copula function. In particular by using the copula functions with tail dependence we employ an index particular suitable to emphasizing the agreement on top ranks, when the top ranks are considered more important than the lower ones. We evaluate the performance of our proposal by an illustrative example on selected rankings, showing that the resulting groups contain subjects whose preferences are more similar on the most important, or top, ranks.