Dissimilarity measure for ranking data via mixture of copulae

We propose a new dissimilarity measure for ranking data by using a mixtureof copula functions. This measure evaluates the dissimilarity between subjects expressingtheir preferences by rankings in order to classify them by a hierarchical cluster analysis. Theproposed measure is based on the Spearman’s grade correlation coefficient on a transforma-tion, operated by the copula, of the rank denoting the level of the importance assigned bysubjects in the classification process. The mixtures of copulae are a flexible way to modeldifferent types of dependence structures in the data and to consider different situations in theclassification process. The advantage by using mixtures of copulae with lower and upper taildependence is that we can emphasize the agreement on extreme ranks, when extreme ranksare considered more important. An example on simulated data illustrates our proposal