Dissimilarity measure for ranking data via mixture of copulae

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