@MISC{Melillo_multidimensionalanalysis, author = {Via Ponte Don Melillo}, title = {Multidimensional Analysis of Rankings Permutations}, year = {} }

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Abstract

In this paper we illustrate an original approach to factorial analysis of rankings data. The proposed technique is based on the decomposition of the Spearmanâ€™s rank correlation matrix defined on a whole set of permutation. The properties of such correlation matrix will be discussed. The complete set of permutation is defined univocally from the size, n, of the ordering task. Indeed, dealing with the class of untied ordinal data, the dataset to reduce is provided, for any given n, by all the possible permutations of the first n integer numbers. The analysis we propose is performed in two steps: firstly aimed at reducing a complete set of permutation data into a few number of orthogonal factors, we define the rank correlation matrix of the permutation set. The factorial decomposition of such matrix by means of Principal Component Analysis allows to transform the huge data set in a reduced number of factors, each of them representing a fixed, ex-ante, latent ordering system. It is referred as an ex-ante because, at this step, there are no actual observed data in its definition. It will act as a reference system for ex-post real data. In the second step, the ex-post ordinal data (empirical observation) can be attribute to