Non-metric unfolding on augmented data matrix: a copula-based approach

In this contribution an effective procedure to avoid degeneracies in multidimensional unfolding for preference rank data is proposed. We adopt the strategy of augmenting the data matrix, trying to build a complete dissimilarity matrix, by using copula-based association measures among rankings (individuals), and between rankings and objects (namely, a rank-order representation of the objects through tied rankings). Our proposal is able to both recover the order of the preferences and reproduce the position of both rankings and objects in a geometrical space. Application on real datasets show that our procedure returns non-degenerate unfolding solutions.