Exploring drug consumption via an ultrametric correlation matrix

In many real applications, the existence of a general concept (a multidimensional phenomenon) composed of nested specific ones is often theorised. In the specialised literature, different sequential methodologies have been proposed to identify a hierarchy of latent dimensions. In this paper, we investigate drug consumption via an ultrametric correlation matrix which allows to detect different, nonoverlapping groups of drugs and their hierarchical relationships, starting from the correlation matrix of the observed data. Since its social and economic relevance, a model-based approach to drug consumption can provide an in-depth understanding of this challenging phenomenon, which turns out to be fundamental to address policies aimed at reducing it.