Exploring Hierarchical Concepts: Theoretical and Application Comparisons

Phenomena are usually multidimensional and their complexity cannot be directly explored via observable variables. For this reason, a hierarchical structure of nested latent concepts representing different levels of abstraction of the phenomenon under study may be considered. In this paper, we provide a comparison between a procedure based on hierarchical clustering methods and a novelty model recently proposed, called Ultrametric Correlation Matrix (UCM) model. The latter aims at reconstructing the data correlation matrix via an ultrametric correlation matrix and supplies a parsimonious representation of multidimensional phenomena through a partition of the observable variables defining a reduced number of latent concepts. Moreover, the UCM model highlights two main features related to concepts: the correlation among concepts and the internal consistency of a concept. The performances of the UCM model and the procedure based on hierarchical clustering methods are illustrated by an application to the Holzinger data set which represents a real demonstration of a hierarchical factorial structure. The evaluation of the different methodological approaches—the UCM model and the procedure based on hierarchical clustering methods—is provided in terms of classification of variables and goodness of fit, other than of their suitability to analyse bottom-up latent structures of variables.