Hierarchical latent variable models for dimensionality reduction: an application on composite indicators

This thesis is devoted to the development of new hierarchical latent variable models for Dimensionality Reduction with a specific focus on the construction of Composite Indicators (CIs). Since our society is producing a huge quantity of data, the construction of model-based CIs represents an interesting and still open methodological challenge. This dissertation is motivated by the necessity to provide model-based CIs which are built according to a statistical approach avoiding subjective choices (e.g., normative weights), therefore, the new insights and proposals hope to represent a contribution to the current literature. This thesis provides an introduction to CIs, a brief review of the most used methods in Multidimensional Data Analysis framework, a discussion about measurement models and methodological proposals to model latent concepts. Factor Analysis and its hierarchical extensions have been introduced in order to set the starting point of the analysis. A first proposal represents a new latent factor model that could be used for building CIs, it aims to investigate the hierarchical structure of the data in order to define two levels of CIs. The model, named Hierarchical Disjoint Non-Negative Factor Analysis is composed of two novelties: a model which is the two level hierarchical extension of FA and its disjoint extension with non-negative loadings. The latter model is enriched by considerations about the CIs used for tracking coherent policy conclusions. A set of features, properties and rules useful to build "good" CIs have been presented and explained. The last proposal in the thesis represents a new model for positive data correlation matrices which aims to detect reliable concepts and to build the hierarchy from them to the most general one. The proposed models are illustrated both via simulation studies and real data applications, to analyze their performances and abilities. In particular, the main application in this thesis regards the construction of a hierarchically aggregated index for the multidimensional phenomenon Waste Management in European Union. Waste Management is becoming even more important for its impact on human-being's lives, and many data have been produced about it, therefore the construction of a CI able to reduce its dimensionality and to highlight the main dimensions of it has a extraordinary usefulness in order to provide support to EU countries' action and policies.