Ultrametric latent variable models: a new approach for composite indicators' construction
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: factor model, latent, ultrametric
Session: IPS 710 - Advances in Multivariate Statistical Methods: Current Insights and Future Prospects
Monday 6 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
Abstract
This paper presents a novel methodology for modeling the dependence structure of observed variables. The approach involves reconstructing their correlation matrix by considering a hierarchy of latent factors that generate an ultrametric correlation matrix. The proposed ultrametric factor analysis model is shown to produce reliable, unidimensional, scale-invariant, and uniquely hierarchical factors. This method addresses the shortcomings of traditional factor analysis techniques, which often oversimplify the complex and multidimensional relationships among variables. The paper provides a comprehensive mathematical description of the model along with an algorithm for parameter estimation.