In this work, we propose a novel framework specifically designed for three-way analysis, emphasizing its utility in examining data related to cost of living and quality of life indices. The core of our approach utilizes a dynamic HJ-Biplot along with a variant of the Tucker3 and Parafac models, employing a sparse technique to compute disjoint components within the loading matrices. This methodology enhances three-way data interpretation and facilitates the generation of new insights. To illustrate the use of this methodology, we include in this manuscript a real example with a three-way table that has ten American countries in the first mode, ten economic variables in the second mode, and six years in the third mode. This case study focuses on analyzing, from a multivariate perspective, the relationship (differences and similarities) between cost of living and quality of life indices in seven South American countries and three North American countries during the period 2019–2024. The analysis carried out has allowed us to characterize the components and obtain important conclusions. The R statistical software was used for all matrix computations.
