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Multidimensional phenomena are usually characterized by nested latent dimensions associated, in turn, with observed variables. These phenomena, for instance, poverty, well-being, and sustainable development, can often differ across countries, or cities within countries, in terms of dimensions, other than in their relationships to each other, on the one hand, and their importance in the definition of the general concept, on the other hand. This paper discusses several parsimonious structures of the covariance matrix reconstructing relationships among variables which can be implemented in Gaussian mixture models to study complex phenomena in heterogeneous populations.