Specification and identification issues in models involving a latent hierarchical structure

The object of this paper is to consider specification and identification problems for the case of models involving a latent hierarchical structure. After making some characteristics of such models explicit, the paper proposes a strategy of model specification characterized by a progressive introduction of hypotheses. Such a strategy allows us a suitable control of the contextual interpretability of each hypothesis. A particular care is devoted to the statistical role of each statistical unit. The difficult identification problem of a mixture is analysed by taking advantage of the decomposition of a global model into contextually meaningful submodels; general results for the identifiability of the statistical model are given. The last section exemplifies how to use the results of the paper for the case of ultrastructural models, mainly known in the biometric literature.