Statistics and Computing

, Volume 27, Issue 4, pp 963–983 | Cite as

A structured Dirichlet mixture model for compositional data: inferential and applicative issues

  • Sonia Migliorati
  • Andrea Ongaro
  • Gianna S. Monti


The flexible Dirichlet (FD) distribution (Ongaro and Migliorati in J. Multvar. Anal. 114: 412–426, 2013) makes it possible to preserve many theoretical properties of the Dirichlet one, without inheriting its lack of flexibility in modeling the various independence concepts appropriate for compositional data, i.e. data representing vectors of proportions. In this paper we tackle the potential of the FD from an inferential and applicative viewpoint. In this regard, the key feature appears to be the special structure defining its Dirichlet mixture representation. This structure determines a simple and clearly interpretable differentiation among mixture components which can capture the main features of a large variety of data sets. Furthermore, it allows a substantially greater flexibility than the Dirichlet, including both unimodality and a varying number of modes. Very importantly, this increased flexibility is obtained without sharing many of the inferential difficulties typical of general mixtures. Indeed, the FD displays the identifiability and likelihood behavior proper to common (non-mixture) models. Moreover, thanks to a novel non random initialization based on the special FD mixture structure, an efficient and sound estimation procedure can be devised which suitably combines EM-types algorithms. Reliable complete-data likelihood-based estimators for standard errors can be provided as well.


Simplex distribution Dirichlet mixture Identifiability Multimodality EM type algorithms 


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Economics, Management and StatisticsUniversity of Milano-BicoccaMilanItaly
  2. 2.NeuroMi - Milan Center for NeuroscienceMilanItaly

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