The Double Flexible Dirichlet: A Structured Mixture Model for Compositional Data

Vectors of proportions arise in a great variety of fields: chemistry, economics, medicine, sociology and many others. Supposing that a whole can be split into D mutually exclusive and exhaustive categories, vectors describing the percentage of each category on the total are referred to as compositional data. This chapter presents a further generalization of the Dirichlet, called double flexible Dirichlet (DFD), that takes advantage of a finite mixture structure similar to that of the FD (depending on D(D + 1)/2 mixture components) and enables positive covariances. Some theoretical results are shown and an estimation procedure based on the EM algorithm is proposed, including an ad hoc initialization strategy. A simulation study aimed at evaluating the performance of the EM algorithm under several parameter configurations is included.