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.
Ascari, R., Migliorati, S., Ongaro, A. (2021). The Double Flexible Dirichlet: A Structured Mixture Model for Compositional Data. In Y. Dimotikalis, A. Karagrigoriou, C. Parpoula, C.H. Skiadas (a cura di), Applied Modeling Techniques and Data Analysis 2 Financial, Demographic, Stochastic and Statistical Models and Methods Volume 8 - Big Data, Artificial Intelligence and Data Analysis (pp. 137-152). Wiley [10.1002/9781119821724.ch10].
The Double Flexible Dirichlet: A Structured Mixture Model for Compositional Data
Ascari, R
;Migliorati, S;Ongaro, A
2021
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.