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Regression for compositions based on a generalization of the Dirichlet distribution

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  • Monique Graf

    (Université de Neuchâtel
    Elpacos Statistics)

Abstract

The simplex is the geometrical locus of D-dimensional positive data with constant sum, called compositions. A possible distribution for compositions is the Dirichlet. In Dirichlet models, there are no scale parameters and the D shapes are assumed dependent on auxiliary variables. This peculiar feature makes Dirichlet models difficult to apply and to interpret. Here, we propose a generalization of the Dirichlet, called the simplicial generalized Beta (SGB) distribution. It includes an overall shape parameter, a scale composition and the D Dirichlet shapes. The SGB is flexible enough to accommodate many practical situations. SGB regression models are applied to data from the United Kingdom Time Use Survey. The R-package SGB makes the methods accessible to users.

Suggested Citation

  • Monique Graf, 2020. "Regression for compositions based on a generalization of the Dirichlet distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 913-936, December.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:4:d:10.1007_s10260-020-00512-y
    DOI: 10.1007/s10260-020-00512-y
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    References listed on IDEAS

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