The Dirichlet distribution provides a tool for modelling data restricted to the unit simplex. It has been used in several disciplines, such as geology, biology, and chemistry. The drawbacks of this distribution are extensively described in Aitchison (1986). They refer to its almost completely negative correlation and strong independence structure. A lot of generalizations were proposed to compensate for this. Among others Monti et al. (2011) proposed a Scaled–Dirichlet distribution as a perturbed random composition with a Dirichlet density. Following the approach suggested by Campbell and Mosimann (1987), and also studied by Hijazi and Jernigan (2009), here we propose a new family of regression models based on the Scaled-Dirichlet distribution. Given a vector of real covariates, one considers the response compositional vector, with a conditional Scaled-Dirichlet distribution. This model is characterized by the fact that its parameters are linear on the covariates. Parameter estimation and prediction issues are explored. An example with real data completes the contribution.
Monti, G., Mateu Figueras, G., Pawlowsky Glahn, V., Egozcue, J. (2014). Scaled-Dirichlet Covariate Models for Compositional Data. In SIS 2014 - 47th SIS Scientific Meeting of the Italian Statistical Society -PROCEEDINGS.
Scaled-Dirichlet Covariate Models for Compositional Data
MONTI, GIANNA SERAFINA;
2014
Abstract
The Dirichlet distribution provides a tool for modelling data restricted to the unit simplex. It has been used in several disciplines, such as geology, biology, and chemistry. The drawbacks of this distribution are extensively described in Aitchison (1986). They refer to its almost completely negative correlation and strong independence structure. A lot of generalizations were proposed to compensate for this. Among others Monti et al. (2011) proposed a Scaled–Dirichlet distribution as a perturbed random composition with a Dirichlet density. Following the approach suggested by Campbell and Mosimann (1987), and also studied by Hijazi and Jernigan (2009), here we propose a new family of regression models based on the Scaled-Dirichlet distribution. Given a vector of real covariates, one considers the response compositional vector, with a conditional Scaled-Dirichlet distribution. This model is characterized by the fact that its parameters are linear on the covariates. Parameter estimation and prediction issues are explored. An example with real data completes the contribution.
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