The Stick-Breaking and Ordering Representations of Compositional Data: Copulas and Regression models

Olivier P. Faugeras ()
Additional contact information
Olivier P. Faugeras: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

Post-Print from HAL

Abstract: Compositional Data (CoDa) is usually viewed as data on the simplex and is studied via a log-ratio analysis, following the classical work of Aitchison (1986). We propose to bring to the fore an alternative view of CoDa as a stick breaking process, an approach which originates from Bayesian nonparametrics. The first stick-breaking approach gives rise to a view of CoDa as ordered statistics, from which we can derive "stick-ordered" distributions. The second approach is based on a rescaled stick-breaking transformation, and give rises to a geometric view of CoDa as a free unit cube. The latter allows to introduce copula and regression models, which are useful for studying the internal or external dependence of CoDa. These stick-breaking representations allow to effectively and simply deal with CoDa with zeroes. We establish connections with other topics of probability and statistics like i) spacings and order statistics, ii) Bayesian nonparametrics and Dirichlet distributions, iii) neutrality, iv) hazard rates and the product integral, v) mixability.

Keywords: Compositional data analysis; Stick-breaking representation; Copula; Regression; Distribution (search for similar items in EconPapers)
Date: 2025
Note: View the original document on HAL open archive server: https://hal.science/hal-05064979v1
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Austrian Journal of Statistics, 2025, 55 (2)

Downloads: (external link)
https://hal.science/hal-05064979v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05064979

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().