A robust Parafac model for compositional data

ABSTRACT

Compositional data are characterized by values containing relative information, and thus the ratios between the data values are of interest for the analysis. Due to specific features of compositional data, standard statistical methods should be applied to compositions expressed in a proper coordinate system with respect to an orthonormal basis. It is discussed how three-way compositional data can be analyzed with the Parafac model. When data are contaminated by outliers, robust estimates for the Parafac model parameters should be employed. It is demonstrated how robust estimation can be done in the context of compositional data and how the results can be interpreted. A real data example from macroeconomics underlines the usefulness of this approach.

KEYWORDS:

• Three-way data analysis
• Parafac
• compositional data
• log-ratio coordinates
• robust statistics

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

M. Gallo  http://orcid.org/0000-0001-7904-0491

K. Hron  http://orcid.org/0000-0002-1847-6598

Additional information

Funding

The paper is supported by the Operational Program Education for Competitiveness – European Social Fund (project CZ.1.07/2.3.00/20.0170 of the Ministry of Education, Youth and Sports of the Czech Republic), the grants IGA PrF 2017 019 Mathematical Models of the Internal Grant Agency of the Palacký University in Olomouc, COST Action CRoNoS IC1408 and by 2015 funds of the University of Naples – L'Orientale (I) and the support by the Austrian Science Fund (FWF), project I 1910-N26.