Tools for compositional data with a total. (April 2015)

• Record Type: Journal Article
• Authors: Pawlowsky-Glahn, Vera; Egozcue, Juan José; Lovell, David
• Other Names: Filzmoser Peter guest-editor.; Hron Karel guest-editor.
• Is Part Of: Statistical modelling. Volume 15:Number 2(2015)
• Page Start: 175
• Page End: 190
• Publication Date: 2015-04
• Subjects: Aitchison geometry -- Euclidean isometry -- ilr coordinates -- product space -- simplex; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X14535526
• Languages: English
• ISSNs: 1471-082X

Abstract

Compositional data analysis usually deals with relative information between parts where the total (abundances, mass, amount, etc.) is unknown or uninformative. This article addresses the question of what to do when the total is known and is of interest. Tools used in this case are reviewed and analysed, in particular the relationship between the positive orthant of D -dimensional real space, the product space of the real line times the D -part simplex, and their Euclidean space structures. The first alternative corresponds to data analysis taking logarithms on each component, and the second one to treat a log-transformed total jointly with a composition describing the distribution of component amounts. Real data about total abundances of phytoplankton in an Australian river motivated the present study and are used for illustration.