What is CoDA?

...parts of a whole...


Compositional Data Analysis (CoDA) refers to the analysis of compositional data (CoDa), which have been defined historically as random vectors with strictly positive components whose sum is constant (e.g., 100, one, a million). More recently, the term covers all those vectors representing parts of a whole which only carry relative information, thus including not only parts per unit or percentages, but also molar compositions.

Typical examples in different fields are: geology (geochemical elements), economy (income/expenditure distribution), medicine (body composition: fat, bone, lean), questionnaire surveys (ipsative data), food industry (food composition: fat, sugar, etc), chemistry (chemical composition), ecology (abundance of different species), paleontology (foraminifera taxa), agriculture (nutrient balance ionomics), sociology (time-use surveys), environmental sciences (soil contamination), and genetics (genotype frequency). This type of data appears in most applications, and the interest and importance of consistent statistical methods cannot be underestimated. Although the concern of the problems related to them was kept alive mainly by researchers from the field of Geosciences, in particular by members of the International Association for Mathematical Geosciences, the awareness of coherent methods is growing in the environmental and biological sciences.

Why choose us

...forum for the exchange...


This hot topic of research has nowadays a broad impact in these fields. However, it took a long time to find a solution to the problem of how to perform a proper statistical analysis of this type of data, i.e. to solve the problem of the spurious correlation, as it was named by Karl Pearson back in 1897, or the closure problem as called by Felix Chayes in the 1960's. Because standard statistical techniques loose their applicability and classical interpretation when applied to compositional data, new techniques were needed. No theoretically sound solution was proposed until the 1980's, when John Aitchison set forth a consistent theory based on log-ratios. Later developments have shown that the mathematical foundation of a proper statistical analysis for this type of data is based on the definition of a specific geometry on the simplex (the sample space of compositional data). Based on it, is possible to rigorously develop any statistical analysis (cluster analysis, discriminant analysis, factor analysis, regression models, to mention just a few).

Practitioners interested in CoDa find in this web site a forum for the exchange of information, material and ideas. This web site has been planned, and is currently maintained, by the members of the Research Group on Compositional Data Analysis at the Dept. Informàtica, Matemàtica Aplicada i Estadística (IMAE-UdG) under the projects COmpositional Data Analysis and RElated meThOdS (CODA-RETOS) and COmpositional and Spatial Data Analysis (COSDA). The core of the group belongs to the University of Girona (UdG), and includes members from the Technical University of Catalonia (UPC), and Biomathematics & Statistics Scotland (BioSS). All the researchers whose interest goes from real case studies to the mathematical foundations of CoDA are welcomed! Join us!

Work team

...let's start working on...


Vera Pawlowsky-Glahn

PhD in Mathematics. Full Professor (UdG).

Germà Coenders

PhD in Management Sciences. Titular Professor (UdG).

Jan Graffelman

PhD in Statistics. Titular Professor (UPC).

Glòria Mateu-Figueras

PhD in Statistics. Associated Professor (UdG).

Santiago Thió-Fdz.-de-Henestrosa

PhD in Computer Science. Titular Professor (UdG).

Juan José Egozcue

PhD in Physics. Full Professor
(UPC).

Pepus Daunis-i-Estadella

PhD in Statistics. Titular Professor (UdG).

Eusebi Jarauta

PhD in Industrial Engineering. Titular Professor (UPC).

Maribel Ortego

PhD in Mathematics. Associated Professor (UPC).

Marina Vives-Mestres

PhD in Statistics. Researcher and part-time university lecturer (UdG).

Carles Barceló-Vidal

PhD in Statistics. Emeritus Professor (UdG).

Berta Ferrer-Rosell

PhD in Tourism. Visiting lecturer at University of Lleida (UdL).

Josep A. Martín-Fernández

PhD in Statistics. Titular Professor (UdG).

Javier Palarea-Albaladejo

PhD in Statistics. Senior Statistical Scientist (BioSS).

Who is Who?

...some CoDa-people...