Compositional data analysis: basic concepts and examples in applied sciences in the agri-food sector

Abstract

Compositional data (CODA) are vectors that describe the different parts of a certain total. Usually, compositional data are presented as vectors of proportions, percentages, concentrations or frequencies. The space to which compositional data belong is called a “simplex of n parts”, which is defined as the set of vectors of n strictly positive components, such that the sum of these components is constant. Since the proportions are expressed as real numbers, there is a temptation to interpret or even analyse compositional data as if they were real multivariate data. This practice can lead to paradoxes or misinterpretations such as spurious correlation and Simpson’s paradox. In applied sciences and engineering, dynamic processes are often studied in which variables evolve over time. A special case of particular interest is the study and characterization of processes in which the variables are compositional and evolve over time (or space). These processes are very common in agri-food and biotechnological sciences. In this type of processes, the systems are represented by compositions and are modelled by value functions in the simplex, defined in intervals of the real line (time, space). This paper presents the compositional linear differential models and their usefulness in the description and estimation of the future behaviour of system variables. Finally, the most important conclusions are discussed so that work with this type of data can be applied in agri-food engineering with reliability guarantees and so that the correct formulation and interpretation of the results obtained is ensured.

Keywords: compositional data, compositions, simplex, Aitchison geometry, compositional differential equations, growth curves, food system.