Modeling and Analysis of Compositional Data

Chapter 9Compositional processes

Compositions can evolve depending on an external parameter such as space, time, temperature, pressure, or global economic conditions. The external parameter may be continuous or discrete. In general, the evolution is expressed as a function , where represents the external variable and the image is a composition in . In order to model compositional processes, the study of simple models appearing in practice is very important. This allows the analyst to distinguish at a glance features in the data useful to identify the type of process governing the phenomenon. Frequently, its evolution is presented as the evolution of components corresponding to amounts or masses, which are typically positive. Denote these vectors of amounts by , with values in , which, after closure, give the compositional process . Comparing visually the curves of evolution of with ...