Compound compositional data processes (original) (raw)

Compositional data is non-negative data subject to the unit sum constraint. The logistic normal distribution provides a framework for compositional data when it satisfies subcompositional coherence in that the inference from a subcomposition should be the same based on the full composition or the sub-composition alone. However, in many cases sub-compositions are not coherent because of additional structure on the compositions, which can be modelled as process(es) inducing change. Sometimes data are collected with a model already well validated and hence with the focus on estimation of the model parameters. Alternatively, sometimes the appropriate model is unknown in advance and it is necessary to use the data to identify a suitable model. In both cases, a hierarchy of possible structure(s) is very helpful. This is evident in the evaluation of, for example, geochemical and household expenditure data. In the case of geochemical data, the structural process might be the stoichiometric ...