Compositional data consist of nonnegative proportions of some whole subject to the constraint that the proportions sum to 1. We propose a model for the analysis of multivariate compositional data (multiple vectors of compositional data) which includes covariate information. The proposed model has several advantages over the traditional logistic normal model used in the analysis of compositional data. The model can also be considered in terms of a chain graphical model and several related results will be discussed. We adopt a Bayesian approach for estimating the parameters of the model.
The model is applied to data from an emerging area of research in ecology, the analysis of functional species assemblages. In essence, the analysis of functional assemblages is concerned with determining and predicting the composition of individuals categorized using different life history traits instead of strict taxa names. Using a Gibbs sampling approach, we apply the proposed model to a data set of fish species richness in the mid-Atlantic region of the U.S.