Optimal designs for a linear-model compositional response

Compositional data play an important role in many disciplines, when the interest is in studying not the total amount but the relative importance or frequency of the involved variables. Due to these proportion/sum constraints, the data belong to a restricted space, the simplex. A special algebraic structure is needed to deal with these kind of data. The use of compositional models has followed an increasing trend during the last years. However, to date not very much has been done about the problem of finding optimal designs for models involving this kind of variables. In this first approach, the application of optimal design theory to models with compositional response is studied, dealing with a possible non-trivial covariance structure between observations. Some analytical results have been obtained, and a clarifying example of application is provided.