We consider the problem of modelling the conditional distribution of a response given a vector of
covariates x when the response is a compositional data vector u. That is, u is defined on the unit
simplex [...]
This definition of the unit simplex differs subtly from that of Aitchison (1982), as we relax the con-
dition that the components of u must be strictly positive. Under this scenario, use of the ratio (or
logratio) to compare different compositions is not ideal since it is undefined in some instances, and
subcompositional analysis is also not appropriate due to the possibility of division by zero. It has long
been recognised that the square root transformation [...]
transforms compositional data (including zeros) onto the surface of the (p-1)-dimensional hyperspher
