“…Aitchison and Shen (1985) introduced a simple model approach for compositional data analysis with the transformation of the vector of G components x into a vector y into R G-1 considering an additive ratio log (ALR) function (see also, Rayens & Srinivasan, 1991). Other model approach is introduced in the literature considering the isometric log-ratio (ILR) transformation (Egozcue et al, 2003;Martin-Fernandez, Daunis-Estadella & Mateu-Figueras, 2015), but the inverse transformation to get the proportions in each class is more complex and the obtained results are similar to the results assuming the ALR transformation (Martinez et al, 2019). A simple way to get inferences for the ALR model is the use of a Bayesian approach (Iyengar & Dey, 1996Tjelmeland & Lund, 2003), especially considering Markov Chain Monte Carlo (MCMC) methods (Gelfand & Smith, 1990;Roberts & Smith, 1993).…”