  A folded type model is developed for analyzing compositional data. The
proposed model involves an extension of the $\alpha$-transformation for
compositional data and provides a new and flexible class of distributions for
modeling data defined on the simplex sample space. Despite its rather seemingly
complex structure, employment of the EM algorithm guarantees efficient
parameter estimation. The model is validated through simulation studies and
examples which illustrate that the proposed model performs better in terms of
capturing the data structure, when compared to the popular logistic normal
distribution, and can be advantageous over a similar model without folding.
