  Simplicial-simplicial regression refers to the regression setting where both
the responses and predictor variables lie within the simplex space, i.e. they
are compositional. For this setting, constrained least squares, where the
regression coefficients themselves lie within the simplex, is proposed. The
model is transformation-free but the adoption of a power transformation is
straightforward, it can treat more than one compositional datasets as
predictors and offers the possibility of weights among the simplicial
predictors. Among the model's advantages are its ability to treat zeros in a
natural way and a highly computationally efficient algorithm to estimate its
coefficients. Resampling based hypothesis testing procedures are employed
regarding inference, such as linear independence, and equality of the
regression coefficients to some pre-specified values. The performance of the
proposed technique and its comparison to an existing methodology that is of the
same spirit takes place using simulation studies and real data examples.
