Transformation-free linear simplicial-simplicial regression via constrained iterative reweighted least squares

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. \cite{fiksel2022} proposed a transformation-free lienar regression model, that minimizes the Kullback-Leibler divergence from the observed to the fitted compositions was recently proposed. To effectively estimate the regression coefficients the EM algorithm was employed. We formulate the model as a constrained logistic regression, in the spirit of \cite{tsagris2025}, and we estimate the regression coefficients using constrained iteratively reweighted least squares. This approach makes the estimation procedure significantly faster.