Scalable approximation of the 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 linear regression model, that minimizes the Kullback-Leibler divergence from the observed to the fitted compositions, where the EM algorithm is used to estimate the regression coefficients. 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. The simulation studies depict that this algorithm makes the estimation procedure significantly faster, and approximates accurately enough the solution of the EM algorithm.