Scalable Approximation of the Transformation‐Free Linear Simplicial–Simplicial Regression via Constrained Iterative Reweighted Least Squares

Simplicial–simplicial regression concerns statistical modeling scenarios in which both the predictors and the responses contain vectors constrained to lie on the simplex. Fiksel et al. introduced a transformation‐free linear regression framework for this setting, wherein the regression coefficients are estimated by minimizing the Kullback–Leibler divergence between the observed and fitted compositions, using an expectation‐maximization algorithm for optimization. In this work, we reformulate the problem as a constrained logistic regression model, in line with the methodological perspective of Tsagris, and we obtain parameter estimates via constrained iteratively reweighted least squares. Simulation results indicate that the proposed procedure substantially improves computational efficiency‐yielding speed gains ranging between 4 and 257× while providing estimates and Kullback–Leibler divergence that closely approximate those obtained from the expectation‐maximization algorithm. Real data examples demonstrate the performance of the constrained algorithm and compare it to the expectation‐maximization algorithm.