Simplicia-simplicial regression concerns statistical modeling scenarios in which both the predictors and the responses are vectors constrained to lie on the simplex. \cite{fiksel2022} 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 (EM) algorithm for optimization. In this work, we reformulate the problem as a constrained logistic regression model, in line with the methodological perspective of \cite{tsagris2025}, 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 from $6\times--326\times$-while providing estimates that closely approximate those obtained from the EM-based approach.

翻译：单纯形-单纯形回归涉及预测变量和响应变量均为受限于单纯形上的向量的统计建模场景。\cite{fiksel2022} 为此场景引入了一种变换自由的线性回归框架，其中通过最小化观测组合与拟合组合之间的 Kullback-Leibler 散度来估计回归系数，并使用期望最大化（EM）算法进行优化。在本工作中，我们依据 \cite{tsagris2025} 的方法论视角，将该问题重新表述为一个约束逻辑回归模型，并通过约束迭代重加权最小二乘法获得参数估计。模拟结果表明，所提出的方法显著提高了计算效率——速度提升范围在 $6\times--326\times$ 之间——同时提供的估计值非常接近基于 EM 方法所得的结果。