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.

翻译：单纯形-单纯形回归指响应变量和预测变量均位于单纯形空间（即均为成分数据）的回归设定。\\cite{fiksel2022}提出了一种无变换线性回归模型，该模型通过最小化观测成分数据与拟合成分数据之间的Kullback-Leibler散度进行参数估计，并采用EM算法求解回归系数。本研究遵循\\cite{tsagris2025}的思想，将该模型构建为约束逻辑回归模型，并采用约束迭代重加权最小二乘法估计回归系数。仿真研究表明，该算法显著提升了估计过程的计算效率，并能以足够高的精度逼近EM算法的解。