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, uses less memory, and in some cases gives a better solution.

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，该模型最小化观测成分数据与拟合成分数据之间的Kullback-Leibler散度，并采用EM算法估计回归系数。受\\cite{tsagris2025}启发，我们将该模型表述为约束逻辑回归，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，该算法显著加快了估计过程，降低了内存占用，并在某些情况下提供了更优的解决方案。