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. For this setting, constrained least squares, where the regression coefficients themselves lie within the simplex, is proposed. The model is transformation-free but the adoption of a power transformation is straightforward, it can treat more than one compositional datasets as predictors and offers the possibility of weights among the simplicial predictors. Among the model's advantages are its ability to treat zeros in a natural way and a highly computationally efficient algorithm to estimate its coefficients. Resampling based hypothesis testing procedures are employed regarding inference, such as linear independence, and equality of the regression coefficients to some pre-specified values. The performance of the proposed technique and its comparison to an existing methodology that is of the same spirit takes place using simulation studies and real data examples.

翻译：单纯形-单纯形回归指的是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。针对该设定，本文提出了约束最小二乘方法，其中回归系数本身也位于单纯形空间内。该模型无需进行数据变换，但可以方便地引入幂变换处理；它能够处理多个成分数据集作为预测变量，并允许在单纯形预测变量之间设置权重。该模型的优势包括：能够以自然方式处理零值数据，以及具有计算效率极高的系数估计算法。在统计推断方面，本文采用基于重采样的假设检验程序来处理线性独立性、回归系数与预设值的相等性等问题。通过模拟研究和实际数据案例，对所提技术的性能及其与同类现有方法进行了比较分析。