2024/03/28 by Michail Tsagris, Tsagris, Michail · 2 citations
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2403.19835
openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 strategy behind the formulation of the new model is implemented is related to an existing methodology, that is of the same spirit, showcasing how other similar models can be employed as well. Finally, the performance of the proposed technique and its comparison to the existing methodology takes place using simulation studies and real data examples.