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Abstract: In many applications, data are not represented by a single number but by a vector of non-negative components that sum to one. Such data are called compositional, because each observation represents parts of a whole and therefore lies in the simplex. In several contexts, the components may correspond to ordered categories — such as levels of agreement, risk classes, or rating scales — so that an ordinal structure naturally arises. We aim to study a regression model defined on the simplex, where the response is ordinal, while the covariates may be either ordinal or nominal. To this end, we propose a regression approach based on the Wasserstein distance from optimal transport theory. The Wasserstein metric incorporates the ordering of categories by measuring the minimal “effort” required to move mass across them, providing a principled way to model changes while respecting the simplex structure. The resulting model respects both the compositional and ordinal nature of the data, offers a clear geometric interpretation in terms of mass displacement, and yields a simple and interpretable regression operator describing how covariates shift mass across ordered categories.