{
  "abstract": "We present a unified, transformation-free linear regression framework tailored for ordinal compositional data, such as distributions across educational levels or aggregate Likert-scale survey responses. Traditional log-ratio approaches often obscure interpretability, ignore the inherent ordering of categories, and struggle with boundary zero values. To overcome these limitations, we propose a deterministic model constrained to the space of column-stochastic transformation matrices, naturally preserving the fundamental geometry of the simplex. By adopting the weighted 1-Wasserstein distance as the loss function, our method directly embeds the ordinal nature of the data into the estimation process. We provide a computationally efficient and globally optimal solution explicitly formulated as a Linear Programming (LP) problem. The framework systematically addresses four distinct regression scenarios, introducing a novel ordinal tensor product to rigorously handle interactions across multiple compositional predictors. Furthermore, we equip the model with a suitable regularization strategy and novel diagnostic tools, including a Wasserstein-based coefficient of determination ($R^2_W$) and an Order Preservation Index (OPI). Extensive simulation studies and two empirical applications demonstrate the robust predictive performance and interpretability of the proposed methodology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05212",
  "author_total": 1,
  "authors": [
    {
      "name": "Beniamino Cappelletti-Montano; Monica Musio; Nicola Piras"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2j6n7ejsg0kn6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05212",
  "fulltext_url": null,
  "id": "2j6n7ejsg0kn6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05212",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Advanced Statistical Methods and Models"
    ]
  ],
  "openalex": "W7220679178",
  "pdf_url": "https://arxiv.org/pdf/2610.05212",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2j6n7ejsg0kn6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05212",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05212"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Regression models for ordinal compositional data",
  "title_text": "Regression models for ordinal compositional data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/2j6n7ejsg0kn6",
  "venue": "arXiv",
  "versions": []
}