Compositional regression using principal nested spheres
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910160208789504 |
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| author | Monem, Mymuna Dryden, Ian L. George, Florence Quinete, Natalia Soares |
| author_facet | Monem, Mymuna Dryden, Ian L. George, Florence Quinete, Natalia Soares |
| contents | Regression with compositional responses is challenging due to the nonlinear geometry of the simplex and the limitations of Euclidean methods. We propose a regression framework for manifold-valued data based on mappings to statistically tractable intermediate spaces. For compositional data, responses are embedded in the positive orthant of the sphere and analysed using Principal Nested Spheres (PNS), yielding a cylindrical intermediate space with a circular leading score and Euclidean higher-order scores. Regression is performed in this intermediate space and fitted values are mapped back to the simplex. A simulation study demonstrates good performance of PNS-based regression. An application to environmental chemical exposure data illustrates the interpretability and practical utility of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20727 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compositional regression using principal nested spheres Monem, Mymuna Dryden, Ian L. George, Florence Quinete, Natalia Soares Methodology Applications 62R30 Regression with compositional responses is challenging due to the nonlinear geometry of the simplex and the limitations of Euclidean methods. We propose a regression framework for manifold-valued data based on mappings to statistically tractable intermediate spaces. For compositional data, responses are embedded in the positive orthant of the sphere and analysed using Principal Nested Spheres (PNS), yielding a cylindrical intermediate space with a circular leading score and Euclidean higher-order scores. Regression is performed in this intermediate space and fitted values are mapped back to the simplex. A simulation study demonstrates good performance of PNS-based regression. An application to environmental chemical exposure data illustrates the interpretability and practical utility of the method. |
| title | Compositional regression using principal nested spheres |
| topic | Methodology Applications 62R30 |
| url | https://arxiv.org/abs/2603.20727 |