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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.25030 |
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| _version_ | 1866911627855527936 |
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| author | Han, Eugene Perez-Tamayo, Marahi Holscher, Hannah D. Zhu, Ruoqing |
| author_facet | Han, Eugene Perez-Tamayo, Marahi Holscher, Hannah D. Zhu, Ruoqing |
| contents | This paper introduces a rectified and renormalized Fisher-Bingham model for compositional data with zeros, motivated in part by the presence of zeros in microbiota studies. The approach represents compositions through a square-root transformation that maps data to the positive orthant of the unit sphere, and models them via a latent Fisher-Bingham followed by a deterministic transformation that induces exact zeros. This construction yields a coherent likelihood without requiring zero imputation or separate modeling of zero and nonzero components. Parameter estimation is performed using a Monte Carlo expectation-maximization algorithm that accommodates the latent structure. We further develop a score test for detecting structured differences in composition across groups, providing a parametric alternative to commonly used distance-based methods. Simulation studies demonstrate that the proposed method closely approximates the induced distribution and achieves higher power for detecting structured compositional changes, particularly when observations include many zero-valued components. An application to a dietary intervention study illustrates that the method identifies meaningful microbiota shifts not detected by standard approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25030 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rectified Fisher-Bingham Model for Compositional Data with Zeros Han, Eugene Perez-Tamayo, Marahi Holscher, Hannah D. Zhu, Ruoqing Methodology This paper introduces a rectified and renormalized Fisher-Bingham model for compositional data with zeros, motivated in part by the presence of zeros in microbiota studies. The approach represents compositions through a square-root transformation that maps data to the positive orthant of the unit sphere, and models them via a latent Fisher-Bingham followed by a deterministic transformation that induces exact zeros. This construction yields a coherent likelihood without requiring zero imputation or separate modeling of zero and nonzero components. Parameter estimation is performed using a Monte Carlo expectation-maximization algorithm that accommodates the latent structure. We further develop a score test for detecting structured differences in composition across groups, providing a parametric alternative to commonly used distance-based methods. Simulation studies demonstrate that the proposed method closely approximates the induced distribution and achieves higher power for detecting structured compositional changes, particularly when observations include many zero-valued components. An application to a dietary intervention study illustrates that the method identifies meaningful microbiota shifts not detected by standard approaches. |
| title | Rectified Fisher-Bingham Model for Compositional Data with Zeros |
| topic | Methodology |
| url | https://arxiv.org/abs/2604.25030 |