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arXiv · 2604.25030

Rectified Fisher-Bingham Model for Compositional Data with Zeros

Eugene Han·Marahi Perez-Tamayo·Hannah D. Holscher·Ruoqing Zhu
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Abstract

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.

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Eugene Han, Marahi Perez-Tamayo, Hannah D. Holscher, Ruoqing Zhu. 2026-04-27. Rectified Fisher-Bingham Model for Compositional Data with Zeros. https://arxiv.org/abs/2604.25030

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