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Robust regression with compositional covariates

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  • Mishra, Aditya
  • Müller, Christian L.

Abstract

Many biological high-throughput datasets, such as targeted amplicon-based and metagenomic sequencing data, are compositional. A common exploratory data analysis task is to infer robust statistical associations between high-dimensional microbial compositions and habitat- or host-related covariates. To address this, a general robust statistical regression framework RobRegCC (Robust Regression with Compositional Covariates) is proposed, which extends the linear log-contrast model by a mean shift formulation for capturing outliers. RobRegCC includes sparsity-promoting convex and non-convex penalties for parsimonious model estimation, a data-driven robust initialization procedure, and a novel robust cross-validation model selection scheme. The procedure is implemented in the R package robregcc. Extensive simulation studies show the RobRegCC's ability to perform simultaneous sparse log-contrast regression and outlier detection over a wide range of settings. To demonstrate the seamless applicability of the workflow to real data, the gut microbiome dataset from HIV patients are analyzed and robust associations between a sparse set of microbial species and host immune response from soluble CD14 measurements are inferred.

Suggested Citation

  • Mishra, Aditya & Müller, Christian L., 2022. "Robust regression with compositional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:csdana:v:165:y:2022:i:c:s0167947321001493
    DOI: 10.1016/j.csda.2021.107315
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    References listed on IDEAS

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    1. Cristofari, Andrea, 2023. "A decomposition method for lasso problems with zero-sum constraint," European Journal of Operational Research, Elsevier, vol. 306(1), pages 358-369.

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