A Bayesian Zero-Inflated Dirichlet-Multinomial Regression Model for Multivariate Compositional Count Data

Matthew D. Koslovsky

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arXiv · 2302.12283

A Bayesian Zero-Inflated Dirichlet-Multinomial Regression Model for Multivariate Compositional Count Data

Matthew D. Koslovsky

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Abstract

The Dirichlet-multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data generated by high-throughput sequencing technology in omics research due to its ability to accommodate the compositional structure of the data as well as overdispersion. A major limitation of the DM distribution is that it is unable to handle excess zeros typically found in practice which may bias inference. To fill this gap, we propose a novel Bayesian zero-inflated DM model for multivariate compositional count data with excess zeros. We then extend our approach to regression settings and embed sparsity-inducing priors to perform variable selection for high-dimensional covariate spaces. Throughout, modeling decisions are made to boost scalability without sacrificing interpretability or imposing limiting assumptions. Extensive simulations and an application to a human gut microbiome data set are presented to compare the performance of the proposed method to existing approaches. We provide an accompanying R package with a user-friendly vignette to apply our method to other data sets.

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Matthew D. Koslovsky. 2023-02-23. A Bayesian Zero-Inflated Dirichlet-Multinomial Regression Model for Multivariate Compositional Count Data. https://arxiv.org/abs/2302.12283

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