A mixture of logistic skew-normal multinomial models

Wangshu Tu, Ryan Browne and Sanjeena Subedi

Computational Statistics & Data Analysis, 2024, vol. 196, issue C

Abstract: The logistic normal multinomial distribution is gaining interest in modelling microbiome data. It utilizes a hierarchical structure such that the observed counts conditional on the compositions are assumed to be multinomial random variables and the log-ratio transformed compositions are assumed to be from a Gaussian distribution. While multinomial distribution accounts for the compositional nature of the data, and a Gaussian prior offers flexibility in the structure of covariance matrices, the log-ratio transformed compositions of the microbiome data can be highly skewed, especially at a lower taxonomic level. Thus, a Gaussian distribution may not be an ideal prior for the log-ratio transformed compositions. A novel mixture of logistic skew-normal multinomial (LSNM) distribution is proposed in which a multivariate skew-normal distribution is utilized as a prior for the log-ratio transformed compositions. A variational Gaussian approximation in conjunction with the EM algorithm is utilized for parameter estimation.

Keywords: Skew-normal; Logistic normal multinomial; Variational Gaussian approximation; Model-based clustering; Mixture model (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:196:y:2024:i:c:s0167947324000306

DOI: 10.1016/j.csda.2024.107946

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