Logistic-t multinomial mixture model for clustering for microbiome data

The logistic-normal multinomial distribution has been used for modelling microbiome data obtained from high-throughput sequencing technologies, which are compositional in nature. A logistic-normal multinomial distribution is a hierarchical multinomial distribution that assumes the latent variable which are the additive log-ratio (ALR) transformed proportions in a multinomial distribution follows a Gaussian distribution. Model-based clustering algorithms have also been developed for clustering microbiome data based on the logistic-normal models. However, the Gaussian assumption may violated when the ALR transformed variable exhibit heavy-tailed distributions or has outliers. Our study introduces a novel mixture of logistic-t multinomial models that effectively address these challenges. Utilizing a multivariate t distribution for ALR transformed latent variables, the proposed approach provides the flexibility to capture heavy tails and thus better accommodates the outliers when clustering microbiome compositional data. We incorporate a variational Expectation-Maximization (EM) algorithm to facilitate efficient parameter estimation for intractable posterior distributions. Our model demonstrates competitive performance in terms of clustering accuracy and parameter recovery as compared to existing approaches through simulation studies and real data analysis, hence offering a robust tool for exploring the complex structures and heterogeneity of microbiome compositional data.