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Microbiome compositional data are often high-dimensional, sparse, and exhibitpervasive cross-sample heterogeneity. Generative modeling is a popular approachto analyze such data, and effective generative models must accuratelycharacterize these key features. While high-dimensionality and abundance ofzeros have received much attention, existing models often lack flexibility incapturing complex cross-sample variability. This limitation can affectstatistical efficiency and lead to misleading conclusions in tasks likedifferential abundance analysis, clustering, and network analysis. We introducea generative model, the "logistic-tree normal" (LTN) model, which addressesthis issue and effectively captures key characteristics of microbiome data,including abundance of zeros. LTN employs a tree-based decomposition toaggregate sparse taxa counts and uses a (multivariate) logistic-normaldistribution at tree splits, allowing for flexible covariance adjustments amongtaxa as needed. The latent Gaussian structure of LTN enables the incorporationof multivariate analysis tools that enforce sparsity or low-rank covarianceassumptions. As a versatile, fully generative model, LTN supports a wide rangeof applications and offers efficient Bayesian inference computational recipesthrough conjugate blocked Gibbs sampling with P\'olya-Gamma augmentation. Wedemonstrate application of LTN in a compositional mixed-effects model fordifferential abundance analysis using numerical experiments and a reanalysis ofthe infant cohort in the DIABIMMUNE study. Our findings illustrate that LTN, byadequately accounting for cross-sample heterogeneity, appropriately generatesthe proportion of zeros without requiring an explicit zero-inflation component,confirming a recent viewpoint that "zero-inflation" in count-based sequencingdata are often results of unaccounted cross-sample variation.

A tree-based model for addressing sparsity and taxa covariance in microbiome compositional count data