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Mixed-membership (MM) models such as Latent Dirichlet Allocation (LDA) havebeen applied to microbiome compositional data to identify latent subcommunitiesof microbial species. These subcommunities are informative for understandingthe biological interplay of microbes and for predicting health outcomes.However, microbiome compositions typically display substantial cross-sampleheterogeneities in subcommunity compositions -- that is, the variability in theproportions of microbes in shared subcommunities across samples -- which is notaccounted for in prior analyses. As a result, LDA can produce inference whichis highly sensitive to the specification of the number of subcommunities andoften divides a single subcommunity into multiple artificial ones. To addressthis limitation, we incorporate the logistic-tree normal (LTN) model into LDAto form a new MM model. This model allows cross-sample variation in thecomposition of each subcommunity around some "centroid" composition thatdefines the subcommunity. Incorporation of auxiliary P\'olya-Gamma variablesenables a computationally efficient collapsed blocked Gibbs sampler to carryout Bayesian inference under this model. By accounting for such heterogeneity,our new model restores the robustness of the inference in the specification ofthe number of subcommunities and allows meaningful subcommunities to beidentified.

Microbiome subcommunity learning with logistic-tree normal latent Dirichlet allocation