Bayesian Covariate-Varying Interaction Analysis for Multivariate Count Data • BCAIA

Bayesian Covariate-varying Interaction Analysis for multivariate count data.

BCAIA implements the Bayesian covariate-varying factor model of Zhang, Patnode and Lee for high-dimensional multivariate count data, with a focus on microbiome studies. The model jointly estimates

how the mean abundance of each feature changes with covariates, and
how the interaction (covariance) structure among features changes with covariates,

directly on discrete, over-dispersed, zero-inflated counts — without ad-hoc log/clr transformations.

The covariance is modelled through a sparse covariate-dependent factor loading matrix,

Σ(x) = Λ(x)Λ(x)’ + σ² I, λ_jk(x) = q_jk f_k’x,

with a Dirichlet–Horseshoe prior on the loadings for joint sparsity, a rounded multivariate log-normal kernel for the counts, and mean-constrained Dirichlet process mixtures for the size factor and baseline abundance.

Installation

# install.packages("devtools")
devtools::install_github("shuang-jie/BCAIA")

The package compiles C++ (via Rcpp / RcppArmadillo), so you need a working toolchain (Rtools on Windows, Xcode command line tools on macOS).

Quick start

library(BCAIA)

## simulate a small covariate-varying dataset (Simulation 1 design)
sim <- simulate_bcaia(n = 30, J = 15, seed = 6)

## choose the working number of factors from a clr-PCA scree rule
K <- choose_K(sim$Y)

## fit the model
fit <- bcaia(Y = sim$Y, Xmean = sim$Xmean, Xcov = sim$Xcov,
             K = 8, niter = 160000, seed = 1)

## posterior covariance / correlation at a covariate setting
Sigma_hat <- posterior_Sigma(fit, x = sim$Xcov[1, ])
rho_hat   <- posterior_cor(fit,   x = sim$Xcov[1, ])

Repeated samples / inter-subject variability

Supply a subject vector to fit the subject-indexed variant (a subject-specific baseline abundance α_s,j), used in Simulations 2 and 3:

fit2 <- bcaia(Y, Xmean, Xcov, subject = subject_id, K = 7, niter = 160000)

Real data

The mice gut microbiome data of Patnode et al. (2019) analysed in the paper are bundled:

data(mice)
fit_mice <- bcaia(mice$Y, mice$Xmean, mice$Xcov, K = 8, niter = 160000)

Reproducing the paper

The vignettes/ reproduce the paper’s analyses:

Vignette	Paper section
`simulation1`	§4.1 Simulation 1 (categorical design)
`simulation2`	§4.2 Simulation 2 (repeated samples)
`simulation3`	§4.3 Simulation 3 (arbitrary covariance)
`mice`	§5 Mice gut microbiome data

Each vignette runs a short chain for illustration; the full paper settings (niter = 160000) are noted inline and are best run on a server, optionally over multiple seeds/replicates.

Reference

Zhang, S., Patnode, M. L. and Lee, J. Bayesian Covariate-Varying Interaction Analysis for Multivariate Count Data: Application to Microbiome Studies.

Contact

Shuangjie Zhang, Department of Statistics and Data Sciences, The University of Texas at Austin — shuangjie.zhang@austin.utexas.edu. Questions and bug reports are welcome via the issue tracker.

BCAIA