Bayesian covariate-varying interaction analysis for multivariate counts

Fits the Bayesian covariate-varying factor model of Zhang, Patnode and Lee by MCMC. The model jointly estimates a covariate-dependent mean abundance and a covariate-dependent covariance (interaction) structure for high-dimensional multivariate count data, using a rounded multivariate log-normal kernel, a sparse covariate-dependent factor loading matrix with a Dirichlet-Horseshoe prior, and mean-constrained Dirichlet process mixtures for the size factor and baseline abundance.

Usage

bcaia(
  Y,
  Xmean,
  Xcov,
  subject = NULL,
  K = 8,
  niter = 160000,
  burnin = NULL,
  thin = 10,
  seed = NULL,
  control = bcaia_control(),
  verbose = TRUE,
  keep_all = FALSE
)

Arguments

Y: An n x J matrix of non-negative integer counts (samples in rows, features/OTUs in columns).
Xmean: An n x Pmean design matrix for the mean regression excluding the intercept (the intercept is absorbed into the size factor / baseline abundance).
Xcov: An n x Pcov design matrix for the covariance regression, including an intercept column (typically the first column of ones).
subject: Optional length-n vector (factor, integer or character) giving the subject each sample belongs to. When supplied, the subject-indexed model is fitted; when NULL, the simple model is fitted.
K: Number of latent factors (the working dimension of the loading matrix). Choose a value large enough to capture the covariance; redundant factors are shrunk out by the prior. See choose_K.
niter: Total number of MCMC iterations. Default 160000.
burnin: Number of burn-in iterations discarded before saving. Default niter/2.
thin: Thinning interval for saved samples. Default 10.
seed: Optional integer seed for reproducible initialisation.
control: A bcaia_control list of hyperparameters and tuning constants.
verbose: Logical; print progress. Default TRUE.
keep_all: Logical; if TRUE, the returned samples also contain the full posterior draws of every model parameter – the latent factors eta, the Dirichlet-Horseshoe parameters phi and zeta, and the Dirichlet-process internals (omega, psi, xi) and membership indicators for the size factor and baseline abundance – in addition to F, Q, tau, beta, ri, alpha/alphasij and sig2. This can be large; default FALSE keeps only the lighter set.

Value

An object of class "bcaia": a list with element samples (posterior draws of F, Q, tau, beta, ri, alpha / alphasij, sig2), together with runtime, data (dimensions and the design matrices), control, and the model variant used. Use posterior_Sigma and posterior_cor to summarise covariate-varying covariance and correlation.

Details

Two model variants are available and selected automatically through the subject argument:

Simple model (subject = NULL): one baseline abundance \(\alpha_j\) per feature. This matches Simulation 1 and the mice data analysis in the paper.
Subject-indexed model (subject supplied): a subject-specific baseline abundance \(\alpha_{s,j}\) to accommodate repeated samples and large inter-subject variability. This matches Simulations 2 and 3.

References

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