BIC from ELBO for a ZIP-PLN latent factor model

Computes a Bayesian Information Criterion (BIC)-like score from the Evidence Lower Bound (ELBO) of a fitted model. The penalty accounts for the number of free parameters in a latent factor model with latent dimension q: $$ \mathrm{BIC} = \mathrm{ELBO} - \frac{\log(n)}{2}\Big[q\{p - (q-1)/2\} + p\,d\Big], $$ where \(n\) is the number of rows (sites/samples), \(p\) the number of columns (species/variables), and \(d\) the number of covariates.

Usage

BIC(Y, X, fit, q)

Arguments

Y

Numeric n x p count matrix.

X

Numeric n x d design matrix of covariates (first column typically an intercept).

fit

A fitted object (list) containing at least $elbo, the maximized ELBO value for the model.

q

Integer, size of the latent space (rank).

Value

A single numeric value: the BIC score (higher is better in this ELBO-based convention).

Details

This criterion mirrors the usual BIC structure but replaces the log-likelihood with the ELBO and uses the parameter count appropriate for a rank-q latent factor structure.

See also

BIC