BIC from the ELBO for PLN-PCA and ZIP-PLN-PCA models

Computes a BIC-like score in which the log-likelihood is replaced by the ELBO of the fitted model (higher is better): $$\mathrm{BIC} = \mathrm{ELBO} - \frac{\log(n)}{2}\Big[q\{p - (q-1)/2\} + k\Big],$$ where $q\{p - (q-1)/2\}$ is the number of free parameters in $C$ (identifiable up to a rotation) and $k$ the number of regression parameters: $2d$ for the ZIP-PLN-PCA model ($\beta$ and $\gamma$), $d$ for the PLN-PCA model with a vectorized design ($(np) \times d$) and $pd$ with a rowwise design ($n \times d$). $n$ is the number of rows of Y (sites), which are the independent units of the model.

Usage

BIC(Y, X, fit, q, model = c("ZIPLNPCA", "PLNPCA"))

Arguments

Y: Numeric n x p count matrix (NAs allowed).
X: Design matrix, (n*p) x d (or n x d for a rowwise PLN-PCA design).
fit: Fitted object containing $elbo (output of Miss.ZIPLNPCA or Miss.PLNPCA).
q: Integer, size of the latent space.
model: "ZIPLNPCA" (default) or "PLNPCA".

Value

A single numeric value, the BIC score.

BIC from the ELBO for PLN-PCA and ZIP-PLN-PCA models

Usage

Arguments

Value

See also