Computes the approximate BIC of a given mixedMemModel, where the lower bound on the log-likelihood
(also called ELBO) is used instead of the intractable true log-likelihood.
Usage
computeBIC(model)
Arguments
model
the mixedMemModel object for which the BIC will be calculated
Value
the approximate BIC value
Details
$BIC = -2 ELBO + p \log(Total)$
where p is the number of estimated parameters and Total is the number of individuals in
the sample.
This BIC model selection criteria is used
in Erosheva (2007). When counting the number of fitted parameters, we only include the
hyperparameters $\theta$ and $\alpha$ and omit the variational parameters $\phi$ and $\delta$.
References
Erosheva, E. A., Fienberg, S. E., & Joutard, C. (2007). Describing disability through individual-level mixture models for multivariate binary data. The annals of applied statistics, 1(2), 346.