computeBIC 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.
computeBIC(model)the mixedMemModel object for which the BIC will be calculated.
computeBIC returns the approximate BIC value, a real number.
\(BIC = -2 ELBO + p \log(Total)\)
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 et al (2007). The number of estimated parameters P includes the parameters \(\theta\) and \(\alpha\), but omits the variational parameters \(\phi\) and \(\delta\).
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.