computeBIC computes the approximate BIC of a given
mixedMemModelVI, where the lower bound on the log-likelihood
(also called ELBO) is used instead of the intractable true log-likelihood.
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 θ and α, but omits the variational parameters φ and δ.
computeBIC returns the approximate BIC value, a real number.
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.
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