The effects of different parametrizations on the convergence of Bayesian
computational algorithms for hierarchical models are well explored. In
particular, techniques such as centered parametrization (CP), non-centered
parametrization (NCP) and partially non-centered parametrization (PNCP) can be
used to accelerate convergence in MCMC and EM algorithms. These ideas are not
well studied, however, for variational Bayes (VB) methods.
Mixtures of linear mixed models (MLMMs) are useful for clustering grouped
data in applications such as gene expression time course experiments. These
models can be estimated by likelihood maximization through the EM algorithm and
the optimal number of components determined by comparing different mixture
models using penalized log-likelihood criteria such as BIC. In this paper, we
propose fitting MLMMs with variational methods which can perform parameter
estimation and model selection simultaneously.