The mixture of common factor analyzers (MCFA) model places additional restrictions on the component means and covariance matrices compared to the mixture of factor analyzers model, thereby further reducing the number of parameters to be estimated. Consequently the model is quite restrictive and, notably, is much more restrictive than the mixture of factor analyzers model. In fact, the MCFA model can be cast as a special case of the mixture of factor analyzers model. The mixture of factor analyzers and a family of mixture models based thereon that is the Parsimonious Gaussian mixture models (PGMM) family can be used for clustering data with higher dimensions. However, model selection can become a problem when even a few hundred variables exist. Parameter estimation for members of the PGMM family can be carried out using alternating expectation-conditional maximization algorithms (AECM). The AECM algorithm allows a different specification of complete-data for each conditional maximization step.