Flexible clustering via extended mixtures of common t-factor analyzers

Mixtures of t-factor analyzers have been broadly used for model-based density estimation and clustering of high-dimensional data from a heterogeneous population with longer-than-normal tails or atypical observations. To reduce the number of parameters in the component covariance matrices, the mixtures of common t-factor analyzers (MCtFA) have been recently proposed by assuming a common factor loading across different components. In this paper, we present an extended version of MCtFA using distinct covariance matrices for component errors. The modified mixture model offers a more appropriate way to represent the data in a graphical fashion. Two flexible EM-type algorithms are developed for iteratively computing maximum likelihood estimates of parameters. Practical considerations for the specification of starting values, model-based clustering, classification of new subject and identification of potential outliers are also provided. We demonstrate the superiority of the proposed methodology by analyzing the Italian wine data and a simulation study.