Model-based clustering via linear cluster-weighted models

A novel family of twelve mixture models with random covariates, nested in the linear t cluster-weighted model (CWM), is introduced for model-based clustering. The linear t CWM was recently presented as a robust alternative to the better known linear Gaussian CWM. The proposed family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Maximum likelihood parameter estimation is carried out within the EM framework, and both the BIC and the ICL are used for model selection. A simple and effective hierarchical-random initialization is also proposed for the EM algorithm. The novel model-based clustering technique is illustrated in some applications to real data. Finally, a simulation study for evaluating the performance of the BIC and the ICL is presented.