Multivariate cluster weighted models using skewed distributions

Much work has been done in the area of the cluster weighted model (CWM), which extends the finite mixture of regression model to include modelling of the covariates. Although many types of distributions have been considered for both the response(s) and covariates, to our knowledge skewed distributions have not yet been considered in this paradigm. Herein, a family of 24 novel CWMs is considered which allows both the responses and covariates to be modelled using one of four skewed distributions (the generalized hyberbolic and three of its skewed special cases, i.e., the skew-t, the variance-gamma and the normal-inverse Gaussian distributions) or the normal distribution. Parameter estimation is performed using the expectation-maximization algorithm and both simulated and real data are used for illustration.