  Cluster-weighted models (CWMs) extend finite mixtures of regressions (FMRs)
in order to allow the distribution of covariates to contribute to the
clustering process. In a matrix-variate framework, the matrix-variate normal
CWM has been recently introduced. However, problems may be encountered when
data exhibit skewness or other deviations from normality in the responses,
covariates or both. Thus, we introduce a family of 24 matrix-variate CWMs which
are obtained by allowing both the responses and covariates to be modelled by
using one of four existing skewed matrix-variate distributions or the
matrix-variate normal distribution. Endowed with a greater flexibility, our
matrix-variate CWMs are able to handle this kind of data in a more suitable
manner. As a by-product, the four skewed matrix-variate FMRs are also
introduced. Maximum likelihood parameter estimates are derived using an
expectation-conditional maximization algorithm. Parameter recovery,
classification assessment, and the capability of the Bayesian information
criterion to detect the underlying groups are investigated using simulated
data. Lastly, our matrix-variate CWMs, along with the matrix-variate normal CWM
and matrix-variate FMRs, are applied to two real datasets for illustrative
purposes.
