  Finite mixtures of regressions with fixed covariates are a commonly used
model-based clustering methodology to deal with regression data. However, they
assume assignment independence, i.e. the allocation of data points to the
clusters is made independently of the distribution of the covariates. In order
to take into account the latter aspect, finite mixtures of regressions with
random covariates, also known as cluster-weighted models (CWMs), have been
proposed in the univariate and multivariate literature. In this paper, the CWM
is extended to matrix data, e.g. those data where a set of variables are
simultaneously observed at different time points or locations. Specifically,
the cluster-specific marginal distribution of the covariates, and the
cluster-specific conditional distribution of the responses given the
covariates, are assumed to be matrix normal. Maximum likelihood parameter
estimates are derived using an ECM algorithm. Parameter recovery,
classification assessment and the capability of the BIC to detect the
underlying groups are analyzed on simulated data. Finally, two real data
applications concerning educational indicators and the Italian non-life
insurance market are presented.
