  Finite Mixture of Regressions (FMR) models are among the most widely used
approaches in dealing with the heterogeneity among the observations in
regression problems. One of the limitations of current approaches is their
inability to incorporate group structure in data when available. In some
applications, it is desired to cluster groups of observations together rather
than the individual ones. In this work, we extend the FMR framework to allow
for group structure among observations, and call the resulting model the
Grouped Mixture of Regressions (GMR). We derive a fast fitting algorithm based
on the Expectation-Maximization (EM) idea. We also show how the group structure
can improve prediction by sharing information among members of each group, as
reflected in the posterior predictive density under GMR. %that they don't
consider clustering the data when there is group structure. In other words,
sometimes it is desired to force the algorithm to cluster groups/blocks of
observations, instead of individual observations. %In this work, we propose a
maximum likelihood approach to cluster groups of observations. We call this
algorithm Group Mixture of Regressions (GMR). Expectation Maximization (EM) is
employed to maximize the likelihood. Posterior prediction density for
predicting new observations is also derived and presented.
  The performance of the approach is assessed using both synthetic data as well
as a real-world example.
