  We consider an equivariant approach imposing data-driven bounds for the
variances to avoid singular and spurious solutions in maximum likelihood (ML)
estimation of clusterwise linear regression models. We investigate its use in
the choice of the number of components and we propose a computational shortcut,
which significantly reduces the computational time needed to tune the bounds on
the data. In the simulation study and the two real-data applications, we show
that the proposed methods guarantee a reliable assessment of the number of
components compared to standard unconstrained methods, together with accurate
model parameters estimation and cluster recovery.
