  The literature on clustering for continuous data is rich and wide;
differently, that one developed for categorical data is still limited. In some
cases, the problem is made more difficult by the presence of noise
variables/dimensions that do not contain information about the clustering
structure and could mask it. The aim of this paper is to propose a model for
simultaneous clustering and dimensionality reduction of ordered categorical
data able to detect the discriminative dimensions discarding the noise ones.
Following the underlying response variable approach, the observed variables are
considered as a discretization of underlying first-order latent continuous
variables distributed as a Gaussian mixture. To recognize discriminative and
noise dimensions, these variables are considered to be linear combinations of
two independent sets of second-order latent variables where only one contains
the information about the cluster structure while the other contains noise
dimensions. The model specification involves multidimensional integrals that
make the maximum likelihood estimation cumbersome and in some cases infeasible.
To overcome this issue the parameter estimation is carried out through an
EM-like algorithm maximizing a pairwise log-likelihood. Examples of application
of the model on real and simulated data are performed to show the effectiveness
of the proposal.
