  The paper proposes a latent variable model for binary data coming from an
unobserved heterogeneous population. The heterogeneity is taken into account by
replacing the traditional assumption of Gaussian distributed factors by a
finite mixture of multivariate Gaussians. The aim of the proposed model is
twofold: it allows to achieve dimension reduction when the data are dichotomous
and, simultaneously, it performs model based clustering in the latent space.
Model estimation is obtained by means of a maximum likelihood method via a
generalized version of the EM algorithm. In order to evaluate the performance
of the model a simulation study and two real applications are illustrated.
