  An extension of the latent class model is presented for clustering
categorical data by relaxing the classical "class conditional independence
assumption" of variables. This model consists in grouping the variables into
inter-independent and intra-dependent blocks, in order to consider the main
intra-class correlations. The dependency between variables grouped inside the
same block of a class is taken into account by mixing two extreme
distributions, which are respectively the independence and the maximum
dependency. When the variables are dependent given the class, this approach is
expected to reduce the biases of the latent class model. Indeed, it produces a
meaningful dependency model with only a few additional parameters. The
parameters are estimated, by maximum likelihood, by means of an EM algorithm.
Moreover, a Gibbs sampler is used for model selection in order to overcome the
computational intractability of the combinatorial problems involved by the
block structure search. Two applications on medical and biological data sets
show the relevance of this new model. The results strengthen the view that this
model is meaningful and that it reduces the biases induced by the conditional
independence assumption of the latent class model.
