  We propose two approaches for selecting variables in latent class analysis
(i.e.,mixture model assuming within component independence), which is the
common model-based clustering method for mixed data. The first approach
consists in optimizing the BIC with a modified version of the EM algorithm.
This approach simultaneously performs both model selection and parameter
inference. The second approach consists in maximizing the MICL, which considers
the clustering task, with an algorithm of alternate optimization. This approach
performs model selection without requiring the maximum likelihood estimates for
model comparison, then parameter inference is done for the unique selected
model. Thus, the benefits of both approaches is to avoid the computation of the
maximum likelihood estimates for each model comparison. Moreover, they also
avoid the use of the standard algorithms for variable selection which are often
suboptimal (e.g. stepwise method) and computationally expensive. The case of
data with missing values is also discussed. The interest of both proposed
criteria is shown on simulated and real data.
