We propose two approaches for selecting variables in latent class analysis, which is the common model-based clustering method for mixed-type data.
The first approach consists in optimizing the BIC with a modified version of the standard EM algorithm. This approach simultaneously performs 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. Both approaches avoid the computation of the maximum likelihood estimates for each model comparison. The interest of both proposed criteria is shown on simulated and several benchmark real data.
The proposal is applied on genomic data generated for 1318 individuals from 35 human populations of western central Africa, and simultaneously to detect the most discriminative genetic markers between the two identified population groups: rainforest hunter-gatherers and Bantu-speaking farmers.
The proposed method implemented in the R package VarSelLCM.2.0