In this work, Bayesian methods for selecting variables in a mixture of logistic regressions model are developed.
In order to simplify its Bayesian estimation, the data augmentation approach with Pólya-Gamma random variables was extended to the mixture of logistic regression models. Through this data augmentation technique, a Gibbs Sampling algorithm for estimating and selecting variables in the model is presented, and the number of components in the mixture is identified by Bayesian model selection criteria. In the variable selection, the performance of two prior distributions for the regression coefficients are investigated, adding a second set of latent variables to indicate the presence and non-presence of the predictor variables at each component of the mixture. The conjugation obtained for the distribution of the regression coefficients, through the inclusion of Pólya-Gamma variables, make it possible to analytically calculate the marginal likelihood and gain computational efficiency in the variable selection process. To analyse the performance, the presented methodologies are applied in simulated and real data.