Objective Variable Selection in Multinomial Logistic Regression: a Conditional Latent Approach

Mixtures of g-priors are well established in linear regression models by \cite{Liang2008} and generalized linear models by \cite{Bove2011} and \cite{Li2013} for variable selection. This approach enables us to overcome the problem of specifying the dispersion parameter by imposing a hyper-prior on it. By this way we allow for our model to "learn" about the shrinkage from the data. In this work, we implement Bayesian variable selection methods based on g-priors and their mixtures in multinomial logistic regression models. More precisely, we follow two approaches: (a) the traditional implementation by extending the approach of \cite{Bove2011} for multinomial models, and (b) an augmented implementation of \cite{Polson2013} based on latent structure. We will study and compare the two approaches. Furthermore, we will focus on handling class imbalance and sparsity issues appearing when the number of covariates is large and the need of specifying different covariate selection across different pairwise logit structures. All proposed methods will be presented in simulation and real datasets.