Bayesian Variable Selection for Gaussian copula regression models
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We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. In particular, a sparse Gaussian copula regression model is used to account for the multivariate dependencies between any combination of discrete and continuous responses and their association with a set of predictors. We utilize the parameter expansion for data augmentation strategy to construct a Markov chain Monte Carlo algorithm for the estimation of the parameters and the latent variables of the model. Based on a centered parametrization of the Gaussian latent variables, we design an efficient proposal distribution to update jointly the latent binary vectors of important predictors and the corresponding non-zero regression coefficients. The proposed strategy is tested on simulated data and applied to two real data sets in which the responses consist of low-intensity counts, binary, ordinal and continuous variables.
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