Bayesian variable selection in a binary quantile regression model for longitudinal data

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In this article, we construct a Bayesian hierarchical model with regression coefficients following a spike-and-slab prior. This model is used for high-dimensional binary quantile regression models with longitudinal data, which fills the gap in literature research. We employ the EM algorithm and Gibbs algorithm to generate posterior samples. Subsequently, we develop a threshold rule to identify important independent variables in the model while eliminating redundant ones. Through simulations in various scenarios, we validate the effectiveness and robustness of our proposed Bayesian model. Finally, we apply our method to the Add Health dataset.