In this package, we implement Bayesian penalized quantile regression for the sparse linear model, binary LASSO, group LASSO and quantile varying coefficient (VC) models. The point-mass spike-and-slab priors and horseshoe family of (horseshoe, horseshoe+ and regularized horseshoe) priors have been incorporated in the Bayesian hierarchical models to facilitate Bayesian shrinkage estimation, variable selection and statistical inference. For the spike-and-slab priors, the four default methods are Bayesian regularized quantile regression with spike-and-slab priors under the sparse linear (i.e. LASSO), binary LASSO, group LASSO and VC model, correspondingly. In addition to the default methods, users can also choose models without robustness and/or spike--and--slab priors. Furthermore, under sparse linear models, we have implemented the horseshoe family of (horseshoe, horseshoe+ and regularized horseshoe) priors and the three non-robust alternatives. Currently, the horseshoe family of priors is only implemented under the sparse linear model.
The user friendly, integrated interface pqrBayes() allows users to flexibly choose fitting models by specifying the following parameters:
| robust: | whether to fit a robust sparse quantile regression model (the sparse linear model, binary LASSO, |
| group LASSO or Varying Coefficient models) or their non-robust counterparts. | |
| prior: | |
| specify which prior to use (the spike-and-slab prior, Laplace prior | |
| and the horseshoe family of priors). | |
| model: | whether to fit a sparse linear model, binary LASSO, group LASSO |
| or a varying coefficient model. |
The function pqrBayes() returns a pqrBayes object that stores the posterior estimates of regression coefficients.
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pqrBayes