pqrBayes-package: Bayesian penalized quantile regression for the sparse linear...

In pqrBayes: Bayesian Penalized Quantile Regression

Bayesian penalized quantile regression for the sparse linear model, binary LASSO, group LASSO and varying coefficient models based on spike-and-slab priors and/or the horseshoe family of priors

Description

In this package, we implement Bayesian penalized quantile regression for a sparse linear model (with a continuous response), 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 (with a continuous response).

Details

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
	with a continuous response, 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 (with a continuous response), binary LASSO, group LASSO
	or a varying coefficient model.

The function pqrBayes() returns a pqrBayes object that stores the posterior estimates of regression coefficients.

References

Fan, K., Subedi, S., Yang, G., Lu, X., Ren, J. and Wu, C. (2024). Is Seeing Believing? A Practitioner's Perspective on High-dimensional Statistical Inference in Cancer Genomics Studies. Entropy, 26(9).794 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3390/e26090794")}

Zhou, F., Ren, J., Ma, S. and Wu, C. (2023). The Bayesian regularized quantile varying coefficient model. Computational Statistics & Data Analysis, 187, 107808 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.csda.2023.107808")}

Ren, J., Zhou, F., Li, X., Ma, S., Jiang, Y. and Wu, C. (2023). Robust Bayesian variable selection for gene-environment interactions. Biometrics, 79(2), 684-694 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/biom.13670")}

Fan, K. and Wu, C. (2025). A New Robust Binary Bayesian LASSO. Stat, 14 (3), e70078 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sta4.70078")}

Fan, K., Srijana, S., Dissanayake, V. and Wu, C. (2026). Robust Bayesian high-dimensional variable selection and inference with the horseshoe family of priors Computational Statistics & Data Analysis, 219, 108358 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.csda.2026.108358")}

Wu, C., and Ma, S. (2015). A selective review of robust variable selection with applications in bioinformatics. Briefings in Bioinformatics, 16(5), 873–883 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/bib/bbu046")}

Zhou, F., Ren, J., Lu, X., Ma, S. and Wu, C. (2021). Gene–Environment Interaction: a Variable Selection Perspective. Epistasis. Methods in Molecular Biology. 2212:191–223 https://link.springer.com/protocol/10.1007/978-1-0716-0947-7_13

Ren, J., Zhou, F., Li, X., Chen, Q., Zhang, H., Ma, S., Jiang, Y. and Wu, C. (2020) Semi-parametric Bayesian variable selection for gene-environment interactions. Statistics in Medicine, 39: 617– 638 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.8434")}

Ren, J., Zhou, F., Li, X., Wu, C. and Jiang, Y. (2019) spinBayes: Semi-Parametric Gene-Environment Interaction via Bayesian Variable Selection. R package version 0.1.0. https://CRAN.R-project.org/package=spinBayes

Wu, C., Jiang, Y., Ren, J., Cui, Y. and Ma, S. (2018). Dissecting gene-environment interactions: A penalized robust approach accounting for hierarchical structures. Statistics in Medicine, 37:437–456 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.7518")}

Wu, C., Shi, X., Cui, Y. and Ma, S. (2015). A penalized robust semiparametric approach for gene-environment interactions. Statistics in Medicine, 34 (30): 4016–4030 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.6609")}

Wu, C., Cui, Y., and Ma, S. (2014). Integrative analysis of gene–environment interactions under a multi–response partially linear varying coefficient model. Statistics in Medicine, 33(28), 4988–4998 \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.6287")}

Wu, C., Zhong, P.S. and Cui, Y. (2018). Additive varying–coefficient model for nonlinear gene–environment interactions. Statistical Applications in Genetics and Molecular Biology, 17(2) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1515/sagmb-2017-0008")}

Wu, C., Zhong, P.S. and Cui, Y. (2013). High dimensional variable selection for gene-environment interactions. Technical Report. Michigan State University.

See Also

pqrBayes

pqrBayes documentation built on March 15, 2026, 1:07 a.m.