IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v40y2025i8d10.1007_s00180-025-01656-9.html

Gaussian variational approximation for Bayesian Lasso quantile regression model with zero-or-one inflated proportional data

Author

Listed:
  • Zhiqiang Wang

    (Luoyang Normal University
    Henan Key Laboratory for Big Data Processing and Analytics of Electronic Commerce)

  • Ying Wu

    (Yunnan Key Laboratory of Statistical Modeling and Data Analysis)

Abstract

Zero-or-one inflated (ZOI) proportional data, common in various fields, presents modelling challenges due to significant zeros and ones. We propose a three-part mixture distribution model that combines degenerate distributions at zero and one with a unit-Weibull distribution for the (0,1) interval. Quantile regression is employed instead of mean regression to capture the global distribution of response variables. Bayesian variational inference, specifically Gaussian variational approximation with a factorized covariance structure, is used for parameter estimation, offering computational efficiency over traditional methods. Bayesian variable selection is achieved using the Bayesian Lasso. Simulation studies and real data analyses demonstrate the effectiveness of the proposed method in parameter estimation and variable selection.

Suggested Citation

  • Zhiqiang Wang & Ying Wu, 2025. "Gaussian variational approximation for Bayesian Lasso quantile regression model with zero-or-one inflated proportional data," Computational Statistics, Springer, vol. 40(8), pages 4853-4874, November.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:8:d:10.1007_s00180-025-01656-9
    DOI: 10.1007/s00180-025-01656-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-025-01656-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-025-01656-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    3. J. Mazucheli & A. F. B. Menezes & L. B. Fernandes & R. P. de Oliveira & M. E. Ghitany, 2020. "The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(6), pages 954-974, April.
    4. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    5. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    6. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407, April.
    7. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407.
    8. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    9. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    2. Linda S. L. Tan, 2021. "Use of model reparametrization to improve variational Bayes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 30-57, February.
    3. Gael M. Martin & David T. Frazier & Christian P. Robert, 2021. "Approximating Bayes in the 21st Century," Monash Econometrics and Business Statistics Working Papers 24/21, Monash University, Department of Econometrics and Business Statistics.
    4. Gael M. Martin & David T. Frazier & Christian P. Robert, 2022. "Computing Bayes: From Then `Til Now," Monash Econometrics and Business Statistics Working Papers 14/22, Monash University, Department of Econometrics and Business Statistics.
    5. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2021. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 60(1), pages 227-259, January.
    6. Mitra Kharabati & Morteza Amini & Mohammad Arashi, 2026. "Variational inference for sparse poisson regression," Computational Statistics, Springer, vol. 41(3), pages 1-50, April.
    7. Luo, Nanyu & Ji, Feng & Han, Yuting & He, Jinbo & Zhang, Xiaoya, 2024. "Fitting item response theory models using deep learning computational frameworks," OSF Preprints tjxab, Center for Open Science.
    8. Weixian Wang & Maozai Tian, 2024. "Variational Bayesian EM Algorithm for Quantile Regression in Linear Mixed Effects Models," Mathematics, MDPI, vol. 12(21), pages 1-16, October.
    9. Lara Delsalle & Oleksii Birulin, 2024. "Family-oriented versus career seekers: mixture regression separation," Empirical Economics, Springer, vol. 67(1), pages 313-335, July.
    10. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    11. Mo, Jiang & Yan, Wang-Ji, 2025. "Explainable neural-networked variational inference: A new and fast paradigm with automatic differentiation for high-dimensional Bayesian inverse problems," Reliability Engineering and System Safety, Elsevier, vol. 264(PA).
    12. Henry R. Scharf & Xinyi Lu & Perry J. Williams & Mevin B. Hooten, 2022. "Constructing Flexible, Identifiable and Interpretable Statistical Models for Binary Data," International Statistical Review, International Statistical Institute, vol. 90(2), pages 328-345, August.
    13. Radka Jersakova & James Lomax & James Hetherington & Brieuc Lehmann & George Nicholson & Mark Briers & Chris Holmes, 2022. "Bayesian imputation of COVID‐19 positive test counts for nowcasting under reporting lag," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 834-860, August.
    14. Petar Jolakoski & Viktor Stojkoski & Dragan Tevdovski, 2026. "Business cycle synchronization between the EU and Western Balkan candidate economies: A Wavelet Analysis," Papers 2603.28951, arXiv.org.
    15. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    16. Aaron Osgood‐Zimmerman & Jon Wakefield, 2023. "A Statistical Review of Template Model Builder: A Flexible Tool for Spatial Modelling," International Statistical Review, International Statistical Institute, vol. 91(2), pages 318-342, August.
    17. Feihong Xia & Rabikar Chatterjee & Jerrold H. May, 2019. "Using Conditional Restricted Boltzmann Machines to Model Complex Consumer Shopping Patterns," Marketing Science, INFORMS, vol. 38(4), pages 711-727, July.
    18. Collin Philipps, 2022. "Interpreting Expectiles," Working Papers 2022-01, Department of Economics and Geosciences, US Air Force Academy.
    19. Nolan, Tui H. & Richardson, Sylvia & Ruffieux, Hélène, 2025. "Efficient Bayesian functional principal component analysis of irregularly-observed multivariate curves," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).
    20. Priya Kedia & Damitri Kundu & Kiranmoy Das, 2023. "A Bayesian variable selection approach to longitudinal quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 149-168, March.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:40:y:2025:i:8:d:10.1007_s00180-025-01656-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.