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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
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    References listed on IDEAS

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    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.
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