IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v137y2018icp251-256.html
   My bibliography  Save this article

Analysis of the Pólya-Gamma block Gibbs sampler for Bayesian logistic linear mixed models

Author

Listed:
  • Wang, Xin
  • Roy, Vivekananda

Abstract

In this article, we construct a two-block Gibbs sampler using Polson et al.’s (2013) data augmentation technique for Bayesian logistic linear mixed models under proper priors. Furthermore, we prove the uniform ergodicity of this Gibbs sampler.

Suggested Citation

  • Wang, Xin & Roy, Vivekananda, 2018. "Analysis of the Pólya-Gamma block Gibbs sampler for Bayesian logistic linear mixed models," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 251-256.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:251-256
    DOI: 10.1016/j.spl.2018.02.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715218300476
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2018.02.003?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Vivekananda Roy & James P. Hobert, 2007. "Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 607-623, September.
    2. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    3. Gareth O. Roberts & Jeffrey S. Rosenthal, 2001. "Markov Chains and De‐initializing Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 489-504, September.
    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. Chu, Amanda M.Y. & Omori, Yasuhiro & So, Hing-yu & So, Mike K.P., 2023. "A Multivariate Randomized Response Model for Sensitive Binary Data," Econometrics and Statistics, Elsevier, vol. 27(C), pages 16-35.
    2. James P. Hobert & Christian P. Robert & Vivekanada Roy, 2010. "Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modelling," Working Papers 2010-29, Center for Research in Economics and Statistics.
    3. Buddhavarapu, Prasad & Bansal, Prateek & Prozzi, Jorge A., 2021. "A new spatial count data model with time-varying parameters," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 566-586.
    4. Niko Hauzenberger & Florian Huber, 2020. "Model instability in predictive exchange rate regressions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 168-186, March.
    5. Anindya Bhadra & Arvind Rao & Veerabhadran Baladandayuthapani, 2018. "Inferring network structure in non†normal and mixed discrete†continuous genomic data," Biometrics, The International Biometric Society, vol. 74(1), pages 185-195, March.
    6. Haoying Wang & Guohui Wu, 2022. "Modeling discrete choices with large fine-scale spatial data: opportunities and challenges," Journal of Geographical Systems, Springer, vol. 24(3), pages 325-351, July.
    7. Johnson, Alicia A. & Jones, Galin L., 2015. "Geometric ergodicity of random scan Gibbs samplers for hierarchical one-way random effects models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 325-342.
    8. Matthew W. Wheeler, 2019. "Bayesian additive adaptive basis tensor product models for modeling high dimensional surfaces: an application to high‐throughput toxicity testing," Biometrics, The International Biometric Society, vol. 75(1), pages 193-201, March.
    9. Bansal, Prateek & Krueger, Rico & Graham, Daniel J., 2021. "Fast Bayesian estimation of spatial count data models," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    10. Tamás Krisztin & Philipp Piribauer, 2021. "A Bayesian spatial autoregressive logit model with an empirical application to European regional FDI flows," Empirical Economics, Springer, vol. 61(1), pages 231-257, July.
    11. Anindya Bhadra & Jyotishka Datta & Nicholas G. Polson & Brandon T. Willard, 2020. "Global-Local Mixtures: A Unifying Framework," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 426-447, August.
    12. Yunyun Wang & Tatsushi Oka & Dan Zhu, 2024. "Inflation Target at Risk: A Time-varying Parameter Distributional Regression," Papers 2403.12456, arXiv.org.
    13. Sylvia Frühwirth-Schnatter & Gertraud Malsiner-Walli, 2019. "From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 33-64, March.
    14. Higgs, Megan Dailey & Hoeting, Jennifer A., 2010. "A clipped latent variable model for spatially correlated ordered categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1999-2011, August.
    15. Lauren Hoskovec & Sheena Martenies & Tori L. Burket & Sheryl Magzamen & Ander Wilson, 2022. "Association between air pollution and COVID‐19 disease severity via Bayesian multinomial logistic regression with partially missing outcomes," Environmetrics, John Wiley & Sons, Ltd., vol. 33(7), November.
    16. Bodnar, Olha & Bodnar, Taras, 2024. "Gibbs sampler approach for objective Bayesian inference in elliptical multivariate meta-analysis random effects model," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    17. Uddin, Md Nazir & Gaskins, Jeremy T., 2023. "Shared Bayesian variable shrinkage in multinomial logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    18. Piero Mazzarisi & Paolo Barucca & Fabrizio Lillo & Daniele Tantari, 2017. "A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market," Papers 1801.00185, arXiv.org.
    19. Kshitij Khare & Malay Ghosh, 2022. "MCMC Convergence for Global-Local Shrinkage Priors," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 211-234, September.
    20. Yeonhee Park & Suyu Liu & Peter F. Thall & Ying Yuan, 2022. "Bayesian group sequential enrichment designs based on adaptive regression of response and survival time on baseline biomarkers," Biometrics, The International Biometric Society, vol. 78(1), pages 60-71, March.

    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:eee:stapro:v:137:y:2018:i:c:p:251-256. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.