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Bayesian quantile regression for count data with application to environmental epidemiology

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  • Duncan Lee
  • Tereza Neocleous

Abstract

Summary. Quantile regression estimates the relationship between covariates and the τth quantile of the response distribution, rather than the mean. We present a Bayesian quantile regression model for count data and apply it in the field of environmental epidemiology, which is an area in which quantile regression is yet to be used. Our methods are applied to a new study of the relationship between long‐term exposure to air pollution and respiratory hospital admissions in Scotland. We observe a decreasing relationship between pollution and the τth quantile of the response distribution, with a relative risk ranging between 1.023 and 1.070.

Suggested Citation

  • Duncan Lee & Tereza Neocleous, 2010. "Bayesian quantile regression for count data with application to environmental epidemiology," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(5), pages 905-920, November.
    • Handle: RePEc:bla:jorssc:v:59:y:2010:i:5:p:905-920
    DOI: 10.1111/j.1467-9876.2010.00725.x
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Wang, Weiwei & Wu, Xianyi & Zhao, Xiaobing & Zhou, Xian, 2018. "Robust variable selection of joint frailty model for panel count data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 60-78.
    2. Geraci, Marco, 2014. "Linear Quantile Mixed Models: The lqmm Package for Laplace Quantile Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i13).
    3. Viviana Carcaiso & Leonardo Grilli, 2023. "Quantile regression for count data: jittering versus regression coefficients modelling in the analysis of credits earned by university students after remote teaching," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1061-1082, October.
    4. Fuzi, Mohd Fadzli Mohd & Jemain, Abdul Aziz & Ismail, Noriszura, 2016. "Bayesian quantile regression model for claim count data," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 124-137.
    5. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    6. 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.
    7. Chawarat Rotejanaprasert & Andrew B. Lawson, 2018. "A Bayesian Quantile Modeling for Spatiotemporal Relative Risk: An Application to Adverse Risk Detection of Respiratory Diseases in South Carolina, USA," IJERPH, MDPI, vol. 15(9), pages 1-15, September.
    8. Paolo Frumento & Nicola Salvati, 2021. "Parametric modeling of quantile regression coefficient functions with count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1237-1258, October.
    9. Yunwen Yang & Huixia Judy Wang & Xuming He, 2016. "Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood," International Statistical Review, International Statistical Institute, vol. 84(3), pages 327-344, December.
    10. Xuejun Jiang & Yunxian Li & Aijun Yang & Ruowei Zhou, 2020. "Bayesian semiparametric quantile regression modeling for estimating earthquake fatality risk," Empirical Economics, Springer, vol. 58(5), pages 2085-2103, May.
    11. Bhattacharya, Indrabati & Ghosal, Subhashis, 2021. "Bayesian multivariate quantile regression using Dependent Dirichlet Process prior," Journal of Multivariate Analysis, Elsevier, vol. 185(C).

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