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Bayesian quantile regression for count data with application to environmental epidemiology


  • Duncan Lee
  • Tereza Neocleous


Quantile regression estimates the relationship between covariates and the "τ"th 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 "τ"th quantile of the response distribution, with a relative risk ranging between 1.023 and 1.070. Copyright (c) 2010 Royal Statistical Society.

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  • 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.
  • Handle: RePEc:bla:jorssc:v:59:y:2010:i:5:p:905-920

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    References listed on IDEAS

    1. Machado, Jose A.F. & Silva, J. M. C. Santos, 2005. "Quantiles for Counts," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1226-1237, December.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    5. Francesca Dominici & Scott L. Zeger & Giovanni Parmigiani & Joanne Katz & Parul Christian, 2006. "Estimating percentile-specific treatment effects in counterfactual models: a case-study of micronutrient supplementation, birth weight and infant mortality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 261-280.
    6. Francesca Dominici & Jonathan M. Samet & Scott L. Zeger, 2000. "Combining evidence on air pollution and daily mortality from the 20 largest US cities: a hierarchical modelling strategy," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 163(3), pages 263-302.
    7. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
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    Cited by:

    1. 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.
    2. repec:bla:istatr:v:84:y:2016:i:3:p:327-344 is not listed on IDEAS

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