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Parametric modeling of quantile regression coefficient functions with count data

Author

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  • Paolo Frumento

    (University of Pisa)

  • Nicola Salvati

    (University of Pisa)

Abstract

Applying quantile regression to count data presents logical and practical complications which are usually solved by artificially smoothing the discrete response variable through jittering. In this paper, we present an alternative approach in which the quantile regression coefficients are modeled by means of (flexible) parametric functions. The proposed method avoids jittering and presents numerous advantages over standard quantile regression in terms of computation, smoothness, efficiency, and ease of interpretation. Estimation is carried out by minimizing a “simultaneous” version of the loss function of ordinary quantile regression. Simulation results show that the described estimators are similar to those obtained with jittering, but are often preferable in terms of bias and efficiency. To exemplify our approach and provide guidelines for model building, we analyze data from the US National Medical Expenditure Survey. All the necessary software is implemented in the existing R package qrcm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:4:d:10.1007_s10260-021-00557-7
    DOI: 10.1007/s10260-021-00557-7
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    1. 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.
    2. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    3. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    4. Sara Moreira & Pedro Pita Barros, 2010. "Double health insurance coverage and health care utilisation: evidence from quantile regression," Health Economics, John Wiley & Sons, Ltd., vol. 19(9), pages 1075-1092, September.
    5. Winkelmann, Rainer, 2006. "Reforming health care: Evidence from quantile regressions for counts," Journal of Health Economics, Elsevier, vol. 25(1), pages 131-145, January.
    6. Alison L. Booth & Hiau Joo Kee, 2009. "Intergenerational Transmission of Fertility Patterns," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(2), pages 183-208, April.
    7. Deb, Partha & Trivedi, Pravin K, 1997. "Demand for Medical Care by the Elderly: A Finite Mixture Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 313-336, May-June.
    8. 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.
    9. Machado, José A.F., 1993. "Robust Model Selection and M-Estimation," Econometric Theory, Cambridge University Press, vol. 9(3), pages 478-493, June.
    10. Yufeng Liu & Yichao Wu, 2011. "Simultaneous multiple non-crossing quantile regression estimation using kernel constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 415-437.
    11. Brian J. Reich, 2012. "Spatiotemporal quantile regression for detecting distributional changes in environmental processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(4), pages 535-553, August.
    12. Das, Priyam & Ghosal, Subhashis, 2018. "Bayesian non-parametric simultaneous quantile regression for complete and grid data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 172-186.
    13. Yun Yang & Surya T. Tokdar, 2017. "Joint Estimation of Quantile Planes Over Arbitrary Predictor Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1107-1120, July.
    14. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    15. Paolo Frumento & Matteo Bottai, 2016. "Parametric modeling of quantile regression coefficient functions," Biometrics, The International Biometric Society, vol. 72(1), pages 74-84, March.
    16. Das, Priyam & Ghosal, Subhashis, 2017. "Bayesian quantile regression using random B-spline series prior," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 121-143.
    17. Brian J. Reich & Luke B. Smith, 2013. "Bayesian Quantile Regression for Censored Data," Biometrics, The International Biometric Society, vol. 69(3), pages 651-660, September.
    18. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    19. Paolo Frumento & Matteo Bottai, 2017. "Parametric modeling of quantile regression coefficient functions with censored and truncated data," Biometrics, The International Biometric Society, vol. 73(4), pages 1179-1188, December.
    20. Fabrizi, Enrico & Salvati, Nicola & Trivisano, Carlo, 2020. "Robust Bayesian small area estimation based on quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    21. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    22. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    23. Eun Ryung Lee & Hohsuk Noh & Byeong U. Park, 2014. "Model Selection via Bayesian Information Criterion for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 216-229, March.
    24. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
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    Cited by:

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