IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v136y2019icp30-46.html
   My bibliography  Save this article

Modelling and estimation of nonlinear quantile regression with clustered data

Author

Listed:
  • Geraci, Marco

Abstract

In regression applications, the presence of nonlinearity and correlation among observations offer computational challenges not only in traditional settings such as least squares regression, but also (and especially) when the objective function is nonsmooth as in the case of quantile regression. Methods are developed for the modelling and estimation of nonlinear conditional quantile functions when data are clustered within two-level nested designs. The proposed estimation algorithm is a blend of a smoothing algorithm for quantile regression and a second order Laplacian approximation for nonlinear mixed models. This optimization approach has the appealing advantage of reducing the original nonsmooth problem to an approximated L2 problem. While the estimation algorithm is iterative, the objective function to be optimized has a simple analytic form. The proposed methods are assessed through a simulation study and two applications, one in pharmacokinetics and one related to growth curve modelling in agriculture.

Suggested Citation

  • Geraci, Marco, 2019. "Modelling and estimation of nonlinear quantile regression with clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 30-46.
    • Handle: RePEc:eee:csdana:v:136:y:2019:i:c:p:30-46
    DOI: 10.1016/j.csda.2018.12.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318302846
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.12.005?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. Oberhofer, Walter & Haupt, Harry, 2016. "Asymptotic Theory For Nonlinear Quantile Regression Under Weak Dependence," Econometric Theory, Cambridge University Press, vol. 32(3), pages 686-713, June.
    2. Stefan Bache & Christian Dahl & Johannes Kristensen, 2013. "Headlights on tobacco road to low birthweight outcomes," Empirical Economics, Springer, vol. 44(3), pages 1593-1633, June.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Xiaohong Chen & Roger Koenker & Zhijie Xiao, 2009. "Copula-based nonlinear quantile autoregression," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 50-67, January.
    5. Galvao Jr., Antonio F., 2011. "Quantile regression for dynamic panel data with fixed effects," Journal of Econometrics, Elsevier, vol. 164(1), pages 142-157, September.
    6. Ying Yuan & Guosheng Yin, 2010. "Bayesian Quantile Regression for Longitudinal Studies with Nonignorable Missing Data," Biometrics, The International Biometric Society, vol. 66(1), pages 105-114, March.
    7. Fu, Liya & Wang, You-Gan, 2012. "Quantile regression for longitudinal data with a working correlation model," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2526-2538.
    8. Parente Paulo M.D.C. & Santos Silva João M.C., 2016. "Quantile Regression with Clustered Data," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 1-15, January.
    9. Ivan A. Canay, 2011. "A simple approach to quantile regression for panel data," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 368-386, October.
    10. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    11. Abrevaya, Jason & Dahl, Christian M, 2008. "The Effects of Birth Inputs on Birthweight," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 379-397.
    12. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    13. 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).
    14. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    15. Jing Wang, 2012. "Bayesian quantile regression for parametric nonlinear mixed effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 279-295, August.
    16. Martha Contreras & Louise M. Ryan, 2000. "Fitting Nonlinear and Constrained Generalized Estimating Equations with Optimization Software," Biometrics, The International Biometric Society, vol. 56(4), pages 1268-1271, December.
    17. Lamarche, Carlos, 2010. "Robust penalized quantile regression estimation for panel data," Journal of Econometrics, Elsevier, vol. 157(2), pages 396-408, August.
    18. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
    19. Vonesh E. F. & Wang H. & Nie L. & Majumdar D., 2002. "Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 271-283, March.
    20. Winkelmann, Rainer, 2006. "Reforming health care: Evidence from quantile regressions for counts," Journal of Health Economics, Elsevier, vol. 25(1), pages 131-145, January.
    21. Angela Noufaily & M. C. Jones, 2013. "Parametric quantile regression based on the generalized gamma distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(5), pages 723-740, November.
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bahram Adrangi & Arjun Chatrath & Madhuparna Kolay & Kambiz Raffiee, 2021. "Dynamic Responses of Standard and Poor’s Regional Bank Index to the U.S. Fear Index, VIX," JRFM, MDPI, vol. 14(3), pages 1-18, March.
    2. Xiaoming Lu & Zhaozhi Fan, 2020. "Generalized linear mixed quantile regression with panel data," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-16, August.
    3. Bahram Adrangi & Arjun Chatrath & Kambiz Raffiee, 2023. "S&P 500 volatility, volatility regimes, and economic uncertainty," Bulletin of Economic Research, Wiley Blackwell, vol. 75(4), pages 1362-1387, October.
    4. Aleida Cobas-Valdés & Javier Fernández-Macho, 2021. "Gender Dissimilarities in Human Capital Transferability of Cuban Immigrants in the US: A Clustering Quantile Regression Coefficients Approach with Consideration of Implications for Sustainability," Sustainability, MDPI, vol. 13(21), pages 1-12, October.

    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. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    2. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2021. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 60(1), pages 227-259, January.
    3. Denis Chetverikov & Bradley Larsen & Christopher Palmer, 2016. "IV Quantile Regression for Group‐Level Treatments, With an Application to the Distributional Effects of Trade," Econometrica, Econometric Society, vol. 84, pages 809-833, March.
    4. Battagliola, Maria Laura & Sørensen, Helle & Tolver, Anders & Staicu, Ana-Maria, 2022. "A bias-adjusted estimator in quantile regression for clustered data," Econometrics and Statistics, Elsevier, vol. 23(C), pages 165-186.
    5. Genya Kobayashi & Hideo Kozumi, 2012. "Bayesian analysis of quantile regression for censored dynamic panel data," Computational Statistics, Springer, vol. 27(2), pages 359-380, June.
    6. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.
    7. Raffaele Miniaci & Paolo Panteghini, 2021. "On the Capital Structure of Foreign Subsidiaries: Evidence from a Panel Data Quantile Regression Model," CESifo Working Paper Series 9085, CESifo.
    8. Lijuan Huo & Tae-Hwan Kim & Yunmi Kim, 2013. "Testing for Autocorrelation in Quantile Regression Models," Working papers 2013rwp-54, Yonsei University, Yonsei Economics Research Institute.
    9. Ali Aghamohammadi, 2018. "Bayesian analysis of dynamic panel data by penalized quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 91-108, March.
    10. Jang, Woosung & Wang, Huixia Judy, 2015. "A semiparametric Bayesian approach for joint-quantile regression with clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 99-115.
    11. Jorge Eduardo Camusso & Ana Inés Navarro, 2021. "Asymmetries in aggregate income risk over the business cycle: evidence from administrative data of Argentina," Asociación Argentina de Economía Política: Working Papers 4447, Asociación Argentina de Economía Política.
    12. Ben-Salha Ousama & Zmami Mourad, 2020. "The impact of private capital flows on economic growth in the MENA region," Economics and Business Review, Sciendo, vol. 6(3), pages 45-67, August.
    13. Cai, Zongwu & Chen, Linna & Fang, Ying, 2018. "A semiparametric quantile panel data model with an application to estimating the growth effect of FDI," Journal of Econometrics, Elsevier, vol. 206(2), pages 531-553.
    14. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers CWP36/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Chao-Qun Ma & Jiang-Long Liu & Yi-Shuai Ren & Yong Jiang, 2019. "The Impact of Economic Growth, FDI and Energy Intensity on China’s Manufacturing Industry’s CO 2 Emissions: An Empirical Study Based on the Fixed-Effect Panel Quantile Regression Model," Energies, MDPI, vol. 12(24), pages 1-16, December.
    16. Zheng Fang & Yoko Niimi, 2015. "Do Losses Bite More than Gains? Evidence from a Panel Quantile Regression Analysis of Subjective Well-being in Japan," Economic Growth Centre Working Paper Series 1507, Nanyang Technological University, School of Social Sciences, Economic Growth Centre.
    17. Damette, Olivier & Kouki, Imen, 2022. "Political influence and banking performance: Evidence from the African countries," The Quarterly Review of Economics and Finance, Elsevier, vol. 84(C), pages 200-207.
    18. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers 36/17, Institute for Fiscal Studies.
    19. Galvao, Antonio F. & Kato, Kengo, 2016. "Smoothed quantile regression for panel data," Journal of Econometrics, Elsevier, vol. 193(1), pages 92-112.
    20. Wu, Chen & Rogers, Cynthia L., 2017. "One Size Does Not Fit All: Foreign Direct Investment Promotion Policies across US States," Journal of Regional Analysis and Policy, Mid-Continent Regional Science Association, vol. 48(1), April.

    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:csdana:v:136:y:2019:i:c:p:30-46. 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/locate/csda .

    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.