IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v5y2009i1n28.html
   My bibliography  Save this article

Mixed-Effects Models for Conditional Quantiles with Longitudinal Data

Author

Listed:
  • Liu Yuan

    (Medical University of South Carolina)

  • Bottai Matteo

    (University of South Carolina)

Abstract

We propose a regression method for the estimation of conditional quantiles of a continuous response variable given a set of covariates when the data are dependent. Along with fixed regression coefficients, we introduce random coefficients which we assume to follow a form of multivariate Laplace distribution. In a simulation study, the proposed quantile mixed-effects regression is shown to model the dependence among longitudinal data correctly and estimate the fixed effects efficiently. It performs similarly to the linear mixed model at the central location when the regression errors are symmetrically distributed, but provides more efficient estimates when the errors are over-dispersed. At the same time, it allows the estimation at different locations of conditional distribution, which conveys a comprehensive understanding of data. We illustrate an application to clinical data where the outcome variable of interest is bounded within a closed interval.

Suggested Citation

  • Liu Yuan & Bottai Matteo, 2009. "Mixed-Effects Models for Conditional Quantiles with Longitudinal Data," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-24, November.
    • Handle: RePEc:bpj:ijbist:v:5:y:2009:i:1:n:28
    DOI: 10.2202/1557-4679.1186
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1557-4679.1186
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1557-4679.1186?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. Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
    2. Guosheng Yin & Jianwen Cai, 2005. "Quantile Regression Models with Multivariate Failure Time Data," Biometrics, The International Biometric Society, vol. 61(1), pages 151-161, March.
    3. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    4. Lindsey, J.K. & Lindsey, P.J., 2006. "Multivariate distributions with correlation matrices for nonlinear repeated measurements," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 720-732, February.
    5. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    6. Eickhoff, Jens C. & Zhu, Jun & Amemiya, Yasuo, 2004. "On the simulation size and the convergence of the Monte Carlo EM algorithm via likelihood-based distances," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 161-171, April.
    7. José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
    8. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
    11. Buchinsky, Moshe, 1995. "Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study," Journal of Econometrics, Elsevier, vol. 68(2), pages 303-338, August.
    12. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    13. Andrews, Donald W. K. & Buchinsky, Moshe, 2001. "Evaluation of a three-step method for choosing the number of bootstrap repetitions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 345-386, July.
    14. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    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. Hanze Zhang & Yangxin Huang, 2020. "Quantile regression-based Bayesian joint modeling analysis of longitudinal–survival data, with application to an AIDS cohort study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 339-368, April.
    2. Christian E. Galarza & Luis M. Castro & Francisco Louzada & Victor H. Lachos, 2020. "Quantile regression for nonlinear mixed effects models: a likelihood based perspective," Statistical Papers, Springer, vol. 61(3), pages 1281-1307, June.
    3. 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.
    4. Yves S. Schüler, 2014. "Asymmetric Effects of Uncertainty over the Business Cycle: A Quantile Structural Vector Autoregressive Approach," Working Paper Series of the Department of Economics, University of Konstanz 2014-02, Department of Economics, University of Konstanz.
    5. Luca Merlo & Lea Petrella & Nikos Tzavidis, 2022. "Quantile mixed hidden Markov models for multivariate longitudinal data: An application to children's Strengths and Difficulties Questionnaire scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 417-448, March.
    6. Elena Fabrizi & Alessio Farcomeni & Valerio Gatta, 2012. "Modelling work history patterns in the Italian labour market," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 227-247, June.
    7. Chen, Xuerong & Tang, Niansheng & Zhou, Yong, 2016. "Quantile regression of longitudinal data with informative observation times," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 176-188.
    8. Chenxi Li & N. Maritza Dowling & Rick Chappell, 2015. "Quantile regression with a change‐point model for longitudinal data: An application to the study of cognitive changes in preclinical alzheimer's disease," Biometrics, The International Biometric Society, vol. 71(3), pages 625-635, September.
    9. Machado, José A.F. & Santos Silva, J.M.C. & Wei, Kehai, 2016. "Quantiles, corners, and the extensive margin of trade," European Economic Review, Elsevier, vol. 89(C), pages 73-84.
    10. 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.
    11. Yuzhu Tian & Manlai Tang & Yanchao Zang & Maozai Tian, 2018. "Quantile regression for linear models with autoregressive errors using EM algorithm," Computational Statistics, Springer, vol. 33(4), pages 1605-1625, December.
    12. Xiaoming Lu & Zhaozhi Fan, 2015. "Weighted quantile regression for longitudinal data," Computational Statistics, Springer, vol. 30(2), pages 569-592, June.
    13. Mohammad Arshad Rahman & Angela Vossmeyer, 2019. "Estimation and Applications of Quantile Regression for Binary Longitudinal Data," Advances in Econometrics, in: Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B, volume 40, pages 157-191, Emerald Group Publishing Limited.
    14. Schüler, Yves S., 2020. "The impact of uncertainty and certainty shocks," Discussion Papers 14/2020, Deutsche Bundesbank.
    15. Maria Marino & Marco Alfó, 2015. "Latent drop-out based transitions in linear quantile hidden Markov models for longitudinal responses with attrition," 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. 9(4), pages 483-502, December.
    16. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    17. 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.
    18. 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.
    19. Yuzhu Tian & Manlai Tang & Maozai Tian, 2018. "Joint modeling for mixed-effects quantile regression of longitudinal data with detection limits and covariates measured with error, with application to AIDS studies," Computational Statistics, Springer, vol. 33(4), pages 1563-1587, December.

    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. Guilherme Resende Oliveira & Benjamin Miranda Tabak & José Guilherme de Lara Resende & Daniel Oliveira Cajueiro, 2012. "Determinantes da Estrutura de Capital das Empresas Brasileiras: uma abordagem em regressão quantílica," Working Papers Series 272, Central Bank of Brazil, Research Department.
    3. 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.
    4. Castagnetti, Carolina & Giorgetti, Maria Letizia, 2019. "Understanding the gender wage-gap differential between the public and private sectors in Italy: A quantile approach," Economic Modelling, Elsevier, vol. 78(C), pages 240-261.
    5. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    6. Firpo, Sergio & Galvao, Antonio F. & Pinto, Cristine & Poirier, Alexandre & Sanroman, Graciela, 2022. "GMM quantile regression," Journal of Econometrics, Elsevier, vol. 230(2), pages 432-452.
    7. Graham, Bryan S. & Hahn, Jinyong & Poirier, Alexandre & Powell, James L., 2018. "A quantile correlated random coefficients panel data model," Journal of Econometrics, Elsevier, vol. 206(2), pages 305-335.
    8. Fu, Liya & Wang, You-Gan, 2016. "Efficient parameter estimation via Gaussian copulas for quantile regression with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 492-502.
    9. Galvao, Antonio F. & Kato, Kengo, 2016. "Smoothed quantile regression for panel data," Journal of Econometrics, Elsevier, vol. 193(1), pages 92-112.
    10. 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.
    11. Kollias Christos & Paleologou Suzanna-Maria & Tzeremes Panayiotis, 2020. "Defence Spending and Unemployment in the USA: Disaggregated Analysis by Gender and Age Groups," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 26(2), pages 1-13, May.
    12. Lixin Cai & Amy Y. C. Liu, 2011. "Public–Private Sector Wage Gap in Australia: Variation along the Distribution," British Journal of Industrial Relations, London School of Economics, vol. 49(2), pages 362-390, June.
    13. 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.
    14. Yu-Yen Ku & Tze-Yu Yen, 2016. "Heterogeneous Effect of Financial Leverage on Corporate Performance: A Quantile Regression Analysis of Taiwanese Companies," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-33, September.
    15. Stacy, Brian, 2014. "Left with Bias? Quantile Regression with Measurement Error in Left Hand Side Variables," EconStor Preprints 104744, ZBW - Leibniz Information Centre for Economics.
    16. Elena Fabrizi & Alessio Farcomeni & Valerio Gatta, 2012. "Modelling work history patterns in the Italian labour market," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 227-247, June.
    17. Meligkotsidou, Loukia & Vrontos, Ioannis D. & Vrontos, Spyridon D., 2009. "Quantile regression analysis of hedge fund strategies," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 264-279, March.
    18. Gareth W. Peters, 2018. "General Quantile Time Series Regressions for Applications in Population Demographics," Risks, MDPI, vol. 6(3), pages 1-47, September.
    19. Akosah, Nana Kwame & Alagidede, Imhotep Paul & Schaling, Eric, 2020. "Testing for asymmetry in monetary policy rule for small-open developing economies: Multiscale Bayesian quantile evidence from Ghana," The Journal of Economic Asymmetries, Elsevier, vol. 22(C).
    20. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.

    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:bpj:ijbist:v:5:y:2009:i:1:n:28. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.