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A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data

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  • Jayabrata Biswas

    (Indian Statistical Institute
    University of Burdwan)

  • Kiranmoy Das

    (Indian Statistical Institute)

Abstract

Quantile regression is a powerful tool for modeling non-Gaussian data, and also for modeling different quantiles of the probability distributions of the responses. We propose a Bayesian approach of estimating the quantiles of multivariate longitudinal data where the responses contain excess zeros. We consider a Tobit regression approach, where the latent responses are estimated using a linear mixed model. The longitudinal dependence and the correlations among different (latent) responses are modeled by the subject-specific vector of random effects. We consider a mixture representation of the Asymmetric Laplace Distribution (ALD), and develop an efficient MCMC algorithm for estimating the model parameters. The proposed approach is used for analyzing data from the health and retirement study (HRS) conducted by the University of Michigan, USA; where we jointly model (i) out-of-pocket medical expenditures, (ii) total financial assets, and (iii) total financial debt for the aged subjects, and estimate the effects of different covariates on these responses across different quantiles. Simulation studies are performed for assessing the operating characteristics of the proposed approach.

Suggested Citation

  • Jayabrata Biswas & Kiranmoy Das, 2021. "A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data," Computational Statistics, Springer, vol. 36(1), pages 241-260, March.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:1:d:10.1007_s00180-020-01002-1
    DOI: 10.1007/s00180-020-01002-1
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    References listed on IDEAS

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    1. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    2. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
    3. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    4. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    5. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    6. Brown, Sarah & Ghosh, Pulak & Su, Li & Taylor, Karl, 2015. "Modelling household finances: A Bayesian approach to a multivariate two-part model," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 190-207.
    7. Drovandi, Christopher C. & Pettitt, Anthony N., 2011. "Likelihood-free Bayesian estimation of multivariate quantile distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2541-2556, September.
    8. Duan, Naihua, et al, 1983. "A Comparison of Alternative Models for the Demand for Medical Care," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 115-126, April.
    9. Jayabrata Biswas & Pulak Ghosh & Kiranmoy Das, 2020. "A semi-parametric quantile regression approach to zero-inflated and incomplete longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 261-283, June.
    10. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    11. Arnab Mukherji & Satrajit Roychoudhury & Pulak Ghosh & Sarah Brown, 2016. "Estimating Health Demand for an Aging Population: A Flexible and Robust Bayesian Joint Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(6), pages 1140-1158, September.
    12. Kiranmoy Das & Michael J. Daniels, 2014. "A semiparametric approach to simultaneous covariance estimation for bivariate sparse longitudinal data," Biometrics, The International Biometric Society, vol. 70(1), pages 33-43, March.
    13. 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.
    14. Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
    15. Reich, Brian J. & Fuentes, Montserrat & Dunson, David B., 2011. "Bayesian Spatial Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 6-20.
    16. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    17. P. J. Heagerty & M. S. Pepe, 1999. "Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 533-551.
    18. Sonja Greven & Thomas Kneib, 2010. "On the behaviour of marginal and conditional AIC in linear mixed models," Biometrika, Biometrika Trust, vol. 97(4), pages 773-789.
    19. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(1), pages 105-121, February.
    20. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:

    1. Kiranmoy Das & Bhuvanesh Pareek & Sarah Brown & Pulak Ghosh, 2022. "A semi-parametric Bayesian dynamic hurdle model with an application to the health and retirement study," Computational Statistics, Springer, vol. 37(2), pages 837-863, April.
    2. Priya Kedia & Damitri Kundu & Kiranmoy Das, 2023. "A Bayesian variable selection approach to longitudinal quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 149-168, March.

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