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A Bayesian variable selection approach to longitudinal quantile regression

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Abstract

The literature on variable selection for mean regression is quite rich, both in the classical as well as in the Bayesian setting. However, if the goal is to assess the effects of the predictors at different levels of the response variable then quantile regression is useful. In this paper, we develop a Bayesian variable selection method for longitudinal response at some prefixed quantile levels of the response. We consider an Asymmetric Laplace Distribution (ALD) for the longitudinal response, and develop a simple Gibbs sampler algorithm for variable selection at each quantile level. We analyze a dataset from the health and retirement study (HRS) conducted by the University of Michigan for understanding the relationship between the physical health and the financial health of the aged individuals. We consider the out-of-pocket medical expenses as our response variable since it summarizes the physical and the financial well-being of an aged individual. Our proposed approach efficiently selects the important predictors at different prefixed quantile levels. Simulation studies are performed to assess the practical usefulness of the proposed approach. We also compare the performance of the proposed approach to some other existing methods of variable selection in quantile regression.

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References

  • Albert JH, Chib S (1993) Bayesian analysis of binary and polychotomous response data. J Am Stat Assoc 88:669–679

    Article  MathSciNet  MATH  Google Scholar 

  • Al-Hamzawi R, Yu K, Benoit D (2012) Bayesian adaptive lasso quantile regression. Stat Model 12:279–297

    Article  MathSciNet  MATH  Google Scholar 

  • Benoit D, Al-Hamzawi R, Yu K (2013) Bayesian lasso binary quantile regression. Comput Stat 28:2861–2873

    Article  MathSciNet  MATH  Google Scholar 

  • Biswas J, Das K (2019) A Bayesian approach of analyzing semi-continuous longitudinal data with monotone missingness. Stat Model 20:148–170

    Article  MATH  Google Scholar 

  • Biswas J, Ghosh P, Das K (2020) A semi-parametric quantile regression approach to zero-inflated and incomplete longitudinal outcomes. Adv Stat Anal 104:261–283

    Article  MathSciNet  MATH  Google Scholar 

  • Biswas J, Das K (2021) A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data. Comput Stat 36:241–260

    Article  MathSciNet  MATH  Google Scholar 

  • Brooks SP, Gelman A (1998) General methods for monitoring convergence of iterative simulations. J Comput Graph Stat 7:434–455

    MathSciNet  Google Scholar 

  • Cai B, Dunson DB (2008) Bayesian variable selection in generalized linear mixed models. Random effect and latent variable model selection. pp 63–91. Springer, New York

  • Das K, Ghosh P, Daniels MJ (2021) Modeling multiple time-varying related groups: a dynamic hierarchical Bayesian approach with an application to the health and retirement study. J Am Stat Assoc 116:558–568

    Article  MathSciNet  MATH  Google Scholar 

  • Das K, Pareek B, Brown S, Ghosh P (2021) A semi-parametric Bayesian dynamic hurdle model with an application to the health and retirement study. Comput Stat (published online). https://doi.org/10.1007/s00180-021-01143-x

    Article  MATH  Google Scholar 

  • Feng Y, Chen Y, He X (2015) Bayesian quantile regression with approximate likelihood. Bernoulli 21:832–850

    Article  MathSciNet  MATH  Google Scholar 

  • Fernandez C, Ley E, Steel MF (2001) Benchmark priors for Bayesian model averaging. J Econ 100:381–427

    Article  MathSciNet  MATH  Google Scholar 

  • George EI, McCulloch RE (1993) Variable selection via Gibbs sampling. J Am Stat Assoc 88:881–889

    Article  Google Scholar 

  • George EI, McCulloch RE (1997) Approaches for Bayesian variable selection. Stat Sin 7:339–373

    MATH  Google Scholar 

  • Geraci M, Bottai M (2007) Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics 8:140–154

    Article  MATH  Google Scholar 

  • Jang W, Wang HJ (2015) A semiparametric Bayesian approach for joint-quantile regression with clustered data. Comput Stat Data Anal 84:99–115

    Article  MathSciNet  MATH  Google Scholar 

  • Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46:33–50

    Article  MathSciNet  MATH  Google Scholar 

  • Koenker R (2004) Quantile regression for longitudinal data. J Multivar Anal 91:74–89

    Article  MathSciNet  MATH  Google Scholar 

  • Kong Y, Li Y, Zerom D (2019) Screening and selection for quantile regression using an alternative measure of variable importance. J Multivar Anal 173:435–455

    Article  MathSciNet  MATH  Google Scholar 

  • Kozumi H, Kobayashi G (2011) Gibbs sampling methods for Bayesian quantile regression. J Stat Comput Simul 81:1565–1578

    Article  MathSciNet  MATH  Google Scholar 

  • Kulkarni H, Biswas J, Das K (2018) A joint quantile regression model for multiple longitudinal outcomes. Adv Stat Anal 103:453–473

    Article  MathSciNet  MATH  Google Scholar 

  • Kuo L, Mallick B (1998) Variable selection for regression models. Sankhyā Indian J Stat Ser B 60:65–81

    MathSciNet  MATH  Google Scholar 

  • Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38:963–974

    Article  MATH  Google Scholar 

  • Li Q, ** R, Lin N (2010) Bayesian regularized quantile regression. Bayesian Anal 5:533–556

    Article  MathSciNet  MATH  Google Scholar 

  • Marino MF, Farcomeni A (2015) Linear quantile regression models for longitudinal experiments: an overview. Metron 73:229–247

    Article  MathSciNet  MATH  Google Scholar 

  • Mukherji A, Roychoudhury S, Ghosh P, Brown S (2016) Estimating health demand for an aging population: a flexible and robust bayesian joint model. J Appl Econ 31:1140–1158

    Article  MathSciNet  Google Scholar 

  • Park T, Casella G (2008) The bayesian lasso. J Am Stat Assoc 103:681–686

    Article  MathSciNet  MATH  Google Scholar 

  • Reich B, Smith L (2013) Bayesian quantile regression for censored data. Biometrics 69:651–660

    Article  MathSciNet  MATH  Google Scholar 

  • Sala-i-Martin X, Doppelhofer G, Miller RI (2004) Determinants of long-term growth: A Bayesian averaging of classical estimates (BACE) approach. Am Econ Rev, pp 813–835

  • Smith M, Kohn R (1996) Nonparametric regression using Bayesian variable selection. J Econ 75:317–344

    Article  MATH  Google Scholar 

  • Taddy M, Kottas A (2010) A Bayesian nonparametric approach to inference for quantile regression. J Am Stat Assoc 28:357–369

    MathSciNet  MATH  Google Scholar 

  • Tokdar S, Kadane J (2012) Simultaneous linear quantile regression: a semiparametric Bayesian approach. Bayesian Anal 7:51–72

    MathSciNet  MATH  Google Scholar 

  • Wu Y, Liu Y (2009) Variable selection in quantile regression. Stat Sin 19:801–817

    MathSciNet  MATH  Google Scholar 

  • Wichitaksorn N, Choy S, Gerlach R (2014) A generalized class of skew distributions and associated robust quantile regression models. Can J Stat 42:579–596

    Article  MathSciNet  MATH  Google Scholar 

  • Yang Y, Tokdar S (2017) Joint estimation of quantile planes over arbitrary predictor space. J Am Stat Assoc 112:1107–1120

    Article  MathSciNet  Google Scholar 

  • Yu K, Moyeed R (2001) Bayesian quantile regression. Stat Probab Lett 54:437–447

    Article  MathSciNet  MATH  Google Scholar 

  • Yu K, Chen CW, Reed C, Dunson DB (2013) Bayesian variable selection in quantile regression. Stat Interface 6:261–274

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. JP Morgan Chase and Co., Mumbai, India

    Priya Kedia

  2. Applied Statistics Division, Indian Statistical Institute, Kolkata, India

    Priya Kedia, Damitri Kundu & Kiranmoy Das

Authors
  1. Priya Kedia
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  2. Damitri Kundu
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  3. Kiranmoy Das
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Correspondence to Kiranmoy Das.

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The HRS dataset and the relevant information on it are all available with this manuscript.

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Kedia, P., Kundu, D. & Das, K. A Bayesian variable selection approach to longitudinal quantile regression. Stat Methods Appl 32, 149–168 (2023). https://doi.org/10.1007/s10260-022-00645-2

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