Bayesian tobit quantile regression model for medical expenditure panel survey data.

*(English)*Zbl 07257882Summary: High expenditure on healthcare is an important segment of the U.S. economy, making healthcare cost modelling valuable in decision-making processes over a wide array of domains. In this paper, we analyze medical expenditure panel survey (MEPS) data. Tobit regression model has been popularly used for the medical expenditures. However, it is no longer sufficient for the MEPS data because: (i) the distribution of the expenditures shows skewness, heavy tails and heterogeneity; (ii) most predictors are categorical, including binary, nominal and ordinal variables; (iii) there are a few predictors which may be nonlinearly related to the response. We therefore propose a Bayesian Tobit quantile regression model to describe a complete distributional view on how the medical expenditures depend on the various predictors. Specifically, we assume an asymmetric Laplace error distribution to adapt the quantile regression to a Bayesian setting. Then, we propose a modified group Lasso for categorical factor selection, and a smoothing Gaussian prior for modelling the nonlinear effects. The estimates and their uncertainties are obtained using an efficient Monte Carlo Markov Chain sampling method. The effectiveness of our approach is demonstrated by modelling 2007 MEPS data.

##### MSC:

62 | Statistics |

##### Keywords:

asymmetric Laplace distribution; group Lasso; MCMC; medical expenditure panel survey; nonlinear effect; tobit quantile regression
PDF
BibTeX
XML
Cite

\textit{Y. R. Yue} and \textit{H. G. Hong}, Stat. Model. 12, No. 4, 323--346 (2012; Zbl 07257882)

Full Text:
DOI

##### References:

[1] | Alemayehu, B, Warner, KE (2004) The lifetime distribution of health care costs. Health Services Research, 39, 627-42. |

[2] | Andrews, DF, Mallows, CL (1974) Scale mixtures of normal distributions. Journal of the Royal Statistical Society, Series B: Methodological, 36, 99-102. · Zbl 0282.62017 |

[3] | Bell, JF, Zimmerman, FJ, Arterburn, DE, Maciejewski, ML (2011) Health-care expenditures of overweight and obese males and females in the medical expenditures panel survey by age cohort. Obesity, 19, 228-32. |

[4] | Cameron, AC, Trivedi, PK (2010) Microeconometrics using stata. Revised edition. College Station, Texas: Stata Press. · Zbl 1182.62213 |

[5] | Carter, CK, Kohn, R (1996) Markov chain Monte Carlo in conditionally Gaussian state space models. Biometrika, 83, 589-601. · Zbl 0866.62018 |

[6] | Chhikara, RS, Folks, L (1989) The inverse gaussian distribution: theory, methodology, and applications. New York: Marcel Dekker. · Zbl 0701.62009 |

[7] | Chib, S (1992) Bayes inference in the tobit censored regression model. Journal of Econometrics, 51, 79-99. · Zbl 0742.62033 |

[8] | Chib, S, Greenberg, E, Jeliazkov, I (2009) Estimation of semiparametric models in the presence of endogeneity and sample selection. Journal of Computational and Graphical Statistics, 18, 321-48. |

[9] | Clements, MP, Hendry, DF (eds) (2011) The Oxford handbook of economic forecasting. New York: Oxford University Press. |

[10] | Dominici, F, Zeger, SL (2005) Smooth quantile ratio estimation with regression: estimating medical expenditures for smoking attributable diseases. Biostatistics, 6, 505-19. · Zbl 1169.62405 |

[11] | Duan, N (1983) Smearing estimate: A nonparametric retransformation method. Journal of the American Statistical Association, 78, 605-10. · Zbl 0534.62021 |

[12] | Escarce, JJ, Kapur, K (2006) Access to and quality of health care. In Tienda, M, Mitchell, F (eds), Hispanics and the future of America, Chapter 10. Washington, DC: National Academies Press, pp. 410-46. |

[13] | Fahrmeir, L, Lang, S (2001) Bayesian inference for generalized additive mixed models based on Markov random field priors. Journal of the Royal Statistical Society, Series C: Applied Statistics, 50, 201-20. |

[14] | Fahrmeir, L, Tutz, G (2001) Multivariate statistical modeling based on generalized linear models. Berlin: Springer. · Zbl 0980.62052 |

[15] | Furrer, R, Sain, SR (2010) spam: A sparse matrix R package with emphasis on mcmc methods for gaussian markov random fields. Journal of Statistical Software, 36, 1-25. |

[16] | Gertheiss, J, Hogger, S, Oberhauser, C, Tutz, G (2011) Selection of ordinally scaled independent variables with applications to international classification of functioning core sets. Journal of the Royal Statistical Society, Series C: Applied Statistics, 60, 377-95. |

[17] | Gertheiss, J, Tutz, G (2009) Penalized regression with ordinal predictors. International Statistical Review, 77, 345-65. |

[18] | Green, PJ, Silverman, BW (1994) Nonparametric regression and generalized linear models: a roughness penalty approach. London: Chapman & Hall Ltd. · Zbl 0832.62032 |

[19] | Jones, AM (2000) Health econometrics. In Culyer, AJ, Newhouse, JP (eds), Handbook of health economics, vol. 1, 1 edn, Chapter 6, pp. 265-344. New York: Elsevier. |

[20] | Jung, J, Tran, C (2010) Medical consumption over the life cycle: facts from a U.S. medical expenditure panel survey. Working paper series, Department of Economics Towson University. |

[21] | Koenker, R, Bassett, GJ (1978) Regression quantiles. Econometrica, 46, 33-50. · Zbl 0373.62038 |

[22] | Kotz, S, Podgorski, K, Kozubowski, TJ, Podgórski, K (2001) The Laplace distribution and generalizations: a revisit with applications to communications, economics, engineering, and finance. Boston: Birkhäuser. · Zbl 0977.62003 |

[23] | Kozumi, H, Kobayashi, G (2011) Gibbs sampling methods for Bayesian quantile regression. Journal of Statistical Computation and Simulation, 81, 1565-78. · Zbl 1431.62018 |

[24] | Li, Q, Xi, R, Lin, N (2010) Bayesian regularized quantile regression. Bayesian Analysis, 5, 533-56. · Zbl 1330.62143 |

[25] | Lindgren, F, Rue, H (2008) On the second-order random walk model for irregular locations. Scandinavian Journal of Statistics, 35, 691-700. · Zbl 1199.60276 |

[26] | Mullahy, J (2009) Econometric modelling of health care costs and expenditures: a survey of analytical issues and related policy considerations. Medical Care, 47. S104-S108. |

[27] | O’Donnell, O, van Doorslaer, E, Wagstaff, A, Lindelow, M (2008) Analyzing health equity using household survey data: a guide to techniques and their implementation. Washington, D.C.: The World Bank. |

[28] | Park, T, Casella, G (2008) The Bayesian Lasso. Journal of the American Statistical Association, 103, 681-86. · Zbl 1330.62292 |

[29] | Rue, H, Held, L (2005) Gaussian Markov random fields: theory and applications, volume 104 of Monographs on Statistics and Applied Probability. London: Chapman & Hall. |

[30] | Taddy, M, Kottas, A (2010) A Bayesian nonparametric approach to inference for quantile regression. Journal of Business and Economic Statistics, 28, 357-69. · Zbl 1214.62045 |

[31] | Tibshirani, R (1996) Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B: Methodological, 58, 267-88. · Zbl 0850.62538 |

[32] | Tobin, J (1958) Estimation of relationships for limited dependent variables. Econometrica, 26, 24-36. · Zbl 0088.36607 |

[33] | Tsionas, EG (2003) Bayesian quantile inference. Journal of Statistical Computation and Simulation, 73, 659-74. · Zbl 1024.62010 |

[34] | van Hasselt, M (2011) Bayesian inference in a sample selection model. Journal of Econometrics, 165, 221-32. · Zbl 1441.62896 |

[35] | Wahba, G (1990) Spline models for observational data. Philadelphia: SIAM [Society for Industrial and Applied Mathematics]. · Zbl 0813.62001 |

[36] | Yu, K, Moyeed, RA (2001) Bayesian quantile regression. Statistics & Probability Letters, 54, 437-47. · Zbl 0983.62017 |

[37] | Yu, K, Stander, J (2007) Bayesian analysis of a Tobit quantile regression model. Journal of Econometrics, 137, 260-76. · Zbl 1360.62484 |

[38] | Yuan, M, Lin, Y (2006) Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 68, 49-67. · Zbl 1141.62030 |

[39] | Yue, YR, Rue, H (2011) Bayesian inference for additive mixed quantile regression models. Computational Statistics and Data Analysis, 55, 84-96. · Zbl 1247.62101 |

[40] | Yue, YR, Speckman, PL, Sun, D (2011) Priors for Bayesian adaptive spline smoothing. Annals of the Institute of Statistical Mathematics, 64(3), 577-613 doi:10.1007/s10463-010-0321-610.1007/s10463-010-0321-6. · Zbl 1237.62037 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.