Bayesian analysis of quantile regression for censored dynamic panel data

Kobayashi, Genya; Kozumi, Hideo

doi:10.1007/s00180-011-0263-3

Cited by 30 publications

(14 citation statements)

References 74 publications

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“…This representation can transform the ALD to smooth conditional normal distribution and has been extensively utilized in the recent studies. [35,45,47,48] Thus, a two-level hierarchical representation of Equation (A9) is given by…”

Section: Appendix Multivariate Skew-t Distribution and Aldmentioning

confidence: 99%

Quantile regression-based Bayesian semiparametric mixed-effects models for longitudinal data with non-normal, missing and mismeasured covariate

Huang

2015

Journal of Statistical Computation and Simulation

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To cite this article: Yangxin Huang (2015): Quantile regression-based Bayesian semiparametric mixed-effects models for longitudinal data with non-normal, missing and mismeasured covariate, Journal of Statistical Computation and Simulation, Quantile regression (QR) models have received increasing attention recently for longitudinal data analysis. When continuous responses appear non-centrality due to outliers and/or heavy-tails, commonly used mean regression models may fail to produce efficient estimators, whereas QR models may perform satisfactorily. In addition, longitudinal outcomes are often measured with non-normality, substantial errors and non-ignorable missing values. When carrying out statistical inference in such data setting, it is important to account for the simultaneous treatment of these data features; otherwise, erroneous or even misleading results may be produced. In the literature, there has been considerable interest in accommodating either one or some of these data features. However, there is relatively little work concerning all of them simultaneously. There is a need to fill up this gap as longitudinal data do often have these characteristics. Inferential procedure can be complicated dramatically when these data features arise in longitudinal response and covariate outcomes. In this article, our objective is to develop QR-based Bayesian semiparametric mixed-effects models to address the simultaneous impact of these multiple data features. The proposed models and method are applied to analyse a longitudinal data set arising from an AIDS clinical study. Simulation studies are conducted to assess the performance of the proposed method under various scenarios.

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Section: Appendix Multivariate Skew-t Distribution and Aldmentioning

confidence: 99%

Quantile regression-based Bayesian semiparametric mixed-effects models for longitudinal data with non-normal, missing and mismeasured covariate

Huang

2015

Journal of Statistical Computation and Simulation

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“…with mean and X 2 ∼ N(0, 1), 1 = (1 − 2 )∕[ (1 − )] and 2 = 2∕[ (1 − )]. This representation can transform the ALD to smooth conditional normal distribution and has been extensively utilized in the recent studies [51][52][53]. Thus, a two-level hierarchical representation of (A8) is given by…”

Section: A2 Asymmetric Laplace Distributionmentioning

confidence: 99%

Bayesian quantile regression-based nonlinear mixed-effects joint models for time-to-event and longitudinal data with multiple features

Huang

Chen

2016

Statist. Med.

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This article explores Bayesian joint models for a quantile of longitudinal response, mismeasured covariate and event time outcome with an attempt to (i) characterize the entire conditional distribution of the response variable based on quantile regression that may be more robust to outliers and misspecification of error distribution; (ii) tailor accuracy from measurement error, evaluate non-ignorable missing observations, and adjust departures from normality in covariate; and (iii) overcome shortages of confidence in specifying a time-to-event model. When statistical inference is carried out for a longitudinal data set with non-central location, non-linearity, non-normality, measurement error, and missing values as well as event time with being interval censored, it is important to account for the simultaneous treatment of these data features in order to obtain more reliable and robust inferential results. Toward this end, we develop Bayesian joint modeling approach to simultaneously estimating all parameters in the three models: quantile regression-based nonlinear mixed-effects model for response using asymmetric Laplace distribution, linear mixed-effects model with skew-t distribution for mismeasured covariate in the presence of informative missingness and accelerated failure time model with unspecified nonparametric distribution for event time. We apply the proposed modeling approach to analyzing an AIDS clinical data set and conduct simulation studies to assess the performance of the proposed joint models and method. Copyright © 2016 John Wiley & Sons, Ltd.

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“…A Bayesian approach based on the AL likelihood was formally discussed in Yu & Moyeed () for linear quantile regression. In recent years, the AL likelihood has been adopted for Bayesian quantile regression in different contexts and applications, for instance, quantile regression with random effects (Geraci & Bottai, ; Yuan & Yin, ; Geraci & Bottai, ; Yue & Rue, ; Luo et al , ; Wang, ), variable selection for quantile regression (Li et al , ; Alhamzawi et al , ; Alhamzawi & Yu, ; ), spatial quantile regression (Lum & Gelfand, ), quantile regression for count data with application to environmental epidemiology (Lee & Neocleous, ), non‐parametric and semiparametric quantile regression models (Chen & Yu, ; Thompson et al , ; Hu et al , ; Waldmann et al , ; Zhu et al , ; Hu et al , ), quantile regression with fixed censoring (Yu & Stander, ; Kozumi & Kobayashi, ; Kobayashi & Kozumi, ; Yue & Hong, ; Alhamazawi & Yu, ; Zhao & Lian, ), and binary quantile regression (Benoit & Poel, ; Benoit et al , ; Miguéis et al , ).…”

Section: Introductionmentioning

confidence: 99%

Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood

Yang

Wang

2015

Int Statistical Rev

106

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The paper discusses the asymptotic validity of posterior inference of pseudo-Bayesian quantile regression methods with complete or censored data when an asymmetric Laplace likelihood is used. The asymmetric Laplace likelihood has a special place in the Bayesian quantile regression framework because the usual quantile regression estimator can be derived as the maximum likelihood estimator under such a model, and this working likelihood enables highly efficient Markov chain Monte Carlo algorithms for posterior sampling. However, it seems to be underrecognised that the stationary distribution for the resulting posterior does not provide valid posterior inference directly. We demonstrate that a simple adjustment to the covariance matrix of the posterior chain leads to asymptotically valid posterior inference. Our simulation results confirm that the posterior inference, when appropriately adjusted, is an attractive alternative to other asymptotic approximations in quantile regression, especially in the presence of censored data.

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Bayesian analysis of quantile regression for censored dynamic panel data

Cited by 30 publications

References 74 publications

Quantile regression-based Bayesian semiparametric mixed-effects models for longitudinal data with non-normal, missing and mismeasured covariate

Quantile regression-based Bayesian semiparametric mixed-effects models for longitudinal data with non-normal, missing and mismeasured covariate

Bayesian quantile regression-based nonlinear mixed-effects joint models for time-to-event and longitudinal data with multiple features

Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood

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