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.

分位数回归是用于对非高斯数据进行建模以及对响应概率分布的不同分位数进行建模的强大工具。我们提出了一种贝叶斯方法，用于估计响应包含多余零的多元纵向数据的分位数。我们考虑使用Tobit回归方法，其中潜在响应是使用线性混合模型估算的。纵向依赖性和不同（潜在）响应之间的相关性是通过特定于受试者的随机效应向量来建模的。我们考虑非对称拉普拉斯分布（ALD）的混合表示，并开发一种有效的MCMC算法来估计模型参数。拟议的方法用于分析美国密歇根大学进行的健康和退休研究（HRS）中的数据；在这里，我们共同建模（i）自付费用的医疗支出，（ii）总金融资产和（iii）老年受试者的总金融债务，并估算不同协变量对不同分位数对这些响应的影响。进行仿真研究以评估所提出方法的操作特性。