Empirical studies in various fields, such as clinical trials, environmental sciences, psychology, as well as finance and economics, often encounter the task of conducting statistical inference for longitudinal data with ordinal responses. In such situation, it may not be valid of using the orthodox modeling methods of continuous responses. In addition, most traditional methods of modeling longitudinal data tend to depict the average variation of the outcome variable conditionally on covariates, which may lead to non-robust estimation results. Quantile regression is a natural alternative for describing the impact of covariates on the conditional distributions of an outcome variable instead of the mean. Furthermore, in regression modeling, excessive number of covariates may be brought into the models which plausibly result in reduction of model prediction accuracy. It is desirable to obtain a parsimonious model that only retains significant and meaningful covariates. Regularized penalty methods have been shown to be efficient for conducting simultaneous variable selection and coefficient estimation. In this paper, Bayesian bridge-randomized penalty is incorporated into the quantile mixed effects models of ordinal longitudinal data to conduct parameter estimation and variable selection simultaneously. The Bayesian joint hierarchical model is established and an efficient Gibbs sampler algorithm is employed to perform posterior statistical inference. Finally, the proposed approach is illustrated using simulation studies and applied to an ordinal longitudinal real dataset of firm bond ratings.

临床试验，环境科学，心理学以及金融和经济学等各个领域的经验研究经常遇到对具有顺序响应的纵向数据进行统计推断的任务。在这种情况下，使用连续响应的正统建模方法可能无效。此外，大多数传统的纵向数据建模方法都倾向于在协变量上有条件地描述结果变量的平均变化，这可能会导致估算结果不稳健。分位数回归是描述协变量对结果变量（而非均值）的条件分布的影响的自然选择。此外，在回归建模中 过多的协变量可能被带入模型，这有可能导致模型预测准确性的降低。期望获得仅保留显着且有意义的协变量的简约模型。已经显示出正则惩罚方法对于进行同时的变量选择和系数估计是有效的。本文将贝叶斯桥随机罚分法引入序数纵向数据的分位数混合效应模型中，以同时进行参数估计和变量选择。建立贝叶斯联合层次模型，并采用有效的吉布斯采样器算法进行后验统计推断。最后，