The monotone data augmentation (MDA) algorithm has been widely used to impute missing data for longitudinal continuous outcomes. Compared to a full data augmentation approach, the MDA scheme accelerates the mixing of the Markov chain, reduces computational costs per iteration, and aids in missing data imputation under nonignorable dropouts. We extend the MDA algorithm to the multivariate probit (MVP) model for longitudinal binary and ordinal outcomes. The MVP model assumes the categorical outcomes are discretized versions of underlying longitudinal latent Gaussian outcomes modeled by a mixed effects model for repeated measures. A parameter expansion strategy is employed to facilitate the posterior sampling, and expedite the convergence of the Markov chain in MVP. The method enables the sampling of the regression coefficients and covariance matrix for longitudinal continuous, binary and ordinal outcomes in a unified manner. This property aids in understanding the algorithm and developing computer codes for MVP. We also introduce independent Metropolis-Hasting samplers to handle complex priors, and evaluate how the choice between flat and diffuse normal priors for regression coefficients influences parameter estimation and missing data imputation. Numerical examples are used to illustrate the methodology.

翻译：单调数据增强（MDA）算法已被广泛用于纵向连续型结果数据的缺失值插补。与完整数据增强方法相比，MDA方案能够加速马尔可夫链的混合，降低每次迭代的计算成本，并有助于在不可忽略的脱落情况下进行缺失数据插补。本文将MDA算法扩展至适用于纵向二分类与有序结果的多元概率单位（MVP）模型。MVP模型假设分类结果是潜在纵向潜变量高斯结果的离散化版本，该潜变量通过重复测量的混合效应模型进行建模。采用参数扩展策略以促进后验抽样，并加速MVP中马尔可夫链的收敛。该方法能够以统一的方式对纵向连续、二分类及有序结果的回归系数与协方差矩阵进行抽样。这一特性有助于理解算法并开发MVP的计算机代码。我们还引入了独立Metropolis-Hasting抽样器来处理复杂先验分布，并评估回归系数的平坦先验与扩散正态先验的选择如何影响参数估计与缺失数据插补。数值算例被用于说明该方法。