Bayesian modeling of multivariate mixed longitudinal responses with scale mixtures of multivariate normal distributions

计划摘要(摘要) 与健康相关的研究通常涉及一个以上的纵向反应，由多种类型的 数据，如二进制、序数、标称或连续变量。由于这些响应是从 同样的个人或单位，最好是联合分析，而不是单独分析，以便将数据理解为 一个完整的。多变量概率位模型已被广泛用于分析多变量纵向二值问题 和有序数据，特别是对于混合的二进制/有序和连续数据，这是由于 潜在的多元正态变量。然而，这是基础多变量正态变量的唯一选择 进行有限的模型比较和诊断。此外，可识别的多变量Probit模型 将潜在多变量正态变量的协方差矩阵约束为相关矩阵， 这对基于似然估计和马尔可夫链蒙特卡罗(MCMC)抽样都提出了严格的要求。 类似的问题也存在于分析名义数据的多项概率模型中。 在这项建议中，我们专注于开发MCMC方法来分析多变量混合纵向数据 主要有三个目的。第一个目的是使用多元正态(SMMVN)分布的尺度混合， 它为潜在变量提供了灵活的多变量分布，如多变量正态分布、多变量正态分布、多变量分布。 T和多变量Logistic分布。第二个目的是使用SMMVN提出可识别的模型 并发展了MCMC抽样方法。第三个目的是解决模型识别问题 通过提出不可识别的模型和发展MCMC方法来规避Metropolis-Hastings 用无限制Gibbs抽样协方差矩阵对受限协方差矩阵进行抽样的算法。 其具体目标是：(1)构建可识别和不可识别的多变量模型 具有SMMVN分布的多元纵向二元/有序数据和MCMC抽样 方法；(2)构造多变量纵向可辨识和不可辨识的多变量模型 标称数据具有SMMVN分布，并发展了MCMC抽样方法；(3)扩展了 文(1)和(2)中提出的多变量混合纵向数据模型及MCMC的发展 对缺失值数据的采样方法，并进行模型评估；(4)实施、分发、 支持和维护本申请中提出的方法的用户友好的软件包。 该提案与NIH Area Program(R15)通过加强基础设施实现的目标一致 密歇根理工大学(MTU)的研究和教育博士。此应用程序将提供一个独特的 有机会让不同的本科生和毕业生群体接触与健康有关的研究，包括 最前沿的统计理论、统计应用、计算方法和数据应用 加强现代研究，并加强MTU与健康相关的研究和研究环境。

Program Summary (Abstract) Health-related studies generally involve more than one longitudinal response composed of multiple types of data, such as binary, ordinal, nominal or continuous variables. Since these responses are collected from the same individual or unit, it is desirable to analyze them jointly instead of separately to understand the data as a whole. The multivariate probit models have been widely utilized for analyzing multivariate longitudinal binary and ordinal data and especially for mixed binary/ordinal and continuous data due to the assumption of the latent multivariate normal variables. However, this only option of the underlying multivariate normal variables makes limited model comparisons and diagnostics. Furthermore, the identifiable multivariate probit models constrain the covariance matrix of the latent multivariate normal variables to be a correlation matrix, which brings a rigorous task for both likelihood-based estimation and Markov chain Monte Carlo (MCMC) sampling. Similar issues also exist in multinomial probit models for analyzing nominal data. In this proposal we focus on developing MCMC methods to analyze multivariate mixed longitudinal data with three main purposes. The first purpose is to use scale mixtures of multivariate normal (SMMVN) distributions, which provide flexible multivariate distributions for latent variables, such as multivariate normal, multivariate- t and multivariate logistic distributions. The second purpose is to propose identifiable models using SMMVN distributions and develop the MCMC sampling methods. The third purpose is to tackle the model identification issue by proposing non-identifiable models and develop MCMC methods to circumvent a Metropolis-Hastings algorithm to sample restricted covariance matrices by a Gibbs sampling covariance matrix without restrictions. The Specific Aims are to: (1) Construct both identifiable and non-identifiable multivariate models for multivariate longitudinal binary/ordinal data with SMMVN distributions and develop the MCMC sampling methods; (2) Construct both identifiable and non-identifiable multivariate models for multivariate longitudinal nominal data with SMMVN distributions and develop the MCMC sampling methods; (3) Extend the multivariate models proposed in (1) and (2) to multivariate mixed longitudinal data and develop the MCMC sampling methods for data with missing values and perform model assessment; (4) Implement, distribute, support and maintain user friendly software packages for the methods proposed in this application. This proposal is consistent with the objectives of NIH AREA Program (R15) by enhancing the infrastructure of research and education at Michigan Technological University (MTU). This application will offer a unique opportunity to expose a diverse group of undergraduates and graduates to health-related research involving statistical theories, statistical applications, computational methods and data applications at the cutting-edge of modern research and strengthen the health-related research and research environment at MTU.