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

具有多元正态分布尺度混合的多元混合纵向响应的贝叶斯建模

• 批准号: 10730714
• 负责人: Xiao NMN Zhang
• 金额: $ 42.58万
• 依托单位: MICHIGAN TECHNOLOGICAL UNIVERSITY
• 依托单位国家: 美国
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://reporter.nih.gov/project-details/10730714
• 关键词: Academic Research Enhancement Awards; Algorithms; Bayesian Analysis; Bayesian Method; Bayesian Modeling; Charge; Communities; Computing Methodologies; Data; Data Set; Development; Diagnostic; Dimensions; Education; Environment; Exposure to; Health; Human; Individual; Likelihood Functions; Logistics; Markov Chains; Markov chain Monte Carlo methodology; Methods; Michigan; Mission; Modeling; Modernization; Normal Statistical Distribution; Parameter Estimation; Performance; Public Health; Research; Research Infrastructure; Sampling; Statistical Data Interpretation; Statistical Methods; Structure; Surveys; Technology; United States National Institutes of Health; Universities; Work; complex data; computerized tools; flexibility; high dimensionality; multiple data types; novel; programs; public health relevance; response; technology development; theories; undergraduate student; user friendly software; Academic Research Enhancement Awards; Algorithms; Bayesian Analysis; Bayesian Method; Bayesian Modeling; Charge; Communities; Computing Methodologies; Data; Data Set; Development; Diagnostic; Dimensions; Education; Environment; Exposure to; Health; Human; Individual; Likelihood Functions; Logistics; Markov Chains; Markov chain Monte Carlo methodology; Methods; Michigan; Mission; Modeling; Modernization; Normal Statistical Distribution; Parameter Estimation; Performance; Public Health; Research; Research Infrastructure; Sampling; Statistical Data Interpretation; Statistical Methods; Structure; Surveys; Technology; United States National Institutes of Health; Universities; Work; complex data; computerized tools; flexibility; high dimensionality; multiple data types; novel; programs; public health relevance; response; technology development; theories; undergraduate student; user friendly software

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.

程序摘要（摘要） 与健康相关的研究通常涉及多种类型的纵向反应 数据，例如二进制，序数，名义或连续变量。由于这些响应是从 相同的个人或单位，希望共同分析它们，而不是单独分析数据，以理解数据 整个。多元概率模型已被广泛用于分析多元纵向二进制 和序数数据，尤其是由于假设的混合二进制/序数和连续数据 潜在多元正常变量。但是，这种基本多元正常变量的唯一选择 进行有限的模型比较和诊断。此外，可识别的多元概率模型 将潜在多元正常变量的协方差矩阵限制为相关矩阵，该矩阵 为基于似然的估计和马尔可夫链蒙特卡洛（MCMC）采样带来了严格的任务。 用于分析名义数据的多项式概率模型中也存在类似的问题。 在此提案中，我们着重于开发MCMC方法，以分析与 三个主要目的。第一个目的是使用多元正常（SMMVN）分布的比例混合物， 为潜在变量提供灵活的多元分布，例如多元正常，多元变量 T和多元逻辑分布。第二目的是使用SMMVN提出可识别的模型 分布并开发MCMC采样方法。第三目的是解决模型标识 通过提出不可识别的模型并开发MCMC方法来绕过大都市危机 通过Gibbs采样协方差矩阵来采样限制协方差矩阵的算法。 具体目的是：（1）构建可识别和不可识别的多元模型 具有SMMVN分布的多元纵向二进制/序数数据并开发MCMC采样 方法; （2）为多元纵向构建可识别和不可识别的多元模型 具有SMMVN分布的名义数据并开发MCMC采样方法； （3）扩展 在（1）和（2）中提出的多元模型用于多元混合纵向数据并开发MCMC 对具有缺失值并执行模型评估的数据采样方法； （4）实施，分发， 支持并维护用户友好的软件包，以适用于本应用程序中提出的方法。 该提案通过增强基础架构来与NIH地区计划（R15）的目标一致 密歇根技术大学（MTU）研究与教育。该应用程序将提供独特的 将一群多样化的本科生和毕业生揭露与健康相关的研究的机会，涉及 统计理论，统计应用，计算方法和数据应用 现代研究并加强了MTU与健康相关的研究和研究环境。