带有缺失数据和随机系数的非线性再生散度结构方程模型的贝叶斯推断

发布时间：2017-12-26 19:42

本文关键词：带有缺失数据和随机系数的非线性再生散度结构方程模型的贝叶斯推断　出处：《云南大学》2015年博士论文　论文类型：学位论文

【摘要】：带有缺失数据和随机系数的非线性再生散度结构方程模型是非线性再生散度结构方程模型的自然推广,在行为学、社会学、生物医学、教育学、公共卫生学、经济学等众多领域的研究中,人们常常遇见如健康状况、个性、忧虑、智力、研究能力、顾客满意度、工作态度等不可观测变量,这类变量常被称为潜变量(latent variable).结构方程模型是目前国内外分析研究显变量(manifest variable)和潜变量之间内在联系的重要工具,已被广泛应用于多个研究领域.本论文针对带有缺失数据和随机系数的非线性再生散度结构方程模型,研究了它的Bayes估计、Bayes数据删除影响分析以及Bayes局部影响分析等一系列问题.现将主要研究内容概述如下：1.在研究结构方程模型的文献中,通常假定因子服从某一特定的指数分布族(如正态分布),或假定结构方程模型的结构系数是固定参数,但在实际应用中,因子不一定都服从指数分布族而是服从一类更广泛的分布族,甚至服从非参数分布族,且结构方程系数同时是随机系数等.因此,在本文中我们考虑显变量服从一类更广泛的分布族-再生散度分布族且带有不可忽略缺失数据机制,因子是带有时间效应的纵向数据且结构系数是随机化的系数进行联合建模.我们使用结合Gibbs抽样和Metropolis-Hastings算法的混合算法从后验分布中进行抽样,从而得到模型的未知参数、随机系数的联合Bayes估计；在此基础上,通过构造路径抽样计算Bayes因子,并基于Bayes因子进行了模型选择.2.本文在Zhu et al.(2012), Tang et al.(2013)等人的基础上,针对所研究的模型建立起一套基于Bayes数据删除影响诊断方法来评价模型对于删除一个数据点或数据组的敏感性.结合Gibbs抽样与Metropolis-Hastings算法的混合算法得到模型的未知参数、随机系数的联合Bayes估计；在此基础上,导出了Bayes数据删除影响测度(φ-差异统计量、Cook后验均值距离统计量)及近似计算公式；并通过模拟和实例研究验证了所提出方法的合理性,并对实例中的影响点删除后重新进行了估计,对比了影响观测删除前后参数估计的变化.3.本文在(Zhu et al.2011)、(Chen et al.2013)等人的基础上,针对所研究的模型建立起一套Bayes局部影响分析方法来评价模型对于个体数据、数据组、先验分布、样本分布、错误结构同时微小扰动的敏感性.针对于此模型,我们构造了Bayes扰动流形,结合多种适当的扰动模式,在扰动流形上构造了切空间及计算出了相关的度量张量；我们还发展了基于目标函数(如Bayes因子,(?)差异统计量)的Bayes局部影响测度.利用MCMC算法从后验分布中产生计算所需的随机观测样本,并基于随机观测样本来计算Bayes局部影响测度,并对实例中的影响点删除后重新进行了估计,对比了影响观测删除前后参数估计的变化.
[Abstract]:With the missing data and random coefficient Nonlinear Reproductive Dispersion structural equation model is a natural generalization of Nonlinear Reproductive Dispersion structural equation model, the research in the fields of behavior, sociology, medicine, education, public health, economics etc., people often encounter such as health status, anxiety, personality, intelligence, ability, research customer satisfaction, work attitude can not be observed variables, this variable is often referred to as latent variables (latent variable). The structural equation model at home and abroad is of significant variables (manifest variable) is an important tool and the relationship between latent variables, has been widely used in many research fields. This thesis focuses on the nonlinear with the missing data and random coefficient Reproductive Dispersion structural equation model, study the estimation of Bayes, Bayes and delete the data analysis as well as Bayes Influence analysis of a series of problems. We will summarize the main research contents are as follows: 1. in the study of structural equation models in the literature, usually assume a particular factor obey the exponential distribution (e.g., normal distribution), or assume that the structural equation model of structure coefficient is fixed parameter, but in practical application, factor some are subject to a much broader class of distributions but obey the exponential distribution, even obeyed non parametric distributions and structural equation coefficient is also random coefficient. Therefore, in this paper we consider the significant variables for a class of more widely distributed family - distribution and Reproductive Dispersion with nonignorable missing data mechanism that factor is with time effect of longitudinal data and the structure coefficient is randomized coefficient of joint modeling. We use hybrid method based on Gibbs sampling and Metropolis-Hastings algorithm from the posterior distribution. For sampling, estimation of Bayes to obtain the unknown parameters, the random coefficient model; on this basis, through the construction of path sampling calculation of Bayes factor, and based on the Bayes factor for model selection in the Zhu.2. et al. (2012), Tang et al. (2013) based on the study of et al, model establish a set of Bayes data delete influence diagnosis method based on the evaluation model for deleting a data or data set. The sensitivity estimation Bayes hybrid method based on Gibbs sampling and Metropolis-Hastings algorithm of the unknown parameters, the random coefficient model; on this basis, derived Bayes data to remove the influence of measure (- difference statistics, Cook posterior mean distance) and approximate calculation formula; and through the simulation and case study to verify the rationality of the proposed method, and a bit of examples. Delete In addition to re estimate, compared the effect of the observation before deleting the parameter estimation based on the changes of.3. (Zhu et al.2011), (Chen et al.2013), on the basis of the research model to establish a set of analysis methods Bayes local influence evaluation model for sensitive data, a data group, prior distribution at the same time, the sample distribution, the error structure perturbation. According to this model, we construct a Bayes perturbation manifold, combined with a variety of mode appropriate, in the manifold structure perturbation tangent space and calculate the relevant metric tensor; we also developed based on the objective function (such as Bayes factor, (?) difference statistics Bayes) local influence measures. Using the MCMC algorithm to generate random samples from the posterior distribution calculation required, and random samples are calculated based on Bayes local influence measure, and the example of After deleting the impact point, the estimation is re carried out, and the changes in the estimation of the parameters before and after the observation are deleted are compared.
【学位授予单位】：云南大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：F224

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