本文關(guān)鍵詞：帶有缺失數(shù)據(jù)和隨機(jī)系數(shù)的非線性再生散度結(jié)構(gòu)方程模型的貝葉斯推斷　出處：《云南大學(xué)》2015年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 非線性再生散度結(jié)構(gòu)方程模型 隨機(jī)化系數(shù) 缺失數(shù)據(jù) 空間因子 Bayes因子 Bayes刪除影響 Bayes局部影響分析

【摘要】：帶有缺失數(shù)據(jù)和隨機(jī)系數(shù)的非線性再生散度結(jié)構(gòu)方程模型是非線性再生散度結(jié)構(gòu)方程模型的自然推廣,在行為學(xué)、社會學(xué)、生物醫(yī)學(xué)、教育學(xué)、公共衛(wèi)生學(xué)、經(jīng)濟(jì)學(xué)等眾多領(lǐng)域的研究中,人們常常遇見如健康狀況、個(gè)性、憂慮、智力、研究能力、顧客滿意度、工作態(tài)度等不可觀測變量,這類變量常被稱為潛變量(latent variable).結(jié)構(gòu)方程模型是目前國內(nèi)外分析研究顯變量(manifest variable)和潛變量之間內(nèi)在聯(lián)系的重要工具,已被廣泛應(yīng)用于多個(gè)研究領(lǐng)域.本論文針對帶有缺失數(shù)據(jù)和隨機(jī)系數(shù)的非線性再生散度結(jié)構(gòu)方程模型,研究了它的Bayes估計(jì)、Bayes數(shù)據(jù)刪除影響分析以及Bayes局部影響分析等一系列問題.現(xiàn)將主要研究內(nèi)容概述如下：1.在研究結(jié)構(gòu)方程模型的文獻(xiàn)中,通常假定因子服從某一特定的指數(shù)分布族(如正態(tài)分布),或假定結(jié)構(gòu)方程模型的結(jié)構(gòu)系數(shù)是固定參數(shù),但在實(shí)際應(yīng)用中,因子不一定都服從指數(shù)分布族而是服從一類更廣泛的分布族,甚至服從非參數(shù)分布族,且結(jié)構(gòu)方程系數(shù)同時(shí)是隨機(jī)系數(shù)等.因此,在本文中我們考慮顯變量服從一類更廣泛的分布族-再生散度分布族且?guī)в胁豢珊雎匀笔?shù)據(jù)機(jī)制,因子是帶有時(shí)間效應(yīng)的縱向數(shù)據(jù)且結(jié)構(gòu)系數(shù)是隨機(jī)化的系數(shù)進(jìn)行聯(lián)合建模.我們使用結(jié)合Gibbs抽樣和Metropolis-Hastings算法的混合算法從后驗(yàn)分布中進(jìn)行抽樣,從而得到模型的未知參數(shù)、隨機(jī)系數(shù)的聯(lián)合Bayes估計(jì)；在此基礎(chǔ)上,通過構(gòu)造路徑抽樣計(jì)算Bayes因子,并基于Bayes因子進(jìn)行了模型選擇.2.本文在Zhu et al.(2012), Tang et al.(2013)等人的基礎(chǔ)上,針對所研究的模型建立起一套基于Bayes數(shù)據(jù)刪除影響診斷方法來評價(jià)模型對于刪除一個(gè)數(shù)據(jù)點(diǎn)或數(shù)據(jù)組的敏感性.結(jié)合Gibbs抽樣與Metropolis-Hastings算法的混合算法得到模型的未知參數(shù)、隨機(jī)系數(shù)的聯(lián)合Bayes估計(jì)；在此基礎(chǔ)上,導(dǎo)出了Bayes數(shù)據(jù)刪除影響測度(φ-差異統(tǒng)計(jì)量、Cook后驗(yàn)均值距離統(tǒng)計(jì)量)及近似計(jì)算公式；并通過模擬和實(shí)例研究驗(yàn)證了所提出方法的合理性,并對實(shí)例中的影響點(diǎn)刪除后重新進(jìn)行了估計(jì),對比了影響觀測刪除前后參數(shù)估計(jì)的變化.3.本文在(Zhu et al.2011)、(Chen et al.2013)等人的基礎(chǔ)上,針對所研究的模型建立起一套Bayes局部影響分析方法來評價(jià)模型對于個(gè)體數(shù)據(jù)、數(shù)據(jù)組、先驗(yàn)分布、樣本分布、錯(cuò)誤結(jié)構(gòu)同時(shí)微小擾動的敏感性.針對于此模型,我們構(gòu)造了Bayes擾動流形,結(jié)合多種適當(dāng)?shù)臄_動模式,在擾動流形上構(gòu)造了切空間及計(jì)算出了相關(guān)的度量張量；我們還發(fā)展了基于目標(biāo)函數(shù)(如Bayes因子,(?)差異統(tǒng)計(jì)量)的Bayes局部影響測度.利用MCMC算法從后驗(yàn)分布中產(chǎn)生計(jì)算所需的隨機(jī)觀測樣本,并基于隨機(jī)觀測樣本來計(jì)算Bayes局部影響測度,并對實(shí)例中的影響點(diǎn)刪除后重新進(jìn)行了估計(jì),對比了影響觀測刪除前后參數(shù)估計(jì)的變化.
[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.
【學(xué)位授予單位】：云南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：F224

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