潜变量模型作为处理多元数据的一种有效的方法，在行为学、教育学、社会心理学以及医学等各个领域都受到了广泛关注。在分析潜变量模型时，大多数现有的统计方法和软件都是基于响应变量为正态分布的假设。尽管一些最近发展的方法可以处理部分的非正态数据，但在分析高度非正态的数据时依然存在问题。此外，在实际研究中还经常会遇到不完全数据，如缺失数据和删失数据。简单地忽略或错误地处理不完全数据可能会严重扭曲统计结果。在本文中，我们发展了贝叶斯惩罚样条方法，同时采用马尔科夫链蒙特卡洛方法，用以分析存有高度非正态和不完全数据的变换潜变量模型。我们在变换潜变量模型中讨论了不同类型的不完全数据，如完全随机缺失数据、随机缺失数据、不可忽略的缺失数据以及删失数据。我们还利用离差信息准则来选择正确的模型和数据缺失机制。我们通过许多模拟研究论证了我们提出的方法。此方法被应用于关于工作满意度、家庭生活、工作态度的研究，以及香港地区2 型糖尿病患者心血管疾病的研究。 / Latent variable models (LVMs), as useful multivariate techniques, have attracted significant attention from various fields, including the behavioral, educational, social-psychological, and medical sciences. In the analysis of LVMs, most existing statistical methods and software have been developed under the normal assumption of response variables. While some recent developments can partially address the non-normality of data, they are still problematic in dealing with highly non-normal data. Moreover, the presence of incomplete data, such as missing data and censoring data, is a practical issue in substantive research. Simply ignoring incomplete data or wrongly managing incomplete data might seriously distort statistical influence results. In this thesis, we develop a Bayesian P-spline approach, coupled with Markov chain Monte Carlo (MCMC) methods, to analyze transformation LVMs with highly non-normal and incomplete data. Different types of incomplete data, such as missing completely at random data, missing at random data, nonignorable missing data, as well as censored data, are discussed in the context of transformation LVMs. The deviance information criterion is proposed to conduct model comparison and select an appropriate missing mechanism. The empirical performance of the proposed methodologies is examined via many simulation studies. Applications to a study concerning people's job satisfaction, home life, and work attitude, as well as a study on cardiovascular diseases for type 2 diabetic patients in Hong Kong are presented. / Detailed summary in vernacular field only. / Liu, Pengfei. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 115-127). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.ii / Acknowledgement --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Latent Variable Models --- p.1 / Chapter 1.2 --- Missing Data --- p.4 / Chapter 1.3 --- Censoring Data --- p.5 / Chapter 1.4 --- Penalized B-splines --- p.6 / Chapter 1.5 --- Bayesian Methods --- p.7 / Chapter 1.6 --- Outline of the Thesis --- p.8 / Chapter 2 --- Transformation Structural Equation Models --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- Model Description --- p.11 / Chapter 2.3 --- Bayesian Estimation --- p.12 / Chapter 2.3.1 --- Bayesian P-splines --- p.12 / Chapter 2.3.2 --- Identifiability Constraints --- p.15 / Chapter 2.3.3 --- Prior Distributions --- p.16 / Chapter 2.3.4 --- Posterior Inference --- p.18 / Chapter 2.4 --- Bayesian Model Selection via DIC --- p.20 / Chapter 2.5 --- Simulation Studies --- p.23 / Chapter 2.5.1 --- Simulation 1 --- p.23 / Chapter 2.5.2 --- Simulation 2 --- p.26 / Chapter 2.5.3 --- Simulation 3 --- p.27 / Chapter 2.6 --- Conclusion --- p.28 / Chapter 3 --- Transformation SEMs with Missing Data that are Missing At Random --- p.43 / Chapter 3.1 --- Introduction --- p.43 / Chapter 3.2 --- Model Description --- p.45 / Chapter 3.3 --- Bayesian Estimation and Model Selection --- p.46 / Chapter 3.3.1 --- Modeling Transformation Functions --- p.46 / Chapter 3.3.2 --- Identifiability Constraints --- p.47 / Chapter 3.3.3 --- Prior Distributions --- p.48 / Chapter 3.3.4 --- Bayesian Estimation --- p.49 / Chapter 3.3.5 --- Model Selection via DIC --- p.52 / Chapter 3.4 --- Simulation Studies --- p.53 / Chapter 3.4.1 --- Simulation 1 --- p.54 / Chapter 3.4.2 --- Simulation 2 --- p.56 / Chapter 3.5 --- Conclusion --- p.57 / Chapter 4 --- Transformation SEMs with Nonignorable Missing Data --- p.65 / Chapter 4.1 --- Introduction --- p.65 / Chapter 4.2 --- Model Description --- p.67 / Chapter 4.3 --- Bayesian Inference --- p.68 / Chapter 4.3.1 --- Model Identification and Prior Distributions --- p.68 / Chapter 4.3.2 --- Posterior Inference --- p.69 / Chapter 4.4 --- Selection of Missing Mechanisms --- p.71 / Chapter 4.5 --- Simulation studies --- p.73 / Chapter 4.5.1 --- Simulation 1 --- p.73 / Chapter 4.5.2 --- Simulation 2 --- p.76 / Chapter 4.6 --- A Real Example --- p.77 / Chapter 4.7 --- Conclusion --- p.79 / Chapter 5 --- Transformation Latent Variable Models with Multivariate Censored Data --- p.86 / Chapter 5.1 --- Introduction --- p.86 / Chapter 5.2 --- Model Description --- p.88 / Chapter 5.3 --- Bayesian Inference --- p.90 / Chapter 5.3.1 --- Model Identification and Bayesian P-splines --- p.90 / Chapter 5.3.2 --- Prior Distributions --- p.91 / Chapter 5.3.3 --- Posterior Inference --- p.93 / Chapter 5.4 --- Simulation Studies --- p.96 / Chapter 5.4.1 --- Simulation 1 --- p.96 / Chapter 5.4.2 --- Simulation 2 --- p.99 / Chapter 5.5 --- A Real Example --- p.100 / Chapter 5.6 --- Conclusion --- p.103 / Chapter 6 --- Conclusion and Further Development --- p.113 / Bibliography --- p.115
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328297 |
| Date | January 2013 |
| Contributors | Liu, Pengfei, Chinese University of Hong Kong Graduate School. Division of Statistics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (xii, 127 leaves) : ill. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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