Selecting an appropriate model is a crucial issue for applying structural equation models (SEMs) in real applications. Due to the model complexity, however, it is quite challenging to perform model selection on semiparametric SEMs with functional structural equations. In this thesis, we propose a modified Bayesian adaptive group Lasso procedure to perform model selection and estimation for semiparametric SEMs. By considering a novel formulation of basis expansions to approximate the unknown functions with certain penalties imposed, we are able to introduce a partial linear structure that combines the advantages of linear and nonparametric formulations for structural equations. The nonlinear, linear, or none structures in structural equations can be automatically detected with the proposed method. In addition, the group Lasso with adaptive penalties not only largely alleviates the model selection difficulties caused by the group effects and correlations introduced by basis expansions of latent variables, but also reduces the bias of traditional Lasso procedures. Simulation studies demonstrate that the proposed methodology performs satisfactorily. The proposed method is applied to analyze a real data set of diabetic kidney disease, which provides us some meaningful insights. / 在结构方程模型的实际应用中，选择一个合适的模型是一个核心问题。但是由于模型的复杂性，对于含有函数型结构的半参数结构方程模型进行模型选择十分困难。在本文中，我们提出了一种新的贝叶斯自适应群Lasso，并应用它来对半参数结构方程模型同时进行参数估计和模型选择。我们在非参数结构方程模型中引入了部分线性结构，并通过一种新的基底函数展开来近似结构方程里的未知函数。这种结构同时具备了线性模型和非参数模型的优势。本文的方法可以自动识别半参数结构方程模型里面的非线性和线性结构，并筛除不重要的变量。这种带有自适应惩罚的群Lasso不仅减小了传统Lasso方法在估计参数时产生的偏差，而且解决了由潜变量的基底表示导致的组效应和相关性引起的模型选择的困难。由模拟实验的结果可以看出本文提出的方法十分有效。我们还应用所提出的方法分析了一组关于糖尿病型肾病的数据，并得到了一些有意义的结果。 / Feng, Xiangnan. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 51-56). / Abstracts also in Chinese. / Title from PDF title page (viewed on 18, October, 2016). / Detailed summary in vernacular field only.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_1291541 |
| Date | January 2014 |
| Contributors | Feng, Xiangnan (author.), Song, Xinyuan (thesis advisor.), Chinese University of Hong Kong Graduate School. Division of Risk Management Science. (degree granting institution.) |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography, text |
| Format | electronic resource, electronic resource, remote, 1 online resource (4, vii, 56 leaves) : illustrations (some color), computer, online resource |
| 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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