含非正态及缺失数据的结构方程模型分析

项目名称： 含非正态及缺失数据的结构方程模型分析

项目编号： No.11501261

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 刘鹏飞

作者单位： 江苏师范大学

项目金额： 18万元

中文摘要： 结构方程模型是一类常见且重要的潜在变量模型。在以往的研究中，多数的统计方法都假定数据服从正态分布，但它们在处理非正态及缺失数据时会出现较大偏差。缺失数据以及包含偏斜数据、重尾数据和异构数据的非正态数据广泛存在于各个领域中，包含此类数据的结构方程模型目前已成为统计学、社会学和心理学等学科研究中的一个热点问题。本项目拟研究的内容如下：(1) 建立新的半参数结构方程模型，有效处理各种类型的非正态及缺失数据；(2) 采用贝叶斯统计方法对所提出的半参数模型进行参数及潜在变量的估计；(3) 在半参数结构方程模型框架下，进一步探索改进模型选择的方法。在理论研究的同时，我们也将适时开发并公布相应的程序。预期研究结果有望拓展和改进目前文献中已有的研究结果，并推动结构方程模型在医学、管理学、社会学和心理学等诸多学科的应用。

中文关键词： 结构方程模型；贝叶斯统计；缺失数据；非参数方法

英文摘要： Latent variables have been widely encountered in many fields of science. Structural equation model (SEM) is a kind of very common and important latent variable model (LVM). However, for most SEMs, almost all existing statistical methods and commonly used software are developed through a parametric approach on the basis of a crucial assumption that the distribution of the latent variables is normal. Thus, they produce bias results for situations with non-normal and missing data. As missing data and non-normal data that included but not limited to highly skewed data, heavy-tailed data, and/or heterogeneous data are very common in substantive research, this problem represents an important and hot research topic in statistics, and/or social and psychological methods. The main objective of this project is to adequately address the above problem from both theoretical and practical perspectives. Our goals are: (1) To develop a novel semi-parametric nonlinear SEM with covariates in which the latent variables are modeled by a general nonparametric distribution so that it can be effectively cope with various kinds of non-normal and missing data. (2) To develop rigorous statistical methods for estimation of the proposed semi-parametric model for obtaining estimates of the latent variables and estimates of the parameters in the semi-parametric components, as well as parameters in the measurement and structural equations of the proposed SEMs. (3) To obtain general results for the difficult issue about model comparison in the context of general semi-parametric SEMs. We will develop efficient and dependable computer programs for producing the statistical results, and putting these programs onto a web-site for general use. In conclusion, the novel semi-parametric model and the newly developed Bayesian methods and computer programs will greatly enhance the applicability of SEMs to medicine, management, social and psychological research.

英文关键词： Structure Equation Model;Bayesian Statistic;Missing Data;Non-parametric Method