变换结构方程模型的非参数贝叶斯分析

项目名称： 变换结构方程模型的非参数贝叶斯分析

项目编号： No.11471277

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 宋心远

作者单位： 香港中文大学深圳研究院

项目金额： 60万元

中文摘要： 在行为学、社会学和心理学中，结构方程模型被广泛用于刻画潜在变量之间的关系。然而现存许多分析结构方程模型的统计方法和统计软件都需要假设数据服从正态分布。虽然近年来的研究提出了一些参数和非参数的方法可以部分放宽这一限制，但是这些方法在处理严重偏离正态分布的数据时仍然存在一些问题。变换模型通过对响应变量进行变换使其满足模型假设，从而得到更为可靠的估计。然而，参数变换模型的局限性在于变换函数常为幂函数，此限制使得参数模型不能准确地描述变量分布的重要特性。因此更为合理的方法是通过非参数方法估计变换函数。遗憾的是，迄今为止仍然没有人系统地提出分析变换结构方程模型的统计方法。本项目致力于从理论和实际两个层面解决上述问题。本项目会建立变换结构方程模型来处理非正态分布的数据，并且提出分析上述模型的统计方法。我们将把模型和方法应用到实际数据集分析中并编写及发布统计分析及计算程序以供有需要的研究者使用。

中文关键词： 结构方程模型；变换模型；非参数方法；贝叶斯方法

英文摘要： In behavioral, social, and psychological sciences, the most widely used models in assessing latent variables are the structural equation models (SEMs). When analyzing SEMs with continuous variables, most existing statistical methods and software have been developed based on the crucial assumption that the response variables are normally distributed. Although some recently developed parametric and nonparametric methods can partially address the violation of this assumption, they encounter serious difficulties in handling data with extremely non-normal distributions. The transformation model allow the resulting model to justify the model assumptions and thus produce more reliable results. One problem with the parametric transformation model is that the choice of transformation is usually restricted to the power or shifted power family. The limited flexibility of this parametric family could cause important features of the distribution to be missed. A more comprehensive approach is to estimate the transformation in a nonparametric way. However, no statistical methods have been developed for analyzing these kinds of transformation SEMs. Our main objective is to address the above problems adequately from both theoretical and practical perspectives. We are going to establish a novel transformation SEM for handling various kinds of highly non-normal data, to develop novel and sound statistical methods to analyze the proposed model, to apply the developed methodologies to analyze real datasets in practical researches. Finally, we will develop efficient and dependable computer programs to produce statistical results and post these programs onto freely available websites for general use.

英文关键词： structural equation models;transformation models;nonparametric methods;Baeysian methods