非线性结构方程模型在老挝高等教育中的实证研究

发布时间：2018-09-05 19:00

【摘要】：在行为学、社会学、心理测量学以及经济管理等研究领域,经常会涉及到一些难以直接准确测量的变量,如智力、学习动机等因素,需要评估这些潜在变量与外显变量之间的关系,对于这些问题,传统的统计分析方法难以解决。结构方程模型(Structural Equation Modeling,简称SEM)是多元统计分析的一个重要工具,相比传统的回归分析,结构方程模型不仅能够度量外显变量与潜在因子之间的关系,同时还能够进一步刻画潜在变量之间复杂的非线性结构。在经典的回归分析中,其通常假定自变量为非随机的,而结构方程模型却没有这种假定,若各影响因子可以直接观测,则结构方程模型就退化为回归分析,此外,结构方程模型还允许自变量和因变量存在测量误差,可以同时估计因子结构以及因子关系,容许更大弹性的测量模型。本文主要研究了非线性结构方程模型的贝叶斯统计推断问题,其研究内容大致分为如下三个方面:(1)非线性结构方程模型的贝叶斯分析;(2)有限混合结构方程模型分析的贝叶斯分析;(3)空间结构方程模型的贝叶斯分析。就研究内容而言,由于模型的复杂性和潜在变量的影响,模型的似然函数涉及到难以处理的多重积分。为此,本文建立起完整的贝叶斯后验抽样程序并采用了结合Gibbs抽样和MH算法的MCMC技术以实现参数估计;由于外显变量的异质性,传统的单个总体的假设往往并不成立,为了解决这一问题,本文建立起有限混合结构方程模型和相应的后验推断程序,众所周知,在有限混合建模中,由于“Label switching"问题常常会导致有偏甚至无效的统计推断结论,为此,通过数据添加策略,建立起关于指标变量的完全数据似然,并有针对性的采用了狄利克雷先验等先验设置获得混合比例的参数估计;在此基础上,本文进一步将前述研究成果推广至含有空间随机效应的结构方程模型的分析中,采用了空间条件自回归模型刻画区域异质性及相关关系,得到空间随机效应的估计。最后,本文应用老挝某大学的学生成绩的实例来说明上述方法的有效性,其相关研究成果对于老挝政府在高等教育方面的政策制定和财政投入均有一定的参考作用。本文的选题来源于实际,其工作是对当代贝叶斯分析的推广和发展,丰富了贝叶斯方法的内涵和应用范围,其中涉及到的一些关键技术如贝叶斯有限混合建模、空间条件自回归建模等均是有针对性的研究策略,适应了实际问题中对复杂数据分析的需要。
[Abstract]:In the fields of behavior, sociology, psychometrics and economic management, there are often variables that are difficult to measure directly and accurately, such as intelligence, learning motivation, and so on. The relationship between these potential variables and explicit variables needs to be evaluated. Traditional statistical analysis methods are difficult to solve these problems. Structural equation model (Structural Equation Modeling,) is an important tool for multivariate statistical analysis. Compared with traditional regression analysis, structural equation model can not only measure the relationship between explicit variables and potential factors. At the same time, it can further describe the complex nonlinear structure between potential variables. In classical regression analysis, the independent variables are usually assumed to be non-random, but the structural equation model does not. If the influence factors can be observed directly, the structural equation model is reduced to regression analysis. The structural equation model also allows for the existence of measurement errors between independent variables and dependent variables, and can simultaneously estimate factor structures and factor relationships, allowing for more elastic measurement models. In this paper, the Bayesian statistical inference problem of nonlinear structural equation model is studied. The research contents are as follows: (1) Bayesian analysis of nonlinear structural equation model; (2) Bayesian analysis of finite mixed structural equation model; (3) Bayesian analysis of spatial structural equation model. As far as the research content is concerned, due to the complexity of the model and the influence of the potential variables, the likelihood function of the model involves multiple integrals which are difficult to deal with. In this paper, a complete Bayesian posteriori sampling procedure is established and the MCMC technique combining Gibbs sampling and MH algorithm is used to realize parameter estimation. Because of the heterogeneity of explicit variables, the traditional assumption of a single population is often not true. In order to solve this problem, the finite mixed structural equation model and the corresponding posteriori inference program are established in this paper. It is well known that in the finite hybrid modeling, the "Label switching" problem often leads to partial or even invalid statistical inference conclusions. For this reason, through the strategy of adding data, the complete data likelihood of index variable is established, and the parameter estimation of mixed ratio is obtained by using prior settings such as Dilikere priori. In this paper, the above research results are extended to the analysis of structural equation models with spatial random effects. Spatial conditional autoregressive models are used to characterize regional heterogeneity and correlation, and the estimation of spatial random effects is obtained. Finally, this paper applies the example of student achievement of a university in Laos to illustrate the effectiveness of the above method, and its related research results have a certain reference role for the policy formulation and financial investment of the Lao government in higher education. The work of this paper is to popularize and develop modern Bayesian analysis, which enriches the connotation and application scope of Bayesian method, and involves some key technologies such as Bayesian finite hybrid modeling. Spatial conditional autoregressive modeling is a targeted research strategy, which meets the needs of complex data analysis in practical problems.
【学位授予单位】：昆明理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C81;G649.334

【参考文献】