正则化结构方程模型的贝叶斯分析及其在心理学研究中的应用

It is well recognized that structural equation modeling (SEM) is the most powerful statistical method for assessing interrelationships among latent variables. This statistical method is very popular in psychological, educational, behavioral and biomedical research. Recently, it has also received a great deal attention in neuroimaging for brain effectual connectivity analysis. In general, SEM consists of two major components. The first component is called measurement model, which is basically a confirmatory factor analysis model for investigating the relationships between the correlated manifest variables and their corresponding latent variables, and the second component is called structural model, which is a regression type model for examining the effects of exogenous latent variables and covariates on endogenous latent variables. The current SEM analyses often impose strict constraints on model setting, which is reflected in parameters fixed at zero. Examples include zero cross-loadings and zero residual correlations in measurement model.. However, in real data analysis, overconstraining models in an attempt to make interpretation easier, can lead to unacceptable levels of misfit and biased parameter estimates. On the other hand, although more complex models typically fit better, improved fit comes at the loss of generalizability. How to solve this dilemma is an important methodology issue that has not been well addressed. In this project, we will propose a novel method that extends the use of regularization in regression analysis to SEM, in which the specific parameters are penalized with the goal of creating easier to understand and simpler models. Hence, the proposed regularized SEM can be regarded as a generalization of the ordinary regularized regression model with the new inclusion of latent variables.. The objectives of our project are listed as follows: (1) To establish novel regularized SEM and its extensions including confirmatory factor analysis, semiparametric SEM, generalized SEM with nonignorable missing data and finite mixtures of SEM, with which researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and creating models that are more likely to generalize to new samples. (2) To develop statistical methods for sparse estimation and model evaluation of the proposed models. Given the complexity of the models and the data structure, we will derive novel methodology to solve the involved difficulties. Bayesian method coupled with data augmentation and Markov chain Monte Carlo techniques will be employed to achieve the statistical inferences. (3) To evaluate and compare the proposed methods with existing approaches. The better methods will be recommended under different data conditions. (4) To achieve novel applications by applying the newly developed models and methodologies to real psychological case studies. (5) To establish an application platform by compiling the sample computer programs and developing R packages, which will promote the convenience of applying the new models and methodologies to applied research. . As both regularization method and SEM have extremely wide applicability, we believe that our newly developed models and methodologies will be very useful in fields of psychology and other social sciences. And the achieved results will open a new research frontier in the study of SEM.

结构方程模型是公认的用于分析潜变量间关系最强有力的现代统计方法，广泛应用于心理学等行为科学领域的建模与数据分析。但传统方法对模型的设定有较严格的限制，如不允许交叉载荷和残差相关等。在实际数据分析中过多的限制会导致拟合程度以及参数估计准确性降低等问题。如何在建模的简洁性、模型的拟合程度、参数估计的准确性以及模型的泛化能力之间取得平衡，一直是结构方程建模中尚未很好解决的一类前沿热点问题。本项目创新地把回归分析中的正则化方法与结构方程模型相结合，建立正则化结构方程模型及其拓展形式，以更好地分析实际数据。主要内容包括：探讨不同研究问题和数据条件下可行的建模技术；提出有效的贝叶斯统计分析方法，完善其方法学基础；基于模拟数据横向对比新方法和传统方法，为应用研究者提供使用建议；将新模型应用于实际数据分析，检验其使用效果；通过编撰示例程序和开发R程序包等方法建立应用平台，促进新模型和新方法的应用和推广。

结构方程模型(Structural Equation Model; SEM)是公认的用于分析潜变量间复杂作用关系的最强有力的现代统计方法，广泛应用于心理学等行为科学领域的建模与数据分析。但在实际数据分析中过多的限制(如需要满足局部独立性假设，不允许交叉载荷等)会导致拟合程度以及参数估计准确性降低等问题。如何在建模的简洁性、模型的拟合程度、参数估计的准确性以及模型的泛化能力之间取得平衡，一直是结构方程建模领域的前沿科学问题，同时也制约着研究结果的有效性和可靠性的提升。.本项目把机器学习和心理统计领域中的两类重要技术——正则化方法和SEM建模结合起来，并围绕如何建立正则化结构方程模型及其扩展模型进行了系统的研究，同时还探讨了不同数据条件下可行的建模技术和统计分析方法及其衍生的一些实际问题（如不同建模方法的表现、先验分布的影响等），并为应用研究者提供了使用建议。.本项目建立的正则化结构方程模型包括正则化部分验证性因子分析模型、多层异质性正则化验证性因子分析模型、协方差自适应Lasso因子分析模型、正则化MIMIC模型和正则化并行潜中介模型等，并根据实际数据分析的需求，对模型进行了相应的拓展，使之能有效处理正态连续型数据、生态瞬时评估数据、有序分类数据、配对二分数据或不可忽略缺失数据等。同时，本项目提出了相应的贝叶斯算法对所提出的模型进行统计推断(包括未知参数估计和模型比较等)。计算机模拟研究表明所提出的新模型和新方法具备有效性、稳健性和实用性。此外，本项目还基于实际数据进行了方法演示和结果解释，并把相关的电脑程序发布于相应学术期刊的网站上供有需要的研究者参考和使用。.正则化方法和SEM在不同研究领域有着广泛应用，创新地将两者结合起来，不仅能在学术研究上进一步丰富和完善SEM的相关研究，进一步拓展其应用空间，而且有助于相关统计分析方法在心理学、教育学等行为科学研究中的推广，并为研究者提供新的研究思路和研究工具，对以SEM作为数据分析工具的相关学科的研究起到积极的推动作用。

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