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。

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.