Standardized Goodness of Fit Assessment and Power Computations in Structural Equation Models

本研究项目将为结构方程模型（SEM）开发具有更好统计特性的新统计方法。结构方程建模方法的通用性使其成为社会科学和行为科学中使用最广泛的数据建模技术之一。然而，与中小企业相关的一些常见做法被认为是有问题的。本项目将开发结构方程模型的拟合优度方法。这些新方法将使应用研究人员能够更好地将他们的研究结果传达给非技术受众。这些方法还将导致更精确地估计在将方程系统拟合到数据时所需的观测次数。后一种结果是至关重要的，因为使用太多的观察结果是浪费的，而使用太少的观察结果会导致无法检测到感兴趣的影响，而不管它是否存在。该项目将支持一名博士后研究员，他将参与研究的实施，并作为南卡罗来纳大学数量心理学新研究生项目的新生的导师。要开发的方法将在R中编程，并集成到Lavaan R包中用于SEM建模。本项目将开发方法来评估方程系统与数据失配的程度。方程系统可能涉及用于建模未观察属性的潜在变量，以及离散和连续测量和预测因子。失配的标准化度量将用于促进研究成果的交流。该项目将检验用连续（可能是非正态）测量和离散测量来估计模型失配的标准化效应大小的准确性。它还将检查这些措施在检测关键模型规格错误方面的能力。在结构方程建模中，当被建模的变量数量很大时，当前确定达到所需功率的样本量的方法就会失败。即使只拟合了几个方程，它们也会导致在自由度较小的模型中对所需样本量的严重高估，而在自由度较大的模型中对所需样本量的严重低估。待开发的方法将提供对达到目标功率所需的样本量更准确的估计，为研究界节省大量宝贵的资源。

This research project will develop new statistical methods with better statistical properties for structural equation models (SEM). The generality of the structural equation modeling approach makes it one of the most widely used data-modeling techniques across the social and behavioral sciences. However, some of the common practices associated with SEMs are considered problematic. This project will develop goodness-of-fit methods for structural equation models. These new methods will enable applied researchers to better communicate the results of their studies to a non-technical audience. The methods also will lead to more precise estimates of the number of observations that are needed when fitting systems of equations to data. This latter result is critical, because the use of too many observations is wasteful and the use of too few leads to failure to be able to detect the effect of interest regardless of whether it exists. The project will support a post-doctoral researcher who will participate in the conduct of the research and serve as a mentor to incoming students in the new graduate program in quantitative psychology at the University of South Carolina. The methods to be developed will be programmed in R and integrated into the Lavaan R package for SEM modeling.This project will develop methods to assess the magnitude of misfit of systems of equations to data. The systems of equations may involve latent variables used to model unobserved attributes, as well as discrete and continuous measures and predictors. Standardized metrics of misfit will be used to facilitate communication of research findings. The project will examine the accuracy with which standardized effect sizes of model misfit can be estimated with continuous (and possibly non-normal) measures as well as when the measures are discrete. It also will examine the power of these measures to detect key model misspecifications. Current methods to determine the sample sizes needed to reach a desired power in structural equation modeling fail when the number of variables being modeled is large. Even when only a few equations are fitted, they lead to a substantial overestimation of the needed sample size in models with few degrees of freedom and to a substantial underestimation in models with large degrees of freedom. The methods to be developed will provide much more accurate estimates of the sample sizes needed to reach a target power, with considerable savings in valuable resources to the research community.