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

本研究计画将针对结构方程模型（SEM）开发具有更佳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，与中小型企业相关的一些常见做法被认为是有问题的。本项目将为结构方程模型开发拟合优度方法。这些新方法将使应用研究人员能够更好地将其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值的数量。后一个结果是关键的，因为使用太多的观察是浪费的，而使用太少的观察会导致无法检测到感兴趣的效应，无论它是否存在。该项目将支持一名博士后研究员，他将参与研究的进行，并担任南卡罗来纳州大学定量心理学新研究生课程新生的导师。 将开发的方法将在R中编程，并集成到Lavaan R软件包中进行SEM建模。该项目将开发评估方程组与数据不匹配程度的方法。 方程组可能涉及用于对未观察到的属性进行建模的潜在变量，以及离散和连续的测量和预测。将使用标准化的不匹配度量来促进研究结果的交流。该项目将研究模型失配的标准化效应量可以用连续（可能是非正态）测量以及离散测量来估计的准确性。它还将检查这些措施的力量，以检测关键的模型错误。当被建模的变量数量很大时，当前确定结构方程建模中达到期望功效所需的样本量的方法失败。即使只拟合了几个方程，它们也会导致自由度少的模型中所需样本量的大幅高估，以及自由度大的模型中所需样本量的大幅低估。待开发的方法将提供更准确的估计样本大小需要达到目标的权力，大量节省宝贵的资源，研究界。

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.