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

点击翻译按钮获取中文摘要

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.