This article delves into the often-overlooked metric of percentage of variance accounted for in structural equation models (SEM). The goodness of fit index (GFI) provides the percentage of variance of the sum of squared covariances explained by the model. Despite being introduced over four decades ago, the GFI has been overshadowed in favor of fit indices that prioritize distinctions between close and nonclose fitting models. Similar to R² in regression, the GFI should not be used to this aim but rather to quantify the model's utility. The central aim of this study is to reintroduce the GFI, introducing a novel approach to computing the GFI using mean and mean-and-variance corrected test statistics, specifically designed for nonnormal data. We use an extensive simulation study to evaluate the precision of inferences on the GFI, including point estimates and confidence intervals. The findings demonstrate that the GFI can be very accurately estimated, even with nonnormal data, and that confidence intervals exhibit reasonable accuracy across diverse conditions, including large models and nonnormal data scenarios. The article provides methods and code for estimating the GFI in any SEM, urging researchers to reconsider the reporting of the percentage of variance accounted for as an essential tool for model assessment and selection. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

---

结构方程模型中方差的百分比：拟合优度指数的重新发现。


本文深入研究了结构方程模型 (SEM) 中经常被忽视的方差百分比指标。拟合优度指数 (GFI) 提供模型解释的协方差平方和的方差百分比。尽管 GFI 是在四十多年前推出的，但它已经被优先考虑紧密拟合模型和非紧密拟合模型之间区别的拟合指数所掩盖。与回归中的 R² 类似，GFI 不应用于此目的，而应用于量化模型的效用。本研究的中心目标是重新引入 GFI，引入一种使用均值和均值与方差校正检验统计量计算 GFI 的新方法，该方法专为非正态数据设计。我们使用广泛的模拟研究来评估 GFI 推断的精度，包括点估计和置信区间。研究结果表明，即使使用非正态数据，也可以非常准确地估计 GFI，并且置信区间在不同条件下（包括大型模型和非正态数据场景）表现出合理的准确性。本文提供了在任何 SEM 中估计 GFI 的方法和代码，敦促研究人员重新考虑报告方差百分比，将其作为模型评估和选择的重要工具。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。