ABSTRACT We propose a Corrected Goodness-of-Fit Index (CGFI) for model evaluation in Structural Equation Modeling (SEM). The CGFI is essentially a corrected index that takes into account model complexity and downward bias caused by small sample size. Using simulations based on pre-set SEM models, we compared the properties of CGFI, Goodness-of-Fit (GFI), and Adjusted Goodness-of-Fit Index (AGFI) under different settings of sample size, estimation method, magnitude of factor loadings, model complexity, and types and degrees of model misspecification. We find that the CGFI is more stable across different sample sizes and much more sensitive to detect model misspecification than the GFI and AGFI. We recommend a critical value of 0.90 for the proposed CGFI to evaluate the goodness of fit of SEM. Our proposed CGFI is easy to implement and can serve as a useful supplementary fit index to existing ones.

中文翻译：

---

用于结构方程建模中模型评估的修正拟合优度指数 (CGFI)

摘要 我们提出了一种修正拟合优度指数 (CGFI)，用于结构方程建模 (SEM) 中的模型评估。CGFI 本质上是一个修正指数，它考虑了模型复杂性和小样本量导致的向下偏差。使用基于预设 SEM 模型的模拟，我们比较了 CGFI、拟合优度 (GFI) 和调整拟合优度指数 (AGFI) 在不同样本量、估计方法、因子大小设置下的特性载荷、模型复杂性以及模型错误指定的类型和程度。我们发现 CGFI 在不同样本量下更稳定，并且比 GFI 和 AGFI 对检测模型错误指定更敏感。我们建议为建议的 CGFI 使用 0.90 的临界值来评估 SEM 的拟合优度。