Decades of published methodological research have shown the chi-square test of model fit performs inconsistently and unreliably as a determinant of structural equation model (SEM) fit. Likewise, SEM indices of model fit, such as comparative fit index (CFI) and root-mean-square error of approximation (RMSEA) also perform inconsistently and unreliably. Despite rather unreliable ways to statistically assess model fit, researchers commonly rely on these methods for lack of a suitable inferential alternative. Marcoulides and Yuan (2017) have proposed the first inferential test of SEM fit in many years: an equivalence test adaptation of the RMSEA and CFI indices (i.e., RMSEAt and CFIt). However, the ability of this equivalence testing approach to accurately judge acceptable and unacceptable model fit has not been empirically tested. This fully crossed Monte Carlo simulation evaluated the accuracy of equivalence testing combining many of the same independent variable (IV) conditions used in previous fit index simulation studies, including sample size (N = 100-1,000), model specification (correctly specified or misspecified), model type (confirmatory factor analysis [CFA], path analysis, or SEM), number of variables analyzed (low or high), data distribution (normal or skewed), and missing data (none, 10%, or 25%). Results show equivalence testing performs rather inconsistently and unreliably across IV conditions, with acceptable or unacceptable RMSEAt and CFIt model fit index values often being contingent on complex interactions among conditions. Proportional z-tests and logistic regression analyses indicated that equivalence tests of model fit are problematic under multiple conditions, especially those where models are mildly misspecified. Recommendations for researchers are offered, but with the provision that they be used with caution until more research and development is available. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

中文翻译：

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判断模型拟合的等价测试：蒙特卡罗模拟。

数十年已发表的方法研究表明，模型拟合的卡方检验作为结构方程模型 (SEM) 拟合的决定因素表现不一致且不可靠。同样，模型拟合的 SEM 指数，例如比较拟合指数 (CFI) 和近似均方根误差 (RMSEA) 的表现也不一致且不可靠。尽管统计评估模型拟合度的方法相当不可靠，但由于缺乏合适的推理替代方案，研究人员通常依赖这些方法。Marcoulides 和 Yuan (2017) 提出了多年来首次对 SEM 拟合进行推论检验：对 RMSEA 和 CFI 指数（即 RMSEAt 和 CFIt）进行等价检验。然而，这种等价测试方法准确判断可接受和不可接受的模型拟合的能力尚未经过实证检验。这种完全交叉的蒙特卡罗模拟结合了先前拟合指数模拟研究中使用的许多相同自变量 (IV) 条件，评估了等效性测试的准确性，包括样本大小 (N = 100-1,000)、模型规范（正确指定或错误指定） 、模型类型（验证性因素分析 [CFA]、路径分析或 SEM）、分析的变量数量（低或高）、数据分布（正态或倾斜）和缺失数据（无、10% 或 25%）。结果显示，等价测试在 IV 条件下的表现相当不一致且不可靠，可接受或不可接受的 RMSEAt 和 CFIt 模型拟合指数值通常取决于条件之间复杂的相互作用。比例 z 检验和逻辑回归分析表明，模型拟合的等价检验在多种条件下是有问题的，特别是在模型轻度指定错误的情况下。为研究人员提供了建议，但前提是在进行更多研究和开发之前应谨慎使用这些建议。（PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。