Recent research has provided formulae for estimating the maximum likelihood (ML) RMSEA when mean or mean and variance, corrections for non-normality are applied to the likelihood ratio test statistic. We investigate by simulation which choice of corrections provides most accurate point RMSEA estimates, confidence intervals, and p-values for a test of close fit under normality, and in the presence of non-normality. We found that, overall, any robust corrections (choices MLM, MLMV, and MLR) provide better results than ML, which assumes normality. When they err, all choices tend to suggest that the model fits more poorly than it really does. Choice MLMV (mean and variance corrections) provided the most accurate RMSEA estimates and p-values for tests of close fit results but its performance decreases as the number of variables being modeled increases.

中文翻译：

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用非正态数据估计近似的最大似然均方根误差 (RMSEA)：蒙特卡罗研究

最近的研究提供了用于估计最大似然 (ML) RMSEA 的公式，当均值或均值和方差、非正态性校正应用于似然比检验统计量时。我们通过模拟调查哪种校正选择提供最准确的点 RMSEA 估计、置信区间和 p 值，用于在正态性和存在非正态性的情况下进行紧密拟合的检验。我们发现，总体而言，任何稳健的修正（选择 MLM、MLMV 和 MLR）都能提供比 ML 更好的结果，ML 假设正态性。当他们出错时，所有选择都倾向于表明模型的拟合效果比实际情况更差。Choice MLMV（均值和方差校正）为接近拟合结果的检验提供了最准确的 RMSEA 估计值和 p 值，但其性能随着建模变量数量的增加而降低。