We examine the accuracy of p values obtained using the asymptotic mean and variance (MV) correction to the distribution of the sample standardized root mean squared residual (SRMR) proposed by Maydeu-Olivares to assess the exact fit of SEM models. In a simulation study, we found that under normality, the MV-corrected SRMR statistic provides reasonably accurate Type I errors even in small samples and for large models, clearly outperforming the current standard, that is, the likelihood ratio (LR) test. When data shows excess kurtosis, MV-corrected SRMR p values are only accurate in small models (p = 10), or in medium-sized models (p = 30) if no skewness is present and sample sizes are at least 500. Overall, when data are not normal, the MV-corrected LR test seems to outperform the MV-corrected SRMR. We elaborate on these findings by showing that the asymptotic approximation to the mean of the SRMR sampling distribution is quite accurate, while the asymptotic approximation to the standard deviation is not.

中文翻译：

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使用标准化残差均方根 (SRMR) 评估结构方程模型中的精确拟合


我们检查使用 Maydeu-Olivares 提出的样本标准化均方根残差 (SRMR) 分布的渐近均值和方差 (MV) 校正获得的 p 值的准确性，以评估 SEM 模型的精确拟合。在模拟研究中，我们发现，在正态性下，MV 校正的 SRMR 统计量即使在小样本和大型模型中也能提供相当准确的 I 类误差，明显优于当前标准，即似然比 (LR) 检验。当数据显示过度峰度时，MV 校正的 SRMR p 值仅在小型模型 (p = 10) 中准确，或者在不存在偏度并且样本大小至少为 500 的中型模型 (p = 30) 中准确。总体而言，当数据不正常时，MV 校正 LR 检验似乎优于 MV 校正 SRMR。我们通过证明 SRMR 采样分布均值的渐近逼近相当准确，而标准差的渐近逼近则不然，来详细阐述这些发现。