Pavlov Goran, Maydeu-Olivares Alberto, Shi Dexin
University of South Carolina, Columbia, SC, USA.
University of Barcelona, Barcelona, Spain.
Educ Psychol Meas. 2021 Feb;81(1):110-130. doi: 10.1177/0013164420926231. Epub 2020 Jun 8.
We examine the accuracy of 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 values are only accurate in small models ( = 10), or in medium-sized models ( = 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.
我们检验了使用渐近均值和方差（MV）校正所得到的值的准确性，该校正是针对Maydeu-Olivares提出的样本标准化均方根残差（SRMR）分布进行的，目的是评估结构方程模型（SEM）的精确拟合度。在一项模拟研究中，我们发现，在正态性条件下，即使对于小样本和大型模型，MV校正后的SRMR统计量也能提供相当准确的I型错误率，明显优于当前标准，即似然比（LR）检验。当数据显示出峰度超标时，MV校正后的SRMR值仅在小模型（=10）中是准确的，或者在中型模型（=30）中，如果不存在偏度且样本量至少为500时才是准确的。总体而言，当数据非正态时，MV校正后的LR检验似乎优于MV校正后的SRMR。我们通过表明SRMR抽样分布均值的渐近近似相当准确，而标准差的渐近近似不准确，来详细阐述这些发现。
