Brosseau-Liard Patricia E, Savalei Victoria, Li Libo
a University of British Columbia.
b University of California Los Angeles.
Multivariate Behav Res. 2012 Nov;47(6):904-30. doi: 10.1080/00273171.2012.715252.
The root mean square error of approximation (RMSEA) is a popular fit index in structural equation modeling (SEM). Typically, RMSEA is computed using the normal theory maximum likelihood (ML) fit function. Under nonnormality, the uncorrected sample estimate of the ML RMSEA tends to be inflated. Two robust corrections to the sample ML RMSEA have been proposed, but the theoretical and empirical differences between the 2 have not been explored. In this article, we investigate the behavior of these 2 corrections. We show that the virtually unknown correction due to Li and Bentler (2006) , which we label the sample-corrected robust RMSEA, is a consistent estimate of the population ML RMSEA yet drastically reduces bias due to nonnormality in small samples. On the other hand, the popular correction implemented in several SEM programs, which we label the population-corrected robust RMSEA, has poor properties because it estimates a quantity that decreases with increasing nonnormality. We recommend the use of the sample-corrected RMSEA with nonnormal data and its wide implementation.
近似均方根误差（RMSEA）是结构方程模型（SEM）中一种常用的拟合指数。通常，RMSEA是使用正态理论极大似然（ML）拟合函数来计算的。在非正态情况下，ML RMSEA的未校正样本估计往往会被夸大。针对样本ML RMSEA已经提出了两种稳健校正方法，但尚未探究这两种方法在理论和实证方面的差异。在本文中，我们研究了这两种校正方法的表现。我们表明，Li和Bentler（2006）提出的几乎不为人知的校正方法（我们将其标记为样本校正稳健RMSEA）是总体ML RMSEA的一致估计，并且在小样本中能极大地减少非正态导致的偏差。另一方面，在几个SEM程序中实现的常用校正方法（我们将其标记为总体校正稳健RMSEA）具有较差的性质，因为它估计的量会随着非正态性的增加而减小。我们建议在非正态数据中使用样本校正RMSEA并广泛应用它。
