Using the Standardized Root Mean Squared Residual (SRMR) to Assess Exact Fit in Structural Equation Models

Abstract

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.