Evaluation of a New Mean Scaled and Moment Adjusted Test Statistic for SEM

Abstract

Recently a new mean scaled and skewness adjusted test statistic was developed for evaluating structural equation models in small samples and with potentially nonnormal data, but this statistic has received only limited evaluation. The performance of this statistic is compared to normal theory maximum likelihood and 2 well-known robust test statistics. A modification to the Satorra–Bentler scaled statistic is developed for the condition that sample size is smaller than degrees of freedom. The behavior of the 4 test statistics is evaluated with a Monte Carlo confirmatory factor analysis study that varies 7 sample sizes and 3 distributional conditions obtained using Headrick's fifth-order transformation to nonnormality. The new statistic performs badly in most conditions except under the normal distribution. The goodness-of-fit χ² test based on maximum-likelihood estimation performed well under normal distributions as well as under a condition of asymptotic robustness. The Satorra–Bentler scaled test statistic performed best overall, whereas the mean scaled and variance adjusted test statistic outperformed the others at small and moderate sample sizes under certain distributional conditions.

Keywords:

• power
• robust statistics
• Satorra-Bentler corrections