Estimating the Maximum Likelihood Root Mean Square Error of Approximation (RMSEA) with Non-normal Data: A Monte-Carlo Study

Recent research has provided formulae for estimating the maximum likelihood (ML) RMSEA when mean or mean and variance, corrections for non-normality are applied to the likelihood ratio test statistic. We investigate by simulation which choice of corrections provides most accurate point RMSEA estimates, confidence intervals, and p-values for a test of close fit under normality, and in the presence of non-normality. We found that, overall, any robust corrections (choices MLM, MLMV, and MLR) provide better results than ML, which assumes normality. When they err, all choices tend to suggest that the model fits more poorly than it really does. Choice MLMV (mean and variance corrections) provided the most accurate RMSEA estimates and p-values for tests of close fit results but its performance decreases as the number of variables being modeled increases.