Estimating the Root Mean Square Error of Approximation (RMSEA) with Multiply Imputed Data Under Non-Normality

Multiple imputation (MI) is one of the recommended modern techniques for handling missing data in structural equation modeling (SEM) and evaluating model fit is a crucial aspect of analyzing SEM models. Methods for pooling model fit indices across imputed datasets are still under development, however, especially in the context of non-normal data. In this study, we considered methods for estimating a robust measure of the Root Mean Square Error of Approximation (RMSEA) fit index and introduced strategies for pooling the robust RMSEA across imputed datasets. We evaluated the performance of the proposed strategies under various conditions by manipulating sample size, level of non-normality, non-normal data generation algorithm, missing data mechanism, and percentage of missing data. Results showed that the MI-based RMSEA approach, extended from the Lai method with complete data, tended to outperform other methods, yielding smaller biases in point estimates. Furthermore, confidence intervals (CIs) for the population RMSEA can be computed with better coverage rates by using a normal approximation. Drawing on our findings, we discuss the practical implications of our study and suggest directions for future research.