Effects of Multivariate Non-Normality and Missing Data on the Root Mean Square Error of Approximation

Abstract

ABSTRACT The root mean square error of approximation (RMSEA) with various corrections for non-normality is a common fit index in structural equation modeling (SEM). The present study analyzed the performance of the uncorrected, the “sample corrected”, and the “population corrected” RMSEA in misspecified models for both complete and incomplete data sets under multivariate normality and multivariate non-normality. Additionally, the effect of the multivariate distribution under non-normality was investigated by comparing two different data generation approaches. The results show that missingness is associated with a downward bias, whereas non-normality tends to incur an upward bias. Because the corrections reduce the RMSEA estimate under non-normality, corrected values exhibited a stronger bias compared to uncorrected values when non-normality and missing data were simultaneously present. However, the extent of bias also depended on properties of the multivariate distribution.