Improving the Root Mean Square Error of Approximation for Nonnormal Conditions in Structural Equation Modeling

Abstract

In this study, the authors investigated incorporating adjusted model fit information into the root mean square error of approximation (RMSEA) fit index. Through Monte Carlo simulation, the usefulness of this adjusted index was evaluated for assessing model adequacy in structural equation modeling when the multivariate normality assumption underlying maximum likelihood estimation is violated. Adjustment to the RMSEA was considered in 2 forms: a rescaling adjustment via the Satorra-Bentler rescaled goodness-of-fit statistic and a bootstrap adjustment via the Bollen and Stine adjusted model p value. Both properly specified and misspecifed models were examined. The adjusted RMSEA was evaluated in terms of the average index value across study conditions and with respect to model rejection rates under tests of exact fit, close fit, and not-close fit.