Correcting the bias of the Root Mean Squared Error of Approximation under missing data

Missing data are ubiquitous in psychological research. They may come about as an unwanted result of coding or computer error, participants' non-response or absence, or missing values may be intentional, as in planned missing designs. We discuss the effects of missing data on χ²-based goodness-of-fit indices in Structural Equation Modeling (SEM), specifically on the Root Mean Squared Error of Approximation (RMSEA). We use simulations to show that naive implementations of the RMSEA have a downward bias in the presence of missing data and, thus, overestimate model goodness-of-fit. Unfortunately, many state-of-the-art software packages report the biased form of RMSEA. As a consequence, the scientific community may have been accepting a much larger fraction of models with non-acceptable model fit. We propose a bias-correction for the RMSEA based on information-theoretic considerations that take into account the expected misfit of a person with fully observed data. The corrected RMSEA is asymptotically independent of the proportion of missing data for misspecified models. Importantly, results of the corrected RMSEA computation are identical to naive RMSEA if there are no missing data.