A Correction for Structural Equation Modeling Fit Indices Under Missingness: Adapting the Root Mean Squared Error of Approximation to Conditions of Missing Data

Missing data is a frequent occurrence in both small and large datasets. Among other things, missingness may be a result of coding or computer error, participant absences, or it may be intentional, as in a planned missing design. Whatever the cause, the problem of how to approach a dataset with holes is of much relevance in scientific research. First, missingness is approached as a theoretical construct, and its impacts on data analysis are encountered. I discuss missingness as it relates to structural equation modeling and model fit indices, specifically its interaction with the Root Mean Square Error of Approximation (RMSEA). Data simulation is used to show that RMSEA has a downward bias with missing data, yielding skewed fit indices. Two alternative formulas for RMSEA calculation are proposed: one correcting degrees of freedom and one using Kullback-Leibler divergence to result in an RMSEA calculation which is relatively independent of missingness. Simulations are conducted in Java, with results indicating that the Kullback-Leibler divergence provides a better correction for RMSEA calculation. Next, I approach missingness in an applied manner with an existing large dataset examining ideology measures. The researchers assessed ideology using a planned missingness design, resulting in high proportions of missing data. Factor analysis was performed to gauge uniqueness of ideology measures