The Influence of Model Components and Misspecification Type on the Performance of the Comparative Fit Index (CFI) and the Root Mean Square Error of Approximation (RMSEA) in Structural Equation Modeling
This thesis examined the performance of two popular fit indices used in structural equation modeling: the comparative fit index (CFI) and the root mean square error of approximation (RMSEA). Of interest were the indices’ sensitivities to different sources of misspecification as well as sensitivities to model components that may affect index behavior over and above misspecification. Index performances were evaluated in confirmatory factor analysis models involving one of three sources of misspecification: omitted error covariances, omitted cross-loadings, or an incorrectly modeled latent structure. In addition, model components—including model complexity, loading size, factor correlation size, and model balance—were manipulated to determine their effects on index behavior. It was revealed that CFI is more sensitive to latent misspecifications, while RMSEA is more sensitive to misspecifications due to omitted error covariances. Both indices are affected to some extent by model components, particularly model complexity and loading size.