Level-Specific Evaluation of Model Fit in Multilevel Structural Equation Modeling

In multilevel structural equation modeling, the standard approach to evaluating the goodness of model fit has a potential limitation in detecting the lack of fit at the higher level. Level-specific model fit evaluation can address this limitation and is more informative in locating the source of lack of model fit. We proposed level-specific test statistics for the test of overall model fit, comparative fit index, and root mean squared error of approximation using partially saturated models, and we also considered another level-specific approach proposed by Yuan and Bentler (2007). A simulation study showed that the standard approach failed to detect the lack of fit at the group level. The fit indexes produced by the level-specific approaches both successfully detected the lack of model fit at each level. There were only minor differences in the performance of the 2 level-specific approaches.