On the Estimation of Fit Indices for the Structural Part of a Model

When a researcher proposes an SEM model to explain the dynamics among some latent variables, the real question in model evaluation is the fit of the model's structural part. A composite index that lumps the fit of the structural part and measurement part does not directly address that question. The need for more attention to structural-level fit has been noted for a long time, but the literature has been limited to conceptual issues such as how to define the structural-level RMSEA or CFI. How to estimate those structural-level fit indices, however, have been overlooked. Traditional estimation methods for composite-fit RMSEA and CFI are not applicable to structural-level fit indices, even if data are complete and normally distributed. In this article, we give correct point estimators and confidence intervals for structural-level RMSEA and CFI. Simulation results suggest that the new methods have satisfactory performance in realistic situations.