Improving Fit Indices in Structural Equation Modeling with Categorical Data

Current computations of commonly used fit indices in structural equation modeling (SEM), such as RMSEA and CFI, indicate much better fit when the data are categorical than if the same data had not been categorized. As a result, researchers may be led to accept poorly fitting models with greater frequency when data are categorical. In this article, I first explain why the current computations of categorical fit indices lead to this problematic behavior. I then propose and evaluate alternative ways to compute fit indices with categorical data. The proposed computations approximate what the fit index values would have been had the data not been categorized. The developments in this article are for the DWLS (diagonally weighted least squares) estimator, a popular limited information categorical estimation method. I report on the results of a simulation comparing existing and newly proposed categorical fit indices. The results confirmed the theoretical expectation that the new indices better match the corresponding values with continuous data. The new fit indices performed well across all studied conditions, with the exception of binary data at the smallest studied sample size (N = 200), when all categorical fit indices performed poorly.