Assessing Fit in Ordinal Factor Analysis Models: SRMR vs. RMSEA

This study introduces the statistical theory of using the Standardized Root Mean Squared Error (SRMR) to test close fit in ordinal factor analysis. We also compare the accuracy of confidence intervals (CIs) and tests of close fit based on the SRMR with those obtained based on the Root Mean Squared Error of Approximation (RMSEA). The current (biased) implementation for the RMSEA never rejects that a model fits closely when data are binary and almost invariably rejects the model in large samples if data consist of five categories. The unbiased RMSEA produces better rejection rates, but it is only accurate enough when the number of variables is small and the degree of misfit is small. In contrast, across all simulated conditions, the tests of close fit based on the SRMR yield acceptable type I error rates. SRMR tests of close fit are also more powerful than those using the unbiased RMSEA.