Confidence Interval for RMSEA or CFI Difference Between Nonnested Models

In addition to evaluating a single model, often one also uses RMSEA and CFI to compare the fit of multiple candidate models. Model selection based on RMSEA and CFI can be meaningful because (a) showing a model is better than another is more scientific and easier than showing a model is "good;" (b) it avoids the problems with cutoffs for fit indices; (c) one is less likely to overlook other equally substantively plausible models. However, currently, such model selection is based on sample RMSEA and sample CFI, which can be much smaller, much larger, or even of opposite sign than the population values. Accordingly, we propose analytic confidence intervals for population RMSEA and CFI. The methods are applicable to both nonnested and nested models, robust to nonnormal data, computationally efficient, and do not assume any candidate model is true. Simulation studies verified our proposed methods are trustworthy.