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Given that the root mean square error of approximation (RMSEA) is currently one of the most popular measures of goodness-of-model fit within structural equation modeling (SEM), it is important to know how well the RMSEA performs in models with small degrees of freedom ( df). Unfortunately, most previous work on the RMSEA and its confidence interval has focused on models with a large df. Building on the work of Chen et al. to examine the impact of small df on the RMSEA, we conducted a theoretical analysis and a Monte Carlo simulation using correctly specified models with varying df and sample size. The results of our investigation indicate that when the cutoff values are used to assess the fit of the properly specified models with small df and small sample size, the RMSEA too often falsely indicates a poor fitting model. We recommend not computing the RMSEA for small df models, especially those with small sample sizes, but rather estimating parameters that were not originally specified in the model.
Kenny et al. (Thu,) studied this question.