RMSEa

RMSEA, the Root Mean Square Error of Approximation, is a measure used in structural equation modeling to assess how well a hypothesized model would fit the population covariance matrix. It combines model misfit with model complexity and is derived from the chi-square statistic.

The RMSEA is defined as RMSEA = sqrt[(χ² − df) / (df (N − 1))], where χ² is the model chi-square statistic, df is the model degrees of freedom, and N is the sample size. If χ² ≤ df, RMSEA is typically set to 0. Values closer to zero indicate better fit.

Interpretation follows general benchmarks: RMSEA ≤ 0.05 suggests close fit, 0.05–0.08 indicates reasonable fit, 0.08–0.10 reflects mediocre fit, and >0.10 signals poor fit. Researchers often report a confidence interval for RMSEA, commonly around 90% or 95%, to reflect sampling uncertainty.

Usage and limitations: RMSEA is sensitive to model complexity and sample size. It tends to perform differently across estimation methods and can be biased in small samples or poorly specified models. It should be considered alongside other fit indices, such as CFI, TLI, and SRMR, and interpreted in the context of theoretical justification. RMSEA measures approximate, not exact, fit and is not a standalone test of model adequacy.

Practical aspects: Calculation requires the model chi-square statistic, degrees of freedom, and sample size. RMSEA is widely reported in structural equation modeling results and is available in most SEM software packages, often accompanied by a confidence interval to convey uncertainty.