Root Mean Square Error of Approximation (RMSEA)
“One of the most widely used measures that attempts to correct for the tendency of the x2 GOF test statistic to reject models with a large samples or a large number of observed variables is the root mean square error of approximation (RMSEA). This measure better represents how well a model fits a population, not just a sample used for estimation [25]. It explicitly tries to correct for both model complexity and sample size by including each in its computation. Lower RMSEA values indicate better fit. The question of what is a “good” RMSEA value is debatable. Although previous research had sometimes pointed to a cut-off value of .05 or .08, more recent research points to the fact that drawing an absolute cut-off for RMSEA is inadvisable [17]. An empirical examination of several measures found that the RMSEA was best suited to use in a confirmatory or competing models strategy as samples become larger [47]. Large samples can be considered as consisting of more than 500 respondents. One key advantage to RMSEA is that a confidence interval can be constructed giving the range of RMSEA values for a given level of confidence. Thus, it enables us to report that the RMSEA is between 0.03 and 0.08, for example, with 95 percent confidence. ”1
Interpretation
The smaller the RMSEA, the better the fit2.
| RMSEA | Interpretation |
|---|---|
| <0.05 | Very Good2 |
| <0.10 | Good2 |
0.05 is generally used a cutoff value for RMSEA which is often the same as the cut-off for p-values, but this is merely a coincidence2