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Null (baseline) model RMSEA in Mplus

Familiarity with statistical computing software - particularly programs as flexible and feature-filled as R and the packages on CRAN - has been a tremendous boon. However, this familiarity has sent me searching the web for a way ask for particular output that is not printed by default. This expectation that the output I want from software is available with the right option or command has led me (more than once) to forget the possibility of simply computing the required output manually.

In particular, I recently needed to compute the RMSEA of the null model for confirmatory factor analysis (CFA). A few months ago, I chose to use Mplus for the CFA because I was familiar with it (moreso than the lavaan R package at least) and it had some estimation methods I needed that other software does not always have implementedĀ (e.g. the WLSMV estimator is not available in JMP 10 with SAS PROC CALIS).

Mplus does not print the RMSEA for the null model (or baseline model, in Mplus parlance) in the standard output, nor does there seem to be an command to request it. Fortunately, this is not an insurmountable problem because the formula for RMSEA is straightforward:

RMSEA = \frac{\sqrt{X^2 - df}}{\sqrt{df(N-1)}}

where X^2 is the observed Chi-Square test statistic, df is the associated degrees of freedom, and N is the sample size. In the Mplus output, look for "Chi-Square Test of Model Fit for the Baseline Model" for theĀ X^2 and df values.

The reason for needing to check the null RMSEA is that incremental fit indices such as CFI and TLI may not be informative if the null RMSEA is less than 0.158 (Kenny, 2014). If you are using the lavaan package, it appears this can be calculated using the nullRMSEA function in the semTools package.

(As an aside, don't let the vintage '90s design fool you: David Kenny's website is a great resource for structural equation modeling. He has the credentials to back up the site, too: Kenny is a Distinguished Professor Emeritus at the University of Connecticut.)

References

Kenny, D. A. (2014). Measuring Model Fit. Retrieved from http://davidakenny.net/cm/fit.htm

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