RMSEA Computation

[T.]

Dear Dr. Rosseel,

I’m wondering if the lavaan on Github is the most recent version?

https://github.com/yrosseel/lavaan/blob/master/R/lav_fit_measures.R

I noticed that the RMSEA code is still 1/N, instead of N-1.
Would you mind giving me the original source for this formula? I have seen different ones for RMSEA but I’m not sure which paper is this one from.

Thank you.

T.

[Terrence Jorgensen]

I’m wondering if the lavaan on Github is the most recent version?

Yes

 

I noticed that the RMSEA code is still 1/N, instead of N-1.

Only when using MLE with likelihood="normal" (see the chunk of code starting at line 47).  Setting likelihood="wishart" (or triggering that by mimic="EQS") will tell lavaan to use n-1 for each group (so N - ngroups), but that is only appropriate for models without a mean structure, and not as efficient as normal likelihood.  Mplus and lavaan use N by default.  Using N-1 is a bit of an anachronism that still appears all over the place because old software (LISREL, EQS) and textbooks they influenced (Bollen, 1989) use N-1.

 

Would you mind giving me the original source for this formula? I have seen different ones for RMSEA but I’m not sure which paper is this one from.

It's not about the RMSEA formula.  The issue there is just translating the chi-squared back to the fit-function metric, which is an average (rather than sum) of casewise log-likelihood ratios comparing the hypothesized to saturated models.  lavaan uses N consistently to calculate chi-squared, and to rescale the sample covariance matrix using (N-1)/N (i.e., "population formula" rather than "sample formula") -- see ?lavOptions about the default sample.cov.rescale=TRUE.  This is all about asymptotic multivariate normal theory, but I don't know of a reference to provide you.  I'd love to have one for my students, too :-)

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[T.]

Thank you very much!