Output interpretation of lavaan in R concerning fit indices of robust estimator

Question

I am doing a path analysis in R using the lavaan package. Because one of my endogenous variables is skewed I used a correction by Satorra & Bentler to receive robust estimators and standard errors.

fit<-sem(trf.model1, data=data2, estimator="MLM")
summary(fit, standardized=T, fit.measures=T, rsquare=T)

My question concerns the output of the fit indices. Usually, there are two columns in the output. Left: normal, and right: robust. But with fit indices like for example the RMSEA there is also an extra line saying robust RMSEA. So my question is which one do I report?

Here is a bit of the output:

Estimator                                         ML      Robust
Minimum Function Test Statistic               10.568       8.574
Degrees of freedom                                 6           6
P-value (Chi-square)                           0.103       0.199
Scaling correction factor                                  1.232
for the Satorra-Bentler correction

...

RMSEA                                          0.081       0.061
90 Percent Confidence Interval          0.000  0.160       0.000  0.137
P-value RMSEA <= 0.05                          0.222       0.355

Robust RMSEA                                               0.068
90 Percent Confidence Interval                             0.000  0.161

I already figured out that the one is the scaled RMSEA and the other one the robust RMSEA. (Because you can ask R to give them out by the commands below) But what is the diffence?

> fitMeasures(fit, "RMSEA.scaled")
rmsea.scaled 
   0.061

> fitMeasures(fit, "RMSEA.robust")
rmsea.robust 
   0.068

A book called "Latent variable modeling using R" says "Most fit measures in lavaan that were derived from a robust estimator have a scales suffix in the name, e.g. chisq.scaled." so I tend to use the scaled one, but I kind of like to understand what I am doing.

I hope somebody can help.

thank you!

Are you asking a statistical question about the difference between the estimates or are you not sure what the software is doing? If the latter would you not be better off on R-help? — mdewey, Oct 23 '16 at 15:29

score 2 · Answer 1 · edited Mar 31 '18 at 17:59

I was curious about this as well and came across the following message from Yves Rosseel (the developer of lavaan):

Dear lavaan users,

lavaan 0.5-21 has been released on CRAN today (7 Sept 2016).

New features and user-visible changes:

robust RMSEA and CFI values are now computed correctly, following Brosseau-Liard, P. E., Savalei, V., and Li, L. (2012), and Brosseau-Liard, P. E. and Savalei, V. (2014); in the output of fitMeasures(), the 'new' ones are called cfi.robust and rmsea.robust, while the 'old' ones are called cfi.scaled and rmsea.scaled

...[there is more, but not relevant to this question]

Hope this is useful to others, since my guess is that you have figured it out and/or moved on at this point!

Source / link to lavaan website: http://lavaan.ugent.be/history/dot5.html

Output interpretation of lavaan in R concerning fit indices of robust estimator

1 Answers1