Estimator for categorical variables on Multigroup CFA

[Maria Cyniak-Cieciura]

Hello,

I'm running quite a challenging Multigroup CFA with 9 samples of very different N (900, 500, 1200, 450, 500, 600, 230, 230 and 500) with categorical variables (4-point Likert scale) and a seven-factor model (each factor loaded by 5-6 items). Thus the general sample is big, and the model is complicated. This is a challenge as it makes it difficult to obtain the good fit indices and obtain measurment invariance. Traditional criteria are too restrictive and less restrictive ones were postulated to be used (like delta CFI of less than.020 instead of.010 for the difference between configural and metric models). Chi square od bot decisive because of the sample size.

Therefore I decided to use WLSM od WLSMV, with the last one being preferable.  Unfortunately, the R lavaan output gives robust CFI, TLI and RMSEA only in the case of WLSM (I mean the lines with robust fit indices, not the column; those reported in the column are frequently much worse than standard fit indices or the other robust ones, which makes it impossible to obtain a good fit with such a complicated model). WLSMV resulted in very good standard fit indices, weak robust indices and strange result in terms of a comparison between configural and metric models, as the metric model had better fit than the configural.

At the same time, the robust CFI, TLI and RMSEA presented only with the use of WLSM are good, and that relates also to configural and metric models.

I have three questions referring to this situation.

1) Is it ok to use WLSM and its robust statistics in such situation? Is it possible that in some cases WLSM is a better choice?

2) in the case of MLM and MLMV point robust fit indices are the same and there is a possibility to correct the RMSEA CIs and use robust fit indices with MLMV. Is this also a case with WLSMV? There is a manuscript from 2018 about it, maybe anything changed since that time?

3) why WLSMV gave better fit for the metric model than for the configural one? 

I will be thankful for any help.

Best wishes,

Maria

[Yves Rosseel]

On 2/3/23 23:18, Maria Cyniak-Cieciura wrote:
> I have three questions referring to this situation.
> 1) Is it ok to use WLSM and its robust statistics in such situation?

I am afraid not. But the WLSMV 'scaled' versions are not ok either. See

Savalei, V. (2021) Improving Fit Indices In SEM with categorical data.
Multivariate Behavioral Research, 56(3), 390-407.

> 2) in the case of MLM and MLMV point robust fit indices are the same and
> there is a possibility to correct the RMSEA CIs and use robust fit
> indices with MLMV. Is this also a case with WLSMV?

In the last version of lavaan (0.6-13), we implemented the Savalei
(2021) method for handling categorical data. This seems to be the best
method we have for the moment. But it is only available for models
without covariates or any other continuous variables. This should result
in 'Robust' values for CFI and RMSEA.

> 3) why WLSMV gave better fit for the metric model than for the
> configural one?

That is (unfortunately) an artifact of the (non-robust) WLSMV fit
measures. They are way too optimistic...

Yves.

[Maria Cyniak-Cieciura]

Dear Yves,

Thank you very very much for your reply. It made it all pretty clear for me. 

One more question about cfa for binary data. I have declared them as ordered and used WLSMV. The scaled robust fit indices are good (CFI, TLI and RMSEA). The robust statistics (in lines) suggest that the model does not fit the data. Which is better/more reliable for binary data?

Maria

[Yves Rosseel]

On 2/11/23 13:08, Maria Cyniak-Cieciura wrote:
> One more question about cfa for binary data. I have declared them as
> ordered and used WLSMV. The scaled robust fit indices are good (CFI, TLI
> and RMSEA). The robust statistics (in lines) suggest that the model does
> not fit the data. Which is better/more reliable for binary data?

The 'Robust' ones.

(Eventually, lavaan will not show the scaled RMSEA/CFI values any longer
(by default))

Yves.