Definitely Mplus (and possibly lavaan - I don't know for sure) can handle a mix of dichotomous and polytomous items within the same CFA model.

Hello Ahmed,

Assuming it makes sense to incorporate both item sets in the same analysis, then yes, you may certainly include them. The classical advice would be to use polychoric correlations rather than Pearson correlations for the starting matrix of observed relationships. However, the issue of ordinal vs. interval scale is likely a concern as well (especially with polytomous response options).

As @Christian Geiser points out, Mplus has a well-earned reputation for being able to handle ordinal variables in SEM/CFA model; the R library, lavaan, can do so as well. A third option would be to first scale the responses via item response theory, then proceed with just about any classical covariance-based SEM software.

Good luck with your work.

Hi there,

that is easy in lavaan/R. Just define the binary indicators as ordered and refer to that in the sem() function of lavaan. This will prompt DWLS as an estimator.

I attached as small R simulation that shows the whole thing.

All the best,

Holger

Thank you very much all for the great help by answer my question. Holger Steinmetz , David Morse , Christian Geiser