Multigroup bifactor Rasch model; WLSM...
Message/Author
 Pablo S. J. posted on Wednesday, December 18, 2019 - 9:45 am
Dear profs Muthen,
I have been working a couple of months trying to run a model a little bit complex, a multigroup bifactor Rasch model (rating scale). I have been reading all the available information but I still have some doubts.
I am using WLSMV with theta method.
-Rasch model:
+Residuals fixed to 1.
+Factor means fixed to 0.
-Bifactor model (one general and three specific factors)
+Variances fixed to 1.
+All correlation fixed to 0 except for one correlation between two of the specific factors.
-Multigroup:
+I am using as a baseline a bifactor model with fixed loadings within factor and free between factors.
My questions doubts:
- If I want to test a multigroup Rasch model, is it necessary to use a baseline model or can I start using the initial Rasch model?
- If I need a baseline model, should it have completely free factor loadings?
- Should I have to fix all the residuals to 1 in all groups?
- I am trying to free the means in the multigroup model but I always have as a result a non-identified model. How could I compare group means?

Thanks a lot for your time and help.
Kind regards,
Pablo
 Pablo S. J. posted on Wednesday, December 18, 2019 - 10:10 am
variable: names= Int Ski Cap Sin Hon Tru Lik War Fri Group;
categorical=Int-Fri;
grouping is Group (11=Roma1 12=ROMA2, 13=Fire, 14=Down, 15=Multi);
usevar=Int Ski Cap Sin Hon Tru Lik War Fri;
ANALYSIS:
estimator = WLSMV;
parameterization = theta;
Model:
Comp by Int-Cap@1(a);
Comp@1;
Mora by Sin-Tru@1(a);
mora@1;
Soci by Lik-Fri@1(a);
Soci@1;
Eva by Int-Fri@1(a);
Eva@1;
Eva with soci@0 mora@0 comp@0;
mora with comp@0;
soci with comp@0;
[comp@0];
[mora@0];
[soci@0];
[Eva@0];
Int-fri@1;
Model Roma2:
Int-fri@1;
Eva with soci@0 mora@0 comp@0;
mora with comp@0;
soci with comp@0;
[...]
 Bengt O. Muthen posted on Wednesday, December 18, 2019 - 1:05 pm
First posting:

The Rasch model can have all the item factor loadings fixed to 1 and a free factor variance - and the he rest is ok as stated. But to prepare for multigroup, you can instead hold loadings equal across items and across levels and fix the within factor variance at 1 and free it for between. Residual variances can be free in all but one group.

Second posting:

 Pablo S. J. posted on Friday, December 20, 2019 - 7:24 am
Thanks a lot for the answer.
I am going correct some mistakes of the syntax and send you the output.
Regards,
Pablo