I have a paper under review with a journal that uses a MIMIC model. One of the covariates in the model is generated from another CFA model from another dataset, but with the estimate included in the MIMIC model. The reviewer says this is a generated regressor and cannot be interpreted in the normal way. Is there a way around this?
The model looks something like: f1 by x1 x2 x3 f2 by x4 x5 x6
f1 f2 on z1 z2 z3
where z3 is a 'generated regressor' from another CFA
Yes the 'generated regressor' is just a factor score. Apparently there is a literature that says if you generate a score such as a factor score and include it in a regression model it invalidates standard statistical inference. This is because the score is only an estimate of the factor and has its own associated error. Pagan 1984.
The CFA that produces the 'generated regressor' is very big and when it is included as part of the MIMIC model the model will not converge. That is why we decided to include the score instead, but now we have the issue with the referee.
I have since seen another paper that does the same thing and they mention the generated regressor issue and use 'robust standard errors' as a solution. But I am not clear what this actually means precisely.
Robust standard errors would help only the non-normality of the factor scores. I think the larger issue is the reliability of the factor scores. What is the factor determinacy of that factor? I think you have more justification in using it if the factor determinacy is high.
Can't you use just the one factor from the CFA not the entire CFA? Also, I wonder why the full model would not converge. This does not seem correct. If you send the output and your license number to email@example.com, perhaps we can help with this problem.