Good day StataList.

I am having a bit of trouble in doing Multidimensional IRT. I have already done confirmatory factor analysis and extracted the latent abilities for the model that I have below.

[ATTACH=CONFIG]temp_19369_1597563864575_544[/ATTACH]

So I would like to ask the following to the community
  1. Is the code I used to extract the latent ability correct?
  2. Is it possible to create a model with another latent ability that is dependent on those 3 latent ability? An overall latent ability if I may say so.
  3. How can I estimate item parameters (item difficulty and discrimination) in a Multidimensional IRT model like this one? Items are dichotomous
Code I used is as follows:
Code:
gsem (L1 -> q1, ) (L1 -> q2, ) (L1 -> q3, ) (L1 -> q4, ) (L1 -> q6, ) (L1 -> q7, ) (L1 -> q9, ) (L1 -> q10, ) (L2 -> q11, ) (L2 -> q12, ) (L2 -> q13, ) (L2 -> q15, ) (L2 -> q16, ) (L2 -> q17, ) (L2 -> q19, ) (L3 -> q21, ) (L3 -> q22, ) (L3 -> q23, ) (L3 -> q24, ) (L3 -> q25, ) (L3 -> q26, ) (L3 -> q27, ) (L3 -> q28, ) (L3 -> q29, ) (L3 -> q30, ), covstruct(_lexogenous, diagonal) latent(L1 L2 L3 ) cov( L2*L1 L3*L1 L3*L2) nocapslatent
predict L*, latent
Thank you to anyone who could shed some light to this.