as in any other count context, you need an approach that considers the particular error structure. For a SEM perspective, only Mplus currently can handly count DVs. If you don't want to buy Mplus, I would stay in the GLM context. "SEM thinking" (i.e., creating a causal model) and "SEM analysis" (i.e., using SEM software) are different things. That is you can create a SEM and use one or more regression analyses, incl. instruments and appropriate control variables to estimate the parameters.
Holger Steinmetz, Thank you very much. But we found a paper (DOI: 10.1177/0361198119845353) in which authors applied maximum likelihood method. Can you suggest us in which background one can apply maximum likelihood in this context?
as i said; I don't think that ML is appropriate here and an estimator reflecting the nature of the variables (even if they are only indicators) should have been used.
In addition, I would not trust the model as the latent variables do not seem reasonable to me.