[wbuchanan]

Dick Campbell in CFA it is fine as you say. If, however, the OP wanted to equate or link their implementation of the form to the existing literature the polytomous response set has fairly significant assumptions and it may be possible that the response set could be simplified (e.g., collapsing the tails to create a 5 category response set). Most importantly, I appreciate your last bit of advice (e.g., acknowledge the limitations and the purpose of the decision that was made in the modeling explicitly).

[Cordula Kiel]

Thank you all very much vor your detailed replies!
This was really helpful for me, and I know I need to invest more time in reading and understanding the underlying concepts.
As adviced, I talked to my supervisor and she said it would be sufficient for my purposes to take the mean of the single items's scores as overall scores, provided that Crombach's alpha, the KMO measure and the single factor loadings for the 1-factor solution are large enough to justify that one factor.

Nevertheless, I will try to get a better understanding for CFA and gsem.