Hints for Modeling a censored multinomial distribution?

Hmm. Interesting!
You wrote:

Do they then pick an item in the same group, or in another group? I assume it’s in a different group, also because you write:

But do you then want to decipher how much the unobserved demand is? In this case more q than what was sold, and less p than what was sold.

This means that not only:

but that this non-availability biases the total count in some other (unknown) group high!

Last question: do they always pick an object in a different group? Or is it possible that they see that something is not available and then they don’t buy at all?

Asking because it’s a tiny bit related to my post in A collection of new posts on logit choice models - #2 by Uri_Shimron.