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I would describe a model (and solve with the stan software) a process like this:

for i = 1...N consumers

  1. the i-th consumer is allowed to choose an item out of 7. 6 items remain.
  2. the same consumer chooses another item out of the 6 remaining items.

I collected the N pairs of choices and I would like to infer if there are some preferences. The first step is a multinomial model. The second is a multinomial process conditioned by the first choice. I really struggle to model the log probability function and code it in stan. Any help?

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This kind of problem cannot be solved as a multinomial but rather using Fisher's noncentral hypergeometric distribution

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