Imagine a setting like speed dating (in a same-sex dating context) where all of the women in the room get acquainted with each other. Subsequently, they provide a full rank-ordering of their peers in terms of their desirability as dating partners. The unit of analysis is the rank assigned by woman i to peer j where each woman has N - 1 peers.
My understanding is that an exploded logit model would be a good choice. Are there implementations in Stan that could serve as a starting point?
A bit late :) but here it is:
Very cool. Thanks for sharing.
Out of curiosity, what would you do if there were some missing rankings? For instance, maybe you elicited rankings by having people line up index cards in the order that matches their preferences for pizza toppings. But one day, the cards for “mushrooms” and “garlic” were inadvertently omitted, leaving you with only 23 rankings from the interviews on that day.
I think I would just assign the vector of prob \theta to \theta', where \theta'_{garlic} = 0, and \theta'_{mushroom}=0, and you just normalize the rest of the probabilities, \theta' = \frac{\theta}{\sum \theta_{[-garlic,-mushroom]}}.
For that interview you fit \theta', and you can deduce \theta from it.