Appropriate model for "pick m from n" discrete choice setting

Question

I am trying to model the selection of panel members from a bench of judges, where the number of choices is assumed to be fixed in advance. (In my application, it is common to pick five or seven judges from a bench of 12).

I am using (time-varying and case-specific) variables measured on the different judges to explain their selection.

I have seen other authors use conditional logit models to assess the effects of judge-specific variables.

However, the conditional logit model does not seem appropriate for cases where multiple choices must be made without replacement.

In simulations that I have carried out, I can recover known coefficients using the mclogit package in R when only one choice is made.

However, when the top two choices are chosen, the estimated coefficients are much, much smaller than their known values.

I therefore wanted to know:

• Am I right to think that the conditional logit model is inappropriate in situations of this type?
• What would be an appropriate model for the situation I have described?
• How (ideally) might it be estimated in R?

Answer 1

I guess you could run separate logits for each of the seven choices, estimating the probability that judge j will be included in the set of chosen judges.

But the clogit assumes that a single choice is made from a discrete, finite set of available choices. So you would have to think of the set of all possible combinations of 7 judges chosen from 12, which is probably a much too large set to work with practically.