[Arne Risa Hole]

At the risk of boring everybody to death, when I said above that "...computationally they are essentially the same but they are substantively different models" it would have been more precise to say that computationally the McFadden model is a special case of the fixed-effects logit model (as stated in the asclogit entry in the Stata manual). The point remains though that they are substantively different models, and to deal with multiple chosen alternatives in the McFadden model in the same way that you would deal with multiple positives in a fixed-effects logit model (which is, I think, what asclogit does since it appears to be clogit which is doing the heavy computational lifting) seems to lack a theoretical foundation, as far as I can see.

Arne

[daniel klein]

Well, I am not bored at all - so that makes at least one.

Arne has made some very interesting and important points concerning the addition of alternatives, as suggested in my latest post #14. The most crucial one is the lack of information for alternative specific variables for those new choices. Any "single imputation" will in my view be problematic, and therefore I guess this solution might even be worse than adding observations and correcting standard errors.

However, as Arne now points out again, the main problem seems to be a theoretical one, and this is solved by neither of the approaches so far. I wonder whether one can motivate the choice model from combining several binary-choice models, in which there is only one alternative and it is chosen, if the utility exceeds a certain threshold. Maybe such a combination of binary-choice models is even implied by the IIA assumption underlying the multinomial model?

Best
Daniel

[Arne Risa Hole]

Possibly, but that would be a departure from the standard random utility theory which discrete choice models are usually derived from.

Just one final comment from me on this issue: other Stata commands for estimating discrete choice models, such as nlogit and asmprobit, do impose the condition that only one alternative can be chosen per choice set, so asclogit is the odd one out in this respect.

These are fairly minor quibbles; asclogit is a very useful command and we are discussing an issue that doesn't arise very frequently, in my experience. Having said that my preference would be that asclogit behaved like nlogit and dropped choice sets with multiple chosen alternatives (and issued a warning message informing users).

Arne