[R-sig-ME] multinomial mixed effects models

[Roger Levy]

Douglas Bates wrote:
> On 7/16/07, Austin Frank <austin.frank at gmail.com> wrote:
>> Hello!
> 
>> I and several of my colleagues are wondering whether it is possible to
>> use any of the methods of lme4 as it exists now to fit a mixed effects
>> model with a response variable drawn from a multinomial distribution.
>> glm does not include a multinomial family, so if it is possible to
>> accomplish this I'm not sure how to do so.  Packages that do allow
>> multinomial response variables (like multinomRob) don't seem to allow
>> for the inclusion of random effects.
> 
>> If it is not currently possible to fit a data set with a categorical
>> dependent variable with more than two levels, might this be possible in
>> the forthcoming update to lme4?
> 
>> Finally, if it isn't possible now and won't be in the next version of
>> the package either, would someone be willing to explain the conceptual
>> or technical difficulties associated with including a response variable
>> from a multinomial distribution in a mixed effects model?
> 
> The big problem is defining the model for a multinomial response.  I
> haven't looked at the multinomRob package so perhaps it is just my
> lack of understanding but I think it is difficult to formulate a
> general model using a linear predictor for a multinomial response.

May I follow up on this question?  Ordinary multinomial regression for K 
categorical outcome responses is generalized from binary logistic 
regression by choosing one outcome as the reference category, and using 
K-1 for the remaining K-1 outcomes.  So what would be the problem with 
just adding random effects to each of the K-1 linear predictors?  Is the 
trouble perhaps that the random effect introduces an asymmetry such that 
the inferred model could depend on the choice of the reference outcome 
category?

Many thanks,

Roger