[R-sig-ME] multinomial mixed effects models

Roger Levy rlevy at ucsd.edu
Wed Jul 25 07:16:56 CEST 2007

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 

Many thanks,


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