[R-sig-ME] multinomial mixed effects models

Douglas Bates bates at stat.wisc.edu
Tue Jul 17 00:34:34 CEST 2007

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.

There is a special case of an ordered categorical response, such as
one gets from questions of the form "on a scale of 1 to 5 ...".  The
polr function from the MASS package fits a proportional odds logistic
regression model for which I think it should be straightforward to
define a version with random effects.

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