[R] ordered logistic regression with random effects. Howto?

[Paul Johnson]

I'd like to estimate an ordinal logistic regression with a random
effect for a grouping variable.   I do not find a pre-packaged
algorithm for this.  I've found methods glmmML (package: glmmML) and
lmer (package: lme4) both work fine with dichotomous dependent
variables. I'd like a model similar to polr (package: MASS) or lrm
(package: Design) that allows random effects.

I was thinking there might be a trick that might allow me to use a
program written for a dichotomous dependent variable with a mixed
effect to estimate such a model.  The proportional odds logistic
regression is often written as a sequence of dichotomous comparisons.
But it seems to me that, if it would work, then somebody would have
proposed it already.

I've found some commentary about methods of fitting ordinal logistic
regression with other procedures, however, and I would like to ask for
your advice and experience with this. In this article,

Ching-Fan Sheu, "Fitting mixed-effects models for repeated ordinal
outcomes with the NLMIXED procedure" Behavior Research Methods,
Instruments, & Computers, 2002, 34(2): 151-157.

the other gives an approach that works in SAS's NLMIXED procedure.  In
this approach, one explicitly writes down the probability that each
level will be achieved (using the linear predictor and constants for
each level).  I THINK I could find a way to translate this approach
into a model that can be fitted with either nlme or lmer.  Has someone
done it?

What other strategies for fitting mixed ordinal models are there in R?

Finally, a definitional question.  Is a multi-category logistic
regression (either ordered or not) a member of the glm family?  I had
thought the answer is no, mainly because glm and other R functions for
glms never mention multi-category qualitative dependent variables and
also because the distribution does not seem to fall into the
exponential family.  However, some textbooks do include the
multicategory models in the GLM treatment.


-- 
Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas