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

[Prof Brian Ripley]

On the definitional question, some texts do indeed consider multi-category 
logistic regression as a glm.  But the original definition by Nelder does 
not.  I've never seen polr considered to be a glm (but it way well have 
been done).

Adding random effects is a whole different ball game: you need to 
integrate over the random effects to find a likelihood.  That integration 
is tricky, and I am not sure we yet have reliable software for it in the 
binary ('dichotomous dependent variable') case: SAS's NLMIXED certainly is 
not reliable.  I've had students run real problems through a variety of 
software, and get quite different results.  (It is possible that the shape 
of the likelihood is a problem but it is not the only one.)

MCMC approaches to that integration are an alternative not mentioned 
below.

On Mon, 7 May 2007, Paul Johnson wrote:

> 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.

You need to combine all the binary comparisons to get the likelihood, and 
the models have parameters in common.

> 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.
>
>
>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595