From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Tue, 08 May 2007 06:45:18 +0100 (BST)

Date: Tue, 08 May 2007 06:45:18 +0100 (BST)

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 ______________________________________________ R-help_at_stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Tue 08 May 2007 - 05:51:03 GMT

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