R help - May 2007 - ordered logistic regression with random effects. Howto?

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

Paul--

I think the options are pretty limited for mixed-effects ordinal regression; it 
might be worth taking a look at Laura Thompson's R/Splus companion to Alan 
Agresti's text on categorical data analysis:

https://home.comcast.net/~lthompson221/Splusdiscrete2.pdf

She discusses some options for both GEE and random-effects approaches, though 
for the ordinal mixed-effects regression, I believe she writes out the 
likelihood function and passes it to optim() (ie, no canned functions).

Hope that helps.

cheers, Dave
-- 
Dave Atkins, PhD
Assistant Professor in Clinical Psychology
Fuller Graduate School of Psychology
Email: datkins at fuller.edu


Paul 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.

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

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

Paul,

I believe the model you describe below can be fitted in GENMOD and GLIMMIX
in SAS.

Alternatively, as Brian Ripley suggests, you could use MCMC.  BUGS has a
nice example of a multinomial logit model in the second example manual.
While this example considers only fixed effects, it's not difficult to
extend the model to include a random effect (see the 'Seeds' example in
the
first example manual).

Regards,
   -Cody



                                                                           
             "Paul Johnson"
             <pauljohn32 at gmail
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                                       [R] ordered logistic regression     
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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

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