ordered multinomial mixed model

Hi,

On 27 May 2011 17:03, Thomas Mang<thomasmang.ng at googlemail.com>  wrote:

Hi,

Consider the need for a mixed-effects model with an ordered multinomial
response variable. To the best of my knowledge, lme4 would not provide such
a thing.

You are right; the lme4 package does not provide functions to fit
ordinal mixed models - at least not without modifications. However,
there are other CRAN (e.g., ordinal and MCMCglmm) and R-Forge (e.g.,
ordinal2) packages that does so.

Thanks for these pointers, very helpful indeed !

However, I was wondering if such a model can be built using a generalized
mixed model with Bernoulli response variables. Here is my thinking, with the
question if this is possible as outlined below:

This is a good idea - so good in fact that others have had it before.
Recently Ken Knoblauch posted the polmer function to this list based
on this idea and using glmer
(https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/005069.html).
I am not sure if polmer is exactly the translation of your description
into an R function, but it seems to me that it is fairly close.

I have checked briefly the function by Ken, and the code snippets by 
Emmanuel Charpentier. On first sight *I think* these functions are 
different, and by the way it is not imminent at all to me that they 
would do the same as a cumulative logit model if the model contains 
covariates (and quick check on an adaptation of Emmanuel's code, 
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/005060.html, 
seems to confirm my point). Also, the likelihood is necessarily 
different (including for an intercept-only model).

The version I had proposed is different from the standard cumulative 
model too, as can be seen in the likelihood description I had provided. 
But on the plus side, it would relax the constraint that the effect of 
the covariates at the latent scale is identical across all factor 
transitions (i.e. shift of the cutpoints has the same magnitude).

I will investigate the material more in depth and then get back to you, 
maybe through private email if it's too technical. So more later.

best and thanks,
Thomas