[R-sig-ME] conditional vs. marginal coefficients in GLMM [was: Shrinkage of ORs in a glmm]

[lorenz.gygax at art.admin.ch]

Thanks to the Davids!

I will brush up on my reading then. 

> The best description of this that I have found is the article by
> Heagerty and Zeger in Statistical Science (2000, I think).

For those interested, this article is available at:
https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/32863/2000-Marginalized.pdf?sequence=1 

> The GLMM are conditional because:
> 
> -- there is a non-identity link function, and
> -- the random-effects are part of the linear predictor
> 
> because of these, the random-effects have zero mean on the scale of the
> linear predictor, but *not* on the scale of the outcome.  Raudenbush and
> Bryk (2002) also discuss this in their book.

That sounds sensible. The full reference to this book is:
Raudenbush, Stephen W.  
Hierarchical linear models : applications and data analysis methods
Thousand Oaks, CA : Sage Publications, 2002  

> To the list generally, I am curious as to how folks have addressed this
> in applied settings -- that is, as far as I can tell, many times we *do*
> want to interpret GLMM fixed-effects as if they were marginal.  Heagerty
> and Zeger present formula for converting between the two, but not sure
> whether that would be possible to use with glmer() output or not.

Any input from others how they deal with the problem in practical application?

Thanks and best regards, Lorenz