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