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GLMER fixed-effect estimates systematically larger than GLM/GEE?

2 messages · Assaf P. Oron, David Atkins

David Atkins
# 
Assaf--

The fixed-effects estimates from GLMM and GEE are not directly 
comparable as the former are conditional on the random-effects, whereas 
the latter are marginal coefficients.  See the following for some 
further chatter and citations.

https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/005527.html

Hope that helps.

cheers, Dave

-- 
Dave Atkins, PhD
Research Associate Professor
Department of Psychiatry and Behavioral Science
University of Washington
datkins at u.washington.edu

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Hi all,

I was trying logistic GLMM via glmer() on a binary outcome in a crossover
trial. One of my research questions was whether there is enough
within-person dependence that had to be accounted for, or whether I can
ignore it and pool data to a simpler analysis.

So I ran the same data on glm() and on glmer(both REML=F and REML=T). The
estimated auto-correlations are relatively mild, and the contribution of
GLMM vs. GLM is borderline significant, depending upon whether you prefer
likelihood, AIC, BIC or some other criterion.

However, I was surprised to see an unexpectedly large difference in the
*fixed* effect estimates. The glmer() estimates were all about 30%-40%
larger in magnitude.

Then I found this Q&A online:
https://stat.ethz.ch/pipermail/r-help/2008-July/166979.html

Which showed a similar discrepancy (about 15%-20% in magnitude), and also a
gee() run that agreed with glm() and not glmer().

So I tried gee() myself, and my estimates too show an gee-glm agreement with
glmer() the odd man out, having larger fixed-effect estimates.

I'm not asking you to diagnose my specific case, but rather whether you know
of this feature/problem with glmer(). Is there some hidden scaling factor in
the estimates or defaults that I am missing?

Thanks in advance, Assaf