Logistic regression (odds ratios) vs. mixed effects model

[lars]

In this thread, Stefan very helpfully showed how to get R to report
odds ratios from a logistic regression model produced by lrm():
http://groups.google.com/group/corpling-with-r/browse_thread/thread/5da1803884e6dd27
The command that gets them is this: (effect.sizes<-exp(1)^model.lrm
$coefficients)
Those odds ratios, as well as the R-square that lrm() reports, are
very dear to me because I know what they mean.

But say you wanted to use a binomial mixed effects model instead.

Can odds ratios like those from a logistic regression be reported for
a binomial mixed effects model that comes out of lmer()?

Also, lmer() only reports Dxy. Is there a way to find out the R-
square? Does that exist for lmer(), or make sense?

[Stefan Th. Gries]

Hi

> Can odds ratios like those from a logistic regression be reported for a binomial mixed effects model that comes out of lmer()?

As is so often the case, Harald's great book provides some help: cf.
Baayen (2008: Section 7.4): on p. 281, he talks about "fitted lok odds
ratios" so I *guess* the answer is "yes."

> Also, lmer() only reports Dxy. Is there a way to find out the R-square? Does that exist for lmer(), or make sense?
As far as I know, there is no R-squared for generalized linear
mixed-effects models. I have never seen that mentioned: neither Baayen
nor Gelman/Hill mention something like that and the latter even make
an explicit difference on a website for their package, (my emphasis:
"Output are the model, the regression coefficients and standard
errors, and the residual sd and *R-squared (for a linear model)*, or
the *null deviance and residual deviance (for a generalized linear
model)*." Maybe this will help:
<http://134.148.236.121/R/e2/help/07/06/18201.html>

HTH,
STG
--
Stefan Th. Gries
-----------------------------------------------
University of California, Santa Barbara
http://www.linguistics.ucsb.edu/faculty/stgries
-----------------------------------------------

[lars]

> > Can odds ratios like those from a logistic regression be reported for a binomial mixed effects model that comes out of lmer()?
> As is so often the case, Harald's great book provides some help: cf.
> Baayen (2008: Section 7.4): on p. 281, he talks about "fitted lok odds
> ratios" so I *guess* the answer is "yes."

Yes, from Harald's book it looks like this is the call for getting
odds ratios for the fixed effects of GLMMs:

oddsratios.glmm <- exp(1)^fixef(mymodel.glmm)


(The function fixef() is part of the lme4 package.)
Cp. the call for models out of lrm() that Stefan posted:

oddsratios.lrm <- exp(1)^mymodel.lrm$coefficients