It is possible to create the correlation matrix of the fixed effects and
the random effects jointly using the results from lmer but I have
difficulty deciding what this would represent statistically.  If you adopt
a Bayesian approach then everything works because the fixed effects and the
random effects are both random variables.  In the classical statistical
approach (i.e. sampling theory), however, I haven't been able to make sense
of the relationship between a model parameter and an unobserved random
variable.  They exist in different worlds.  You can talk about the
probability model for the random effects and describe the conditional
distribution of the random effects given the observed data and assumed
values of the parameters.  Remember that in probability land the parameters
are known.  You can also talk about the distribution of the estimators of
the parameters given the observed data.  But I am at a loss to describe a
combination of parameter estimators and a conditional distribution given
the observed data with known parameters.

I appreciate that people want to know these quantities but without a
Bayesian model I can't think of what they are.


On Tue, Feb 5, 2013 at 12:49 PM, Doran, Harold <HDoran@air.org> wrote:

> Ben,
>
> I'm not sure the predictions of the conditional modes and the estimates of
> the fixed effects are orthogonal. I don't think it's possible to spit out
> that covariance from lmer(), though I could be wrong.
>
> My own software for fitting mixed models uses henderson's method. Under
> this framework, I output the matrix giving the covariance between the fixed
> effects and the BLUPs.
> The easiest way to see thi is to go to this wiki page and look at the eqn
> under estimation.
>
> The matrix in the upper right block (X'R^{-1}Z) is the one giving those
> covariances.
>
> http://en.wikipedia.org/wiki/Mixed_model
>
> > -----Original Message-----
> > From: r-help-bounces@r-project.org [mailto:r-help-bounces@r-project.org]
> > On Behalf Of Ben Bolker
> > Sent: Tuesday, February 05, 2013 1:31 PM
> > To: r-help@stat.math.ethz.ch
> > Subject: Re: [R] lmer - BLUP prediction intervals
> >
> > Daniel Caro <dcarov <at> gmail.com> writes:
> >
> > >
> > > Dear all
> > >
> > > I have a model that looks like this:
> > >
> > > m1 <- lmer(Difference ~ 1+  (1|Examiner) + (1|Item),
> > > data=englisho.data)
> > >
> > > I know it is not possible to estimate random effects but one can
> > > obtain BLUPs of the conditional modes with
> > >
> > > re1 <- ranef(m1, postVar=T)
> > >
> > > And then dotplot(re1) for the examiner and item levels gives me a nice
> > > prediction interval. But I would like to have the prediction interval
> > > for the individual intercepts, not the conditional modes of the random
> > > effects, that is, the fixed effect (overall estimated intercept) + the
> > > conditional mode of the random effect (examiner or item level). Does
> > > this make sense? And if so, how would I calculate this? I'd like to do
> > > the same thing to obtain prediction intervals of individual growth
> > > rates in longitudinal models (i.e., overall growth rate + random
> > > effect).
> >
> >   I think this belongs on the r-sig-mixed-models@r-project.org list.
> > Could you please re-post it there?  (I would redirect it myself but am
> reading
> > via gmane ...)  For a start, I would probably assume independence of the
> > uncertainty in the conditional modes and in the overall slope parameter
> and
> > compute the overall variance by adding the variances ... ?  (Not sure
> that's
> > right.)
> >
> >   Ben Bolker
> >
> > ______________________________________________
> > R-help@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/posting-
> > guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
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>

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