[R-sig-ME] [R] lmer - BLUP prediction intervals

[Doran, Harold]

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 at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of Ben Bolker
> Sent: Tuesday, February 05, 2013 1:31 PM
> To: r-help at 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 at 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
> 
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