Thanks so much for the reply.  This still seems very strange.  Even if the
differences between population and subject effects is the issue, wouldn't
one expect a bit more similarity between the actual effects for the subjects
and the population effects inferred from those effects?  Dr. Bates or anyone
else, can you resolve this mystery?  Alternatively, is there a way to get
population estimates of the random effects for subjects (contradiction in
terms?), like fitted.lme with the level = 0 argument?

All this is in service of an attempt to gain a simple scatterplot between
two random effects that closely reflect the estimates from VarCorr or
summary.  I'm sure someone must have a method for this already worked out.
pairs.lme plots the raw data from ranef, so the discrepancy is still a
problem there.

Thanks so much for your help.

- DC

On Sun, Aug 31, 2008 at 6:13 AM, Daniel Ezra Johnson <
danielezrajohnson@gmail.com> wrote:

> On Sun, Aug 31, 2008 at 6:53 AM, D Chaws <cat.dev.urandom@gmail.com>
> wrote:
> > Can someone tell me why correlations between raw random effects are
> > different from that provided in VarCorr for lme models?
> > For example:
> >
> > fm1 = lme(distance ~ I(age-8), random = ~ 1 + I(age-8) | Subject, data =
> > Orthodont)
> > R# VarCorr(fm1)
> > Subject = pdLogChol(1 + I(age - 8))
> >            Variance StdDev Corr
> > (Intercept) 3.55937  1.8866 (Intr)
> > I(age - 8)  0.05127  0.2264 0.209
> > Residual    1.71620  1.3100
> >
> > and
> >
> > R# cor(ranef(fm1))
> >            (Intercept) I(age - 8)
> > (Intercept)      1.0000     0.5764
> > I(age - 8)       0.5764     1.0000
> >
>
> This isn't a complete answer, but the figures in VarCorr and the model
> summary are the population estimates for the random effects (the
> parameters) while everything derived from ranef() refers to the actual
> Subjects in the data (the BLUPs).
>
> Look at:
>
> > sd(ranef(fm1))
> (Intercept)  I(age - 8)
>  1.7359554   0.1557322
>
> Those figures don't match the VarCorr standard deviations either,
> especially the second.
>
> I don't know why the BLUPs pattern differently, exactly, but I did
> look at plot(coefs(fm1)) which suggested Sex should be added as a
> fixed effect. Once I did that, the correlation between the random
> effects changed quite a lot (but was still different between VarCorr
> and ranef; the population correlation was actually negative...)
>
> D
>

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