Hi,
Thanks for the reply and advice.  unfortunately when incorporating
correlation structures(e.g. AR(1)) into a mixed model, lme() uses numerical
methods for the calculation of the related parameters(e.g. Phi).  (the
numerical methods used are in the nlminb()).  In any case, it is because no
closed form of the derivative of the log-likelihood with respect to these
parameters is available.  This suggests to me that the inverse Hessian of
the log ML function is also unavailable.

If anyone knows of a source that can confirm or refute any of these
thoughts, that would be GREAT!

Harlan

On Mon, Jul 20, 2009 at 8:09 PM, Kingsford Jones
<kingsfordjones@gmail.com>wrote:

> Hi Harlan,
>
> From ?intervals.lme it sounds as though normal approximations are
> used, with standard errors coming from the inverse Hessian of the log
> (RE)ML function evaluated at the
> estimates.  I don't have P&B with me, but IIRC Ch 5 begins with a
> discussion of how the likelihood functions are adjusted to accommodate
> error covariance parameters.
>
> hth,
>
> Kingsford Jones
>
> On Mon, Jul 20, 2009 at 12:55 PM, H c<harlancampbell@gmail.com> wrote:
> > Hello all,
> > When incorporating correlation structures into a lme model with the
> nlme()
> > library, one can produce confidence intervals for the correlation
> parameter
> > estimates.  The Pinheiro and Bates book has a simple example:
> >
> > "We can assess the precision of the correlation parameter estimate in
> > fm20var.lme with the 'intervals'  method.
> >
> >> fm1 <- lme(distance ~ age, data =
> > Orthodont,correlation=corAR1(0.5,fixed=FALSE)) # random is ~ age
> >> intervals(fm1)
> > Approximate 95% confidence intervals
> > ...
> >  Correlation structure:
> >         lower       est.       upper
> > Phi -0.7615846 -0.4898957 -0.07174523
> > attr(,"label")
> > [1] "Correlation structure:"
> >
> >  Within-group standard error:
> >    lower      est.     upper
> > 0.9002138 1.0900639 1.3199522
> > "
> >
> > Any thoughts on how these C.I.s are obtained?
> > As far as I cant tell, the Pinheiro and Bates book does not go into
> details,
> > but perhaps I am wrong.
> >
> > Any thoughts or references would be greatly appreciated,
> >
> > Harlan Campbell
> > McGill University
> > Montreal, Canada
> >
> >        [[alternative HTML version deleted]]
> >
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> >
>

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