[R-sig-ME] Confidence intervals on correlation parameter estimates

[Kingsford Jones]

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 at 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
>
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