[R] gnls or nlme : how to obtain confidence intervals of fitted values

[Rogers, James A [PGRD Groton]]

I believe what Pierre means to be asking for are "prediction intervals", or
possibly "tolerance intervals", which are different from "confidence
intervals". A great reference is:

Hahn G and Meeker WQ: Statistical Intervals. John Wiley and Sons, New York,
1991

For example, in a one-sample Normal problem, \bar{X} \pm 2
\hat{sigma}/\sqrt{n} is an approximate 95% confidence interval, while
\bar{X} \pm 2 \hat{sigma} is an approximate 95% prediction interval
(assuming \bar{X} and \hat{sigma} are high precision estimates; if they are
not you probably want to consider tolerance intervals, which are discussed
in the above reference). 

Both intervals.lme{nlme} and estimable{gmodels} will give you confidence
intervals, but neither will give you prediction intervals. I am not aware of
any published R function that gives you prediction intervals or tolerance
intervals for lme models. It is not easy to write such a function for the
general case, but it may be relatively easy to write your own for special
cases of lme models.  

Jim 

> Message: 9
> Date: Mon, 4 Oct 2004 21:42:20 +1000
> From: Andrew Robinson <andrewr at uidaho.edu>
> Subject: Re: [R] gnls or nlme : how to obtain confidence intervals of
> 	fitted	values
> To: David Scott <d.scott at auckland.ac.nz>
> Cc: r-help at stat.math.ethz.ch, Spencer Graves <spencer.graves at pdf.com>
> Message-ID: <20041004114220.GJ67507 at uidaho.edu>
> Content-Type: text/plain; charset=us-ascii
> 
> The function estimable() from the gmodels part of the gregmisc package
> will do this, if applied appropriately.
> 
> It allows for the estimation of arbitrary linear combinations of the
> parameter estimates of a model object, and calcualtes confidence
> intervals.
> 
> I hope that this helps,
> 
> Andrew
> 
> 
> 
> On Tue, Oct 05, 2004 at 12:31:48AM +1300, David Scott wrote:
> > On Mon, 4 Oct 2004, Pierre MONTPIED wrote:
> > 
> > >Thanks Spencer but the intervals function gives confidence intervals of

> > >the parameters of the model not the predicted values. In the Soybean 
> > >example it would be the CI of predicted weight for a given time,
knowing 
> > >all the parameters (Asym, xmid, scal, variance function and residual)
and 
> > >their distributions.
> > >
> > >And what I need to calculate is precisely this CI.
> > >
> > >My question is therefore is there an analytical way to calculate such
CI, 
> > >whatever the model, or could I try some randomizing techniques such as 
> > >bootstrap or other ?
> > >


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