[R] Correct variance for prediction intervals from nlme and gnls objects

From: Nicholas Lewin-Koh <nikko_at_hailmail.net>
Date: Sat 23 Jul 2005 - 04:26:40 EST

An approximate prediction interval for f(x,b) from Rupert and Carrol (1988) on pg 53
define q^2=g^2((f(x0,b),x0,a) + 1/N f'b(x0,b)^T S^-1 f'b(x0,b)

where g is the variance function and f'b is the derivative in terms of b evaluted at x0
and S is

      S=(1/N) Sum(1,N) f'b(xi,b)f'b(xi,b)^T/g^2((f(xi,b),a)

 and the interval is defined at f(x0,b)+/- t(N-p,alpha/2) sqrt(sigma^2  q^2)

My question is if I were to fit the model fit<-gnls(y~SSlogis(x,Asymp,xmid,scal),data=foo, weights=varPower)

is attr(fit$parAssign,"varBetaFact") the correct quantity to use for S^-1? or is (fit$dim$N/fit$sigma^2)*fit$VarBeta. I looked in Pinero and Bates chapter 7.5 but i could not figure out exactly how
varBeta is estimated in gnls. A pointer to a reference or some guidance would be very helpful.


PS Sorry for the sloppy notation, email is not latex

On Tue, 19 Jul 2005 11:48:18 -0500, "Douglas Bates" <dmbates@gmail.com> said:
> On 7/19/05, Nicholas Lewin-Koh <nikko@hailmail.net> wrote:
> > Hello,
> > I am writing a set of functions to do prediction and calibration
> > intervals
> > for at least the subset of selfstarting models if not some more general
> > ones.
> >
> > I need to be able to extract the varFunction from a fit object
> > and evaluate it at a predicted point. Are there any examples around?
> >
> > Also in a self start model, say SSlogis, how would I get the gradient
> > at a point?
> I think that the output of
> example(SSlogis)
> should answer that question for you.

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