[R] Confident interval for nls predictions

[Ben Bolker]

Ben Ridenhour wrote:
> 
> Hello all,
> I'm trying to establish some confidence intervals on predictions I am
> making using 
> 
>>predict(nls(...))
> 
> and predict.nls (unfortunately) does not utilize the se.fit option. A
> little more background is that I am trying to match the output with older
> SAS routines to maintain consistency. Because predict.nls does not provide
> se's for individual predictions, I have been using a method suggested on
> r-help previously (by P. Dalgaard) using deriv() and vcov(). 
> Specifically,
> 
> se.fit<-sqrt(apply(gradient, 1, function(x)
>                 sum(vcov(myNLSmodel)*outer(x,x))))
> 
> where I determine "gradient" by using deriv() and the points for which I
> am making the predictions.  This works for predicting the confidence
> interval for the mean predicted Y, however, I need the confidence interval
> for the individual predicted Y. According to the stats text I looked at, I
> need to change the above formula to 
> 
> se.fit<-sqrt(apply(gradient, 1, function(x)
>                 sum(vcov(myNLSmodel)*outer(x,x))+NEWTERM)) 
> 
> where NEWTERM is
> 
> NEWTERM<-myNLSmodel$m$deviance()/(nObservations - nParameters)
> 
> So the problem is that while the confidence intervals are close to those
> provided by SAS, they are always smaller. This, in the end, makes a large
> difference for the application. Can anyone suggest how I might make the
> confidence intervals I calculate in R match up with those of SAS for nls?
> 
> Thanks in advance,
> Ben Ridenhour
> 
> 

Are you multiplying the confidence intervals by +/- 2 or are you using the
critical
value of the t statistic? Are your formulas above matching those suggested
by
http://support.sas.com/documentation/cdl/en/statug/59654/HTML/default/statug_nlin_sect026.htm
?
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