[R] gam confidence interval (package mgcv)

[Simon Wood]

not sure if I'm missing something here, but since you are using a log 
link, isn't the ratio you are looking for given by the `treatmentB' 
parameter in the summary (independent of X)

 > summary(gfit)
[snip]

Parametric coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)  1.83183    0.03885  47.152 < 2e-16 ***
treatmentB   0.44513    0.05567   7.996  1.4e-09 ***
---
[snip]

Let mu = E(y), and b be a binary indicator for treatment B. You want
mu|b=1/mu|b=0

log(mu|b=1) = intercept + treatmentB + s(X)
log(mu|b=0) = intercept + s(X)

=> log(mu|b=1) - log(mu|b=0) = treatmentB

so mu|b=1/mu|b = exp(treatmentB)

So you can get the required interval by finding and interval for 
treatment B and exponentiating...

tB <- coef(gfit)[2]
se.tB <- sqrt(vcov(gfit)[2,2])
exp(c(tB - 2*se.tB,tB+2*se.tB))

On 06/28/2011 03:45 AM, Remko Duursma wrote:
> Dear R-helpers,
>
> I am trying to construct a confidence interval on a prediction of a
> gam fit. I have the Wood (2006) book, and section 5.2.7 seems relevant
> but I am not able to apply that to this, different, problem.
>
> Any help is appreciated!
>
> Basically I have a function Y = f(X) for two different treatments A
> and B.  I am interested in the treatment ratios : Y(treatment = B) /
> Y(treatment = A) as a function of X, including a confidence interval
> for this treatment ratio (because we are testing this ratio against
> some value, across the range of X).
>
> The X values that Y is measured at differs between the treatments, but
> the ranges are similar.
>
>
> # Reproducible problem:
> X1<- runif(20, 0.5, 4)
> X2<- runif(20, 0.5, 4)
>
> Y1<- 20*exp(-0.5*X1) + rnorm(20)
> Y2<- 30*exp(-0.5*X2) + rnorm(20)
>
> # Look at data:
> plot(X1, Y1, pch=19, col="blue", ylim=c(0,max(Y1,Y2)), xlim=c(0,5))
> points(X2, Y2, pch=19, col="red")
>
> # Full dataset
> dfr<- data.frame(X=c(X1,X2), Y=c(Y1,Y2), treatment=c(rep("A",20),rep("B",20)))
>
> # Fit gam
> # I use a gamma family here although it is not necessary: in the real
> problem it is, though.
> gfit<- gam(Y ~ treatment + s(X), data=dfr, family=Gamma(link=log))
>
> # I am interested in the relationship:
> # Y(treatment =="B") / Y(treatment=="A") as a function of X, with a
> confidence interval!
>
> Do I just do a bootstrap here? Or is there a more appropriate method?
>
> Thanks a lot for any help.
>
> greetings,
> Remko
>
>
>
>
>
> -------------------------------------------------
> Remko Duursma
> Research Lecturer
>
> Hawkesbury Institute for the Environment
> University of Western Sydney
> Hawkesbury Campus, Richmond
>
> Mobile: +61 (0)422 096908
> www.remkoduursma.com
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>