[R] gam confidence interval (package mgcv)

[Remko Duursma]

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