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
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